Rosemount 485 Annubar Flow Handbook Manuals & Guides

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar® Flow Handbook

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Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Table of Contents

SECTION 1 Fluid Flow Theory

SECTION 2 Annubar Primary Element Flow Calculations

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Physical Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4

Density, Specific Weight, Specific Gravity . . . . . . . . . . . . . . . . . . . 1-4

Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5

Nature of Fluid Flow in Pipes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6

Flow Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6

Average Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7

Reynolds Number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8

Bernoulli's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9

Actual and Standard Volumetric Flowrate for Gases . . . . . . 1-12

Actual and Standard Volumetric Flowrate for Liquids . . . . . . . . 1-15

Annubar Primary Element Flow Equations . . . . . . . . . . . . . . . . . . . . . 2-1

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

Flow Coefficient Reynolds Number Dependency . . . . . . . . . . . . . 2-9

Flow Coefficient Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

Shape Differential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

Blockage Differential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10

The Importance of the Flow Coefficient, or K vs. B Theory . . . . . 2-10

Operating Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11

Flow Calculation Examples: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12

SECTION 3 Installation and Operational

Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

Upstream Flow Disturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

Instrument Lines and Connections Leakage . . . . . . . . . . . . . . . . . . . 3-4

Flow Parameter Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4

Dirt Accumulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4

Gas Entrapment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

Flow Parameter Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

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Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

APPENDIX A Fluid Properties and Pipe Data

APPENDIX B Pipe Data

APPENDIX C Unit and Conversion Factors

APPENDIX D Related Calculations

APPENDIX E Flow Turndown and Differential Pressure Requirements

Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

Ideal and Real Specific Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D-1

Derivation of Annubar primary element flow equations . . . . . . . . . . . .D-3

Flow Turndown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E-1

Differential Pressure (DP Turndown). . . . . . . . . . . . . . . . . . . . . . . . . .E-2

Accuracy and Flow Turndown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E-2

Flow Measurement System Turndown . . . . . . . . . . . . . . . . . . . . . . . .E-2

Percent of Value and Percent of Full Scale accuracy . . . . . . . . . . . . . E-2

Annubar Turndown Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-3

Minimum measurable differential pressure . . . . . . . . . . . . . . . . . . . . .E-4

Putting it all together: The flow system turndown . . . . . . . . . . . . . . . . E-4

APPENDIX F References

APPENDIX G Variable List

TOC-2

Reference Manual

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May 2006

Rosemount 485 Annubar

Section 1 Fluid Flow Theory

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 1-1

Physical Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 1-1

Nature of Fluid Flow in Pipes . . . . . . . . . . . . . . . . . . . . . . . . . .page 1-6

INTRODUCTION The Emerson Process Management DP-Flow Engineering Department has

prepared this book to provide all of the information necessary to accurately
measure fluid flow using the Rosemount 485 Annubar primary element.

Fluid flow measurement involves many variables. In this handbook fluid
properties that affect flow measurement are discussed and defined. We hope
this will bring all readers to a point where they are comfortable with the flow
equations which follow. The flow equations are developed from Bernoulli's
Theorem, which is the application of the law of conservation of energy to fluid
flow. These equations are then developed and modified for use with 485
Annubar Flow Sensors. After all the terms have been defined and the
equations developed, you are then ready to do the precise flow calculations
necessary to apply an Annubar and an associated secondary readout
instrument to your flow situation.

We realize that many intricacies of fluid flow have been neglected in this book.
We feel that we have presented enough theory and data for you to accurately
measure fluid flow using the Annubar Flow Sensor. For difficult flow
measurement problems, contact your local Emerson Process Management
representative for assistance.

PHYSICAL FLUID
PROPERTIES

Pressure Pressure is the force exerted by a fluid per unit area. The most common unit

To solve any flow problem a knowledge of the physical properties of the fluid
is required. Appendix A gives fluid property data for the most common fluids.
Definitions and descriptions of the most common properties are given below.

2

of pressure measurement is pounds force per square inch (lbf/in
English system of units and pascal or kilopascal (Pa or kPa) in the SI system
of units.

In most flow problems (especially gas flow problems), the absolute pressure
must be used in the calculations. However, most pressure gages measure a
pressure that is referenced to atmospheric pressure (atmospheric pressure =
0 psig or 0 kPa g). To obtain absolute pressure, the atmospheric pressure
must be added to the gage pressure. Vacuum gages measure a pressure that
is lower than atmospheric pressure. To obtain absolute pressure, the vacuum
pressure must be subtracted from the atmospheric pressure. All of these
pressure terms are described in detail below and the relationship between
these pressures is shown graphically in Figure 1-1.

or psi) in the

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Rosemount 485 Annubar

Figure 1-1. Pressure
Relationships

Absolute pressure that

is greater than

atmospheric pressure

Absolute zero pressure, or a perfect vacuum, would exist if all molecules were
removed from an enclosed space. In reality, this is impossible to achieve, but
it does serve as a convenient reference for pressure measurement.

Atmospheric pressure is the amount of pressure exerted by the atmosphere
above absolute zero pressure. The “standard” atmospheric pressure used in
this handbook is 14.696 psia (101.325 kPa). It is important to realize that
atmospheric pressure at any one location varies with day to day weather
conditions. More important, the atmospheric pressure changes rapidly with
elevation above sea level. The following table gives the U.S. Standard
Atmosphere (1962) for various altitudes above sea level.

Barometer reads

atmospheric pressure

Reference Manual

00809-0100-1191, Rev CB

May 2006

Pressure above
atmospheric pressure

Ordinary pressure gauge measures
pressure above atmospheric pressure

Atmospheric pressure

Ordinary vacuum gauge measures
pressure below atmospheric pressure

Pressure less than
atmospheric pressure

Absolute pressure that is less
than atmospheric pressure

Perfect vacuum

Table 1-1. Atmospheric
Pressure by Altitude

Altitude Atmospheric Pressure

feet meters psia bar

0 0 14.696 1.01

500 152.4 14.433 0.995
1000 304.8 14.173 0.977
1500 457.2 13.917 0.959
2000 609.6 13.664 0.942
2500 762.0 13.416 0.925
3000 914.4 13.171 0.908
3500 1066.8 12.930 0.891
4000 1219.2 12.692 0.875
4500 1371.6 12.458 0.859
5000 1524.0 12.227 0.843
6000 1828.8 11.777 0.812
7000 2133.6 11.340 0.782
8000 2438.4 10.916 0.753
9000 2743.2 10.505 0.724

10000 3048.0 10.106 0.697
15000 4572.0 8.293 0.572
20000 6096.0 6.753 0.466

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Rosemount 485 Annubar

Example:

A manometer at an elevation of 5,000 feet above sea level measures 10
inches of mercury vacuum. Express this pressure in absolute terms (psia).

Solution:

From Table 1-1 on page 1-2, the average atmospheric pressure at 5,000
feet elevation is 12.227 psia.

10 inches of mercury = 4.912 psia.

(2.036" Hg @ 0°C = 1 psi - see Appendix B Unit and Conversion Factors)

Absolute pressure = 12.227 - 4.912 = 7.315 psia.

Differential pressure is just what the name implies, a difference between two
pressures. Frequently, a differential pressure is measured with a pressure
transmitter or a manometer which contains water, mercury, alcohol, oil, or
other fluids. The differential pressure can be calculated by the relation:

ΔP ρh=

where:

ΔP = differential pressure in lbf/ft
ρ = density of the fluid in lbm/ft

h = elevation difference of the fluid in feet

2

3

Figure 1-2. Differential Pressure

Fluid

h

Commercial instruments used for indicating or recording the differential
pressure operate using various principles; such as variable reluctance,
capacitance, or strain gage. These instruments generally give the true
differential pressure without the need for additional corrections.

1-3

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May 2006

Temperature Although temperature is a property which is familiar, an exact definition is

difficult. Temperature is a measure of the degree of hotness or coldness of a
substance. Temperature scales are defined such that the temperature of
boiling water at standard atmospheric pressure is 212 °F (100 °C) and the
freezing temperature of water is 32 °F (0 °C).

Most flow problems require that the temperature be expressed in absolute
units. The absolute temperature of a substance is the measure of the
temperature intensity of the substance above the datum known as “absolute
zero.” According to kinetic theory, all molecular activity ceases at absolute
zero. The Rankine and Kelvin temperature scales are based on absolute
zero.

Absolute zero temperature is -459.69 °F (-273.15 °C).

Thus:

Density, Specific Weight,
Specific Gravity

°R = °F + 459.69

Where:

°R = degrees Rankine
°F = degrees Fahrenheit

°K = °C + 273.15

Where:

°K = degrees Kelvin
°C = degrees Celsius

In most engineering work, the value of 459.69 is rounded off to 460 so that
degrees Rankine is approximated as:

°R = °F + 460

It is important that absolute temperatures be used in gas flow problems.

Density is defined as the mass of a substance per unit volume. Density is
usually expressed in pounds-mass-per cubic foot (lbm/ft
cubic meter (kg/m

3

).

3

) or kilograms per

Specific Weight is defined as the weight, due to the gravitational pull of the
earth, of a substance per unit volume. Specific weight is expressed in
pounds-force per cubic foot (lbf/ft

3

) or Newtons per cubic meter (N/m3). As
can be seen, specific weight and density are not synonymous terms. Only at
locations where the local acceleration of gravity is equal to the standard
acceleration of gravity (g

= 32.1740 ft/s2 or gc = 9.807 m/s2) does the

c

numerical value of specific weight equal the numerical value of density.

Specific Gravity is defined as the ratio of the density of one substance to the
density of a second or reference substance. The reference substance
depends on whether the flowing media is liquid or gas.

1-4

For liquids, water at either 60 °F (15°C) or 77 °F (25 °C) is used as the
reference substance. The density of distilled water at 60 °F is 62.3707 lbm/ft
The density of distilled water is 25 °C is 997 kg/m

3

.

3

The determination of the specific gravity of a liquid can be made by comparing
the weights of equal volumes of the liquid and water. If the quality of the work
justifies it, these weights may be corrected for the buoyancy of air as well as
for temperature effects. For most commercial work, the specific gravities of
liquids are obtained with hydrometers. The scales of hydrometers are
graduated to read directly in specific gravities, in degrees Baume or in
degrees API (American Petroleum Institute). The relationship between
specific gravity and degrees Baume is defined by the following formulas:

.

Reference Manual

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May 2006

Rosemount 485 Annubar

⎛⎞
⎜⎟

1. For liquids heavier than water:

2. For liquids lighter than water:

°B 145

⎛⎞
⎜⎟

°B

--------------------------- -

⎜⎟

SpGr60

⎜⎟

⎛⎞

----------------------

⎝⎠

⎝⎠

3. For use in the American petroleum industry, the following relation
between degrees API and specific gravities is
used:

⎛⎞
⎜⎟

API

141.5

--------------------------- -

⎜⎟

SpGr60

⎜⎟

⎛⎞

----------------------

⎝⎠

⎝⎠

60° F

131.5–=

In the above equations, the term “Sp Gr 60/60” means that the specific gravity
value to be used is that which exists when the temperatures of the reference
liquid (water) and of the oil, or other liquid, are both at 60 °F.

For gases, air is used as the reference fluid. However, instead of a ratio of
densities, the ideal specific gravity of a gas is defined as the ratio of the
molecular weight of the gas of interest to the molecular weight of air. The
molecular weight of air is 28.9644.

145

--------------------------- -

–=

⎜⎟

SpGr60

⎜⎟

⎛⎞

----------------------

⎝⎠

⎝⎠

60° F

140

60° F

130–=

The reason for not using the ratio of the densities is that the effects of
pressure and temperature on the densities of gases vary from one gas, or gas
mixture, to another. Thus, even though the densities may be determined at
very nearly identical ambient conditions and the resulting values adjusted to a
common basis of pressure and temperature, an error may be incurred when
the resulting ratio is used at a state differing from the common basis. The
magnitude of this error is likely to increase as the state of use departs further
and further from the common starting basis. On the other hand, so long as the
composition of the gas used undergoes no change, the ratio of molecular
weights will remain the same regardless of changes of pressure, temperature,
and location.

For a more complete discussion or real and ideal specific gravities, see
Appendix C Related Calculations.

Viscosity Absolute viscosity may be defined simply as the temporary resistance to flow

of a liquid or gas. It is that property of a liquid or gas which tends to prevent
one particle from moving faster than an adjacent particle. The viscosity of
most liquids decreases with an increase in temperature, but the viscosity of
gases increases with an increase in temperature.

In the English System of units, the absolute viscosity has units of lbm/ft-sec.
However, it is common practice to express the value of the viscosity in poise
or centipoise (1 poise = 100 centipoise). The poise has units of dyne seconds
per square centimeter or of grams per centimeter second. Less confusion will
exist if the centipoise is used exclusively for the unit of viscosity. For this
reason, all viscosity data in this handbook are expressed in centipoise, which
is given the symbol µ

cp

.

1-5

Rosemount 485 Annubar

If it is necessary to express the viscosity in the English System of units, the
following conversion factors should be used.

Poise x 0.067197 = lbm/ft-sec

Centipoise x 0.00067197 = lbm/ft-sec

The Annubar primary element is a head-type meter and requires fluid to
convey the DP signal to the meter. For this reason a practical viscosity limit of
50 centipoise should be followed.

Kinematic viscosity or kinetic viscosity is the absolute viscosity divided by the
density of the fluid at the same temperature.

ν

cs

(36.13 converts to lbm/ft

Like the units of absolute viscosity, the units of kinematic viscosity are usually
expressed in metric units. To be consistent and to reduce confusion, the
kinematic viscosities used in this handbook will have units of centistokes

2

/sec) and will be denoted υcs.

(cm

μ

cp

------------------=

36.13ρ

ν

cs

3

to gm/cm3)

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00809-0100-1191, Rev CB

May 2006

μ

cp

-------- -=

ρ

There is no name for kinematic viscosities in the English System of units, but
the following conversion factor can be used:

υ

x 0.00001076 = υ(ft2/s)

cs

NATURE OF FLUID
FLOW IN PIPES

In the foregoing sections on the physical properties of fluids, subjects were
discussed that had to do with the type of fluid being used. However, one
property of fluid flow which is independent of the type of fluid is velocity.

Flow Patterns Depending upon the magnitude of the velocity, three distinct flow regimes can

be encountered. These three types of flows are known as laminar, transition,
and turbulent.

The classic experiment of introducing dye into a flowing stream was first
conducted by Reynolds in 1883. The experiment consists of injecting a small
stream of dye into a flowing liquid and observing the behavior of the dye at
different sections downstream of the injection point. Figure 1-3 shows the
three possible types of flow with the dye injected.

1-6

Reference Manual

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May 2006

Figure 1-3. Types of Flow
Development

Rosemount 485 Annubar

Laminar occurs when the velocity is small and the dye remains in a straight
line.

Dye Filament

Needle

Ta nk

Transition occurs at a slightly higher velocity than laminar flow. The dye does
not remain in a straight line and does not spread throughout the pipe.

Dye Filament

Needle

Tank

Turbulent occurs at velocities above transition flow. The dye spreads
throughout the pipe as shown below. It is this type of flow which is important
to the general user. Turbulent flow is, by far, the most common type of flow
encountered in pipes.

Dye Filament

Needle

Ta nk

Average Velocity Unless it is stated otherwise, the term velocity will refer to the average velocity

in the pipe. The average velocity is determined by the continuity equation for
steady state flow.

lbm

W = ρAV

⎛⎞

----------

⎝⎠

⎛⎞
⎝⎠

kg

------

s

s

⎛⎞

=

⎝⎠

kg

⎛⎞

-------

=

⎝⎠

m

This equation states that for steady state flow, the mass rate of flow lbm/sec
(kg/s) at any point in the pipeline can be calculated from the product of the
density lbm/ft

3

(kg/m3), the cross-sectional area of the pipe ft2 (m2), and the

average velocity ft/s (m/s).

lbm

----------

ft

3

3

2

()

ft

2

⎛⎞

()

m

⎝⎠

ft

⎛⎞

---

⎝⎠

s

m

---- -

s

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May 2006

Reynolds Number The work that Osborne Reynolds accomplished in the late 1800's led to a flow

parameter that now carries his name, e.g. the Reynolds Number. His work
showed that the nature of flow in a pipe depends on the pipe diameter (D), the
density (ρ), viscosity, and the velocity of the fluid.

m

ft

lbm

⎛⎞

⎛⎞

---

ft()

----------

⎝⎠

⎝⎠

3

s

Dνρ

R

-----------

D

---------------------------------- -==

μ

ft

lbm

⎛⎞

---------- -

⎝⎠

ft s⋅

Dνρ

-----------

R

D

m()

---------------------------------- -==

μ

As can be seen, the Reynolds Number has no dimensions and it may be
considered as the ratio of dynamic forces to viscous forces.

For the three types of flow previously discussed, it has been found that
generally laminar flow exists below a Reynolds Number of 2000. Transition
flow generally exists between a Reynolds Number range of 2000 to 4000.
However, the values of 2000 and 4000 are not precisely fixed. The laminar
flow range can terminate between a Reynolds Number range of 1200 to
13000 depending on the smoothness of the pipe. If heat is added to the pipe,
laminar flow can be extended to even higher Reynolds Numbers. The
turbulent flow exist above pipe Reynolds numbers from 4,000 to 13,000.

kg

⎛⎞

⎛⎞

---- -

-------

⎝⎠

⎝⎠

3

s

m

kg

⎛⎞

------------

⎝⎠

ms⋅

Since the product is dimensionless, the numerical value will be the same for
any given set of conditions, so long as all the separate factors are expressed
in a consistent system of units. This makes the Reynolds Number an ideal
correlating parameter. Therefore, the flow coefficient of flow meters are
generally expressed as functions of Reynolds Number.

Although the combination DVρ / µ is the classical expression for the Reynolds
Number, there are several other equivalent combinations. First, the ratio ρ/ µ
may be replaced by 1 /υ giving:

DV

--------=

R

D

υ

3

Also, the volume rate of flow (ft

/s or m3/s) is Q = π(D2/4)V, thus another

alternate combination for Reynolds Number is:

4Qρ

R

-------------- -= R

D

πD

μ

ft

4Qρ

--------------- -=

D

πD

μ

m

Also, the mass rate of flow (lbm/s or kg/s) is W = Qρ so that a third alternate
combination is:

4W

R

-------------- -= R

D

πD

μ

ft

4W

--------------- -=

D

πD

μ

m

If the viscosity (µ) is given in centipoise, the last combination for Reynolds
Number becomes:

1895W

R

------------------ -= R

D

D

ftμcp

D

1298W

------------------ -=

D

mμcp

1-8

The pipe Reynolds Number (R
following equations:

Liquid:

3160 G PM G⋅⋅

-----------------------------------------= R

R

D

⋅

D μ

cp

) can be calculated by using any of the

D

21230 L PM G⋅⋅

-------------------------------------------=

D

⋅

D μ

cp

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Rosemount 485 Annubar

Gas:

0.4831 S CF H G⋅⋅

-------------------------------------------------= R

R

D

⋅

D μ

cp

432 N CM H G⋅⋅

------------------------------------------ -=

D

⋅

D μ

cp

Liquid, Gas and Steam:

lbm

⎛⎞

----------

⋅

6.316

⎝⎠

R

-----------------------------------= R

D

D μ

⋅

hr

cp

353.6

------------------------------- -=

D

D μ

⋅

kg

⎛⎞

------

⋅

⎝⎠

hr

cp

where:
G = specific gravity of flowing fluid (air = 1.0, water = 1.0)
GPM = U.S. gallons per minute
kg/hr = flowrate of fluid in kilograms per hour
LPM = flowrate of fluid in liters per minute
NCMH = flowrate of gas in normal cubic meters per hour
SCFH = flowrate of gas in standard cubic feet per hour

Bernoulli's Theorem Bernoulli's Theorem is a means of expressing the application of The Law of

Conservation of Energy to the flow of fluids in a pipe. The total energy at any
location in the pipe, above some arbitrary datum, is equal to the sum of the
elevation head, the velocity head, and the pressure head.

Figure 1-4. Bernoulli's Theorem

2

V

/2g

2

Constant Energy Line

2

/2g

V

2

P

/ρ

1

P2/ρ

12

Flow

Z

Z

1

Arbitrary Datum Plane

2

In a steady incompressible flow, without friction, the sum of the velocity head,
pressure head, and elevation head is a constant along any streamline (see
Figure 1-4). Assuming that the elevation difference between two measuring
points is negligible (Z

= Z2), Bernoulli's Equation can then be written:

1

Equation 1-1.

2

V

⎛⎞

1

---------

+

⎜⎟

2g

⎝⎠

P

1

⎛⎞

------

⎝⎠

ρ

2

V

⎛⎞

2

---------

+=

⎜⎟

2g

⎝⎠

P

2

⎛⎞

------

⎝⎠

ρ

where,

V = velocity, ft/s (m/s)
g = gravitation constant, ft/s
P = pressure, lbf/ft
ρ = density, lbm/ft
A = area, ft

2 (m2

3

)

2

(kg/m3)

(kPa)

2

(m/s2)

1-9

Rosemount 485 Annubar

Since Bernoulli's Theorem states that the flow is steady, the continuity
equation must apply. The continuity equation states that the mass rate of flow
between two points must be constant.

Equation 1-2.

ρ1A1V1ρ2A2V

=

Reference Manual

00809-0100-1191, Rev CB

May 2006

2

since the flow is incompressible (ρ

Equation 1-3.

A

=

1V1A2V2

solving for V

in Equation 1-4:

1

Equation 1-4.

A2V

2

------------- -=

V

1

A

1

and substituting into Equation 1-1:

1

------ -

2g

2

A

⎛⎞

2V2

------------- -

⎜⎟
⎝⎠

+

A

1

2

V

⎛⎞

1

2

------ -

------ -

⎜⎟

2g

2g

⎝⎠

2

V

⎛⎞

2

------ - 1

–

⎜⎟

2g

⎝⎠

2

2g

V

2

P

V

⎛⎞

1

2

1

2

A

⎛⎞

2

------

⎜⎟

A

⎝⎠

1

–

1P2

ρ

2

---------

⎜⎟

2g

⎝⎠

⎛⎞
⎝⎠

------------------------=

⎛⎞

------

⎝⎠

ρ

A

2V2

------------- -

A

–

P

⎛⎞

-------------------

⎝⎠

1

2

P

1

------

ρ

P

-------------------=

–

= ρ2), Equation 1-3 reduces to:

1

P

2

⎛⎞

------

+=

⎝⎠

ρ

P

2

⎛⎞

------

+=–

⎝⎠

ρ

–

1P2

ρ

1

2

A

⎛⎞

2

------

⎜⎟

A

⎝⎠

1

1-10

–

P

1P2

2g

-------------------

ρ

V

2

------------------------=

1

1

A

⎛⎞

------

–

⎜⎟

A

⎝⎠

2

2

1

Again, using the continuity equation, the theoretical mass rate of flow would
be:

Equation 1-5.

1

W

theoρA2

V=

A22gρ P1P2–()

2

------------------------=

1

A

⎛⎞

------

–

⎜⎟

A

⎝⎠

2

2

1

The theoretical equation for volumetric flow is:

Equation 1-6.

Q

theoA2

2gρ P1P2–()

V=

2

----------------------------------- -

A

2

ρ

------------------------=

1

1

A

⎛⎞

------

–

⎜⎟

A

⎝⎠

2

2

1

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

By definition the discharge coefficient of a flow meter is the ratio of the actual
rate of flow to the theoretical rate of flow.

Equation 1-7.

W

C

actual

------------------------------- -

W

theoretical

Therefore, the actual volumetric flow for liquid is:

Equation 1-8.

actual

QA2C==

Q

By defining the flow coefficient K of an Annubar primary element as:

C

---------------------------- -=

K

A

⎛⎞

2

1

------

–

⎜⎟

A

⎝⎠

1

The volumetric flow Equation 1-8 reduces to:

Q

------------------------------ -==

Q

theoretical

2gρ P

----------------------------------- -

2

actual

–()

1P2

ρ

1

------------------------

A

⎛⎞

2

1

------

–

⎜⎟

A

⎝⎠

1

2

Equation 1-9.

2g P

–()

1P2

=

------------------------------- -

2

ρ

QKA

In a like manner, the mass rate of flow reduces to:

Equation 1-10.

W

WKA

== 2gρ P1P2–()

actual

2

By using consistent units Equation 1-9 can be checked as follows:

2

Qft

=

lbf

⎛⎞

------ -

ft

⎝⎠

2

ft

------------------ -

2

lbf

⎛⎞

------ -

s

⎝⎠

ft

3

ft

------=

s

3

Qm

=

m()

2

------------------------

s

kgf

⎛⎞

--------

⎝⎠

2

m

2

kgf

⎛⎞

--------

⎝⎠

3

m

3

m

-------=

s

Likewise, Equation 1-10 is:

2

Wft

=

ft

lbm

lbf

-----

----------

2

s

ft

lbm

------ -

----------= Wm

3

2

s

ft

2

m

kgm

kgf

=

-----

----------- -

2

3

s

m

--------

m

kgm

----------- -=

2

s

NOTE:

In the above units conversion, lbf is set equal to lbm. This is only true at
standard gravity (g
surface of the earth, the assumption of lbf = lbm is fairly good.

= 32.174 ft/sec2). However, for measurements on the

c

It is also interesting to note that this assumption leads to the historical name
“head-type meters”. By using the following:

lbf

------ -

2

ft

h

---------- ft== h
lbm

----------

3

ft

kgf

--------

2

m

----------- - m==
kgm

----------- -

3

m

Where h is feet (meters) of head of flowing fluid, equation (2-9) can be written
as:

⎛⎞
⎝⎠

QKA2g

--------------- - KA 2gh==

⎛⎞
⎝⎠

lbf

------ -

ft

lbm

----------

ft

2

QKA2g

3

kgf

⎛⎞

--------

⎝⎠

2

m

----------------- KA 2gh==
kgm

⎛⎞

----------- -

⎝⎠

3

m

1-11

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

Actual and Standard
Volumetric Flowrate for
Gases

The equation will be recognized as the well known hydraulic

QKA2gh=

equation for liquids.

The most common unit of volumetric measurement in English Units is the
cubic foot. The most common unit in SI units is the cubic meter. Many others
exist, such as the cubic inch, the gallon (231 cubic inches), and the barrel (42
gallons); but these are generally defined as portions of a cubic foot.

3

In Equation 1-9 the volumetric flow (Q) can be calculated in ft

/s (m3/s) if all
the other parameters have the consistent set of units shown. The most
important aspect of this equation is that the volumetric flow is given in actual
units.

Example:

Suppose a flowmeter is operating according to Equation 1-10, and that the
equation shows that the flowrate is 5 ft

3

/s. Also suppose that the fluid can
be poured or dumped into one (1) cubic foot containers. At the end of one
second, five containers would be full of fluid. In other words, the equation
gave the flowrate in actual cubic feet per second.

For gases, especially fuel gases, the cubic foot is still the unit of
measurement. However, a cubic foot of gas has no absolute or comparative
value unless the pressure and temperature of the gas are specified. Common
sense tells us that the amount of matter within a one cubic foot space at a
pressure of 1000 psia is greater than the amount of matter within that space if
the pressure is atmospheric. Since the fuel gas industry is interested in selling
energy, which is the amount of heat that can be generated by that cubic foot
of gas, and that the amount of energy is directly proportional to the number of
molecules (matter) within the cubic foot space, it is easy to see why the
pressure and temperature of the gas are specified.

Table 1-2. Standard Conditions

Since it is the amount of matter (mass) that is required to be measured as the
gas flows along the pipeline, the actual volumetric flowrate terms do not lend
themselves to this task easily.

Example:

Suppose a gas in a pipeline at 140 kPa abs and 5 °C is flowing at 50
actual m
flow through a pipeline at 5100 kPa abs and 30.8 °C if the flowrate was

1.54 actual m

3

/s; it is not obvious that the same amount of matter (mass) would

3

/s.

Because of the inability to compare the amounts of mass of a gas in actual
volumetric terms, the standard volumetric term was developed. The most
common unit of gaseous measurement is the amount of a gas that would be
contained in a one cubic foot enclosure at standard conditions. Standard
conditions can be defined as any combination of temperature and pressure.
Some common standard sets are provided in the table below.

Temperature Pressure

60 °F 14.73 psia
68 °F 14.73 psia
0 °C 101.393 kPa abs

The approximate conversion from actual volumetric flowrate to standard
volumetric flowrate is accomplished by the BOYLES-CHARLES law. These
laws state the following:

1-12

Reference Manual

Q

Q

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

1. If an ideal gas were contained within an enclosure at constant

temperature, the pressure would increase in proportion to the volume
decrease. Example: the pressure would double if the volume was
reduced by half. The equation takes the form of:

P1V1P2V

=

2

Which states that the product of the pressure and volume at one
condition must equal the product of the pressure and volume at any
other condition provided the temperature is the same at both
conditions.

2. Again, if an ideal gas were contained within an enclosure of constant

volume, the pressure would increase in proportion to the absolute
temperature increase. The equation for this process takes the form:

P

P

1

2

------

------=

T

T

1

2

Which states that the ratio of the pressure and temperature at any
one condition must equal the ratio of the pressure and temperature at
any other conditions provided the volume of the container has not
changed.

Both of these laws can be combined to form a single equation:

P

------------- -

1V1

T

1

P

------------- -=

2V2

T

2

If, instead of considering actual volumes, the flowrate (actual volume per unit
time) is used, the equation becomes:

P

-------------- -

V

1

------= Q

Q

Since and where t is a common unit of time (hours, minutes

1

t

V

2

------=

2

t

1Q1

T

1

P

-------------- -=

2Q2

T

2

or seconds).

Now, if P
conditions of 14.73 psia and 60°F (101.393 kPa A and 0 °C), the flowrate Q
is the standard volumetric flowrate Q

and T1 are always considered to be at the standard specified

1

.

14.73

---------------------- -

460 60+

P

s

fQA

---------------------=
Tf460+

s

101.325

-----------------------------

273.15 0+

P

s

----------------------------- -=

Tf273.15+

fQA

1

This equation allows the standard volumetric flowrate (Qs) to be calculated
from any actual volumetric flowrate (QA) where the pressure and temperature
are known.

P

460 60+

f

-------------- -

---------------------- - Q

Q

s

⋅⋅= Q

T

14.73

460+

f

A

s

P

f

---------------------

101.325

273.15 0+

----------------------------- - Q

⋅⋅=

T

273.15+

f

A

In an example on page 1-12, two actual volumetric flowrates were given, and
it was stated that the amount of mass flowing was the same. To check this,
the standard volumetric can be calculated for each flowrate:

1-13

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

Flowrate #1:

3

ft

QA50

P

T

Q

Q

------=

s

20psia=

f

40° F=

f

20

460 60+

-------------- -

s

s

---------------------- - 50⋅⋅=

14.73

460 40+

70.6S CF S= Qs67.8NMCS=

Q

A

P

f

T

f

Q

s

m

-------=

50

s

140kPaabs=

5° C=

140

---------------------

101.325

3

273.15 0+

--------------------------- - 50⋅⋅=

273.15 5+

Flowrate #2

3

ft

Q

P

T

f

Q

Q

------=

1.5

A

f

s

s

s

750p si a=

102.5° F=

460 60+

750

------------------------------ - 1.5⋅⋅=

-------------- -

460 102.5+

14.73

70.6S CF S= Qs67.8N MC S=

Q

A

P

f

T

f

Q

s

1.54

5100k Pa A=

39.2° C=

5100

---------------------

101.325

m

-------=

s

3

----------------------------------- - 1.54⋅⋅=

273.15 39.2+

273.15 0+

As can be seen, the two actual volumetric flowrates are identical in terms of
standard volumetric flowrates. However, only ideal gases have been
considered so far. Real gases deviate from the Boyles-Charles relationships.
The amount of deviation depends upon pressure, temperature, and type or
composition of the gas. The deviation is known as the compressibility factor of
the gas. For most flow conditions, the conversion to standard volumetric
flowrate using only the Boyles-Charles relationship will be accurate within a
few percent. To be correct, the Boyles-Charles relationship must be modified
as follows:

1V1

P

2V2

------------- -=

ZfT

1

2

P

------------- -

ZaT

Where Z is the compressibility factor at each pressure and temperature
condition. This modification leads to the following:

P

460 60+

Q

f

---------------------- -

⋅⋅⋅= Q

-------------- -

s

14.73

Z

b

------ Q

T

f

A

Z

f

s

P

f

---------------------

101.325

273.15 0+

--------------------------- -

⋅⋅⋅=

Z

b

------ Q

T

f

A

Z

f

Where:

1-14

=compressibility factor at base or standard conditions and is generally

Z

b

considered to be unity (Z

=compressibility factor at Pf and Tf.

Z

f

=1.000).

b

More discussion on compressibility factors can be found in “Ideal and Real
Specific Gravity” on page D-1.

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Actual and Standard
Volumetric Flowrate for
Liquids

In general, liquid flowrates are not converted into standard volumetric
flowrates. They are usually expressed in actual volumetric terms.

However, some industries do convert actual liquid flows to standard liquid
flows. The petroleum industry is probably the largest industry which does
convert its actual volumes to standard volumes. This is done primarily
because that industry is concerned with the selling and buying of energy. The
energy content of a barrel of oil at 1000 °F is less than the energy content of a
barrel of oil at 60 °F because the oil expands with temperature. Since the
energy content is directly proportional to the amount of matter (mass) within
the barrel, the temperature (thermal) expansion is considered.

Industries which convert liquids to standard volumetric flows have generally
established 60 °F as the reference temperature. To convert actual volumetric
flow to standard volumetric flows, the following equation can be used.

ρ

QsQ

A

------=

A

ρ

s

Where,

= standard volumetric flowrate

Q

S

= actual volumetric flowrate

Q

A

= density of fluid at actual flowing conditions

ρ

A

= density of fluid at standard or base conditions

ρ

S

As can be seen, the conversion to standard volumetric flow can be
accomplished simply by multiplying the density ratio. One alternate that is
commonly encountered is that the conversion is accomplished by multiplying
by the ratio of the specific gravities. That is:

G

Q

sQA

f

------ -=

G

s

Where,

=specific gravity at flowing conditions

G

f

=specific gravity at base conditions

G

S

Since specific gravity is defined as the ratio of the density of the fluid to the
density of the fluid to the density of water at 60°F, these conversions are
identical.

1-15

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

1-16

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Section 2 Annubar Primary Element Flow

Calculations

Annubar Primary Element Flow Equations . . . . . . . . . . . . . . . page 2-1

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 2-6

ANNUBAR PRIMARY
ELEMENT FLOW
EQUATIONS

The Annubar primary element flow equations are all derived from the
hydraulic equations which are shown on page 1-11. For a detailed example of
a derivation of an Annubar primary element equation, see the Rosemount 485
Annubar Flow Test Data Book (document number 00821-0100-4809).

Equation 2-1. : Volume rate of flow - Liquids (Actual Conditions)

2

Q

a

QaC' hw⋅=

OR

⎛⎞

-------

h

=

w

⎝⎠

C'

where:

C' F

na

KD2F

aa

1

----- -⋅⋅ ⋅ ⋅=

G

f

NOTE:

For description of standard volumetric flow equations, see page 1-12.

Equation 2-2. : Mass rate of flow - Liquids

2

W

WC' hw⋅= h

OR

⎛⎞

-----

=

w

⎝⎠

C'

where:

C' FnaKD2Faaρ

⋅⋅ ⋅ ⋅=

f

Equation 2-3. : Mass rate of flow - Gas and Steam

2

W

WC' hw⋅= h

OR

⎛⎞

-----

=

w

⎝⎠

C'

www.rosemount.com

where:

C' FnaKD2YaF⋅

⋅⋅ ⋅ ⋅=

aa

ρ

f

Equation 2-4. : Volume rate of flow - Gas (Standard Conditions)

QsC' hwPf⋅⋅= h

OR

w

-----

P

⋅=

⎝⎠

f

------ -

C'

2

Q

1

s

⎛⎞

where:

C' FnaKD2YaFpbFtbFtfFgFpvF⋅⋅⋅⋅⋅⋅

⋅⋅ ⋅=

aa

Rosemount 485 Annubar

Equation 2-5. : Volume rate of flow - Gas (Actual Conditions)

QaC' hw⋅= h

where:

For a detailed description of each term in the above equations, see
“Nomenclature” on page 2-6. Please note that each of the above equations
has a C' constant. It is not intended that the C' constant of one equation is
equal to the C' constant of another equation. The numerical value of any C'
constant is the product of the appropriate factors for that equation only.

The following tabulations of the flow equations will serve as handy work pads.
Also, the table numbers where the necessary information can be found are
given in the headings of these tabulations. Several completed examples of
flow calculations are given beginning on page 2-11.

NOTE

The 485 Annubar primary element needs no correction for the Reynolds
Number.

OR

C' FnaKD2YF⋅

aa

w

⎛⎞

=

⎝⎠

1

----⋅⋅ ⋅ ⋅=
ρ

f

Q

-------

Reference Manual

00809-0100-1191, Rev CB

May 2006

2

a

C'

2-2

Reference Manual

00809-0100-1191, Rev CB
May 2006

w

h

Differential Pressure

Flowing Specific

Gravity

.

1

----- -

G

...

O at 68 °F

2

inch H

f

O at 68 °F

O at 68 °F

O at 68 °F

2

2

inch H

inch H

inch H

O at 68 °F

2

2

inch H

Rosemount 485 Annubar

O at 68 °F

O at 68 °F

O at 68 °F

O at 68 °F

kPa

kPa

kPa

kPa

kPa

kPa

2

inch H

inch H

2

2

inch H

2

inch H

kPa

aa

F

I

Thermal Expansion

Factor (Table A-11)

Internal Pipe

Diameter

.

2

D

Annubar Flow Constant C

K

Annubar Flow

Coefficient

na

F

Unit Conversion

Factor

Rate of Flow

Table 2-1. Equation for Liquid – Volume Rate of Flow

=

a

Q

2

2

2

2

2

2

/H 4.0005E-03 (mm)

3

m

/M 6.6675E-05 (mm)

3

m

2

/s 1.1112E-06 (mm)

3

m

2

2

2

2

2

2

2

2

2

/D 9.6012E-02 (mm)

GPM 5.6664 (in)

GPH 339.99 (in)

GPD 8159.7 (in)

BPH (42 gal) 8.0949 (in)

BPD (42 gal) 194.28 (in)

3

/min 0.75749 (in)
ft

CFH 45.4494 (in)

CFM 0.7575 (in)

LPH 4.00038 (mm)

lmp. GPM 4.7183 (in)

LPM 6.6673E-02 (mm)

LPS 1.1112E-03 (mm)

3

m

2-3

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

w

h

Differential Pressure

f

ρ

Flowing Specific

Gravity

aa

F

I

Thermal Expansion

Factor (Table A-11)

2

D

Internal Pipe

Diameter

Annubar Flow Constant C

O at 68 °F

O at 68 °F

2

2

inch H

inch H

2

2

O at 68 °F

O at 68 °F

2

2

inch H

inch H

2

2

kPa

2

2

kPa

2

kPa

kPa

2

2

kPa

Differential Pressure

Flowing

Specific

Gravity

Thermal

Expansion

Factor (Table A-11)

I

Annubar

Expansion

Factor

Annubar Flow Constant C

Internal Pipe

Diameter

w

h

.

f

ρ

aa

F

. .Y

a

.

2

D

O at 68 °F

O at 68 °F

2

2

inch H

inch H

2

2

O at 68 °F

O at 68 °F

2

2

inch H

inch H

2

2

kPa

2

kPa

2

2

kPa

2

kPa

kPa

2

2-4

K

Annubar Flow

Coefficient

Unit Conversion

Factor

. . . . .

na

=

WF

PPD 8614.56 (in)

Rate of Flow

Table 2-2. Liquid – Mass Rate of Flow

PPH 358.94 (in)

PPS 0.0997 (in)

PPM 5.9823 (in)

kg/D 3.03471 (mm)

T(met)/hr 1.2645E-04 (mm)

Kg/H 0.12645 (mm)

kg/M 2.1074E-03 (mm)

kg/S 3.5124E-05 (mm)

K

Annubar

Flow

Coefficient

Unit

Conversion

Factor

. .

na

=

WF

PPD 8614.56 (in)

Table 2-3. Gas and Steam– Mass Rate of Flow

Rate of Flow

PPH 358.94 (in)

PPS 0.0997 (in)

PPM 5.9823 (in)

kg/D 3.03471 (mm)

T(met)/hr 1.2645E-04 (mm)

Kg/H 0.12645 (mm)

kg/M 2.1074E-03 (mm)

kg/S 3.5124E-05 (mm)

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Pressure

Differential

Gravity

Flowing

Specific

w

h

0 @ 68° F

2

H

.

f

ρ

0 @ 68° F

0 @ 68° F

2

2

H

H

kPa

kPa

kPa

kPa

kPa

.

aa

I

Annubar Flow Constant C

F

pv

F

. .

g

F

.

tf

F

.

tb

F

.

pb

F

a

Y

. .

2

2

2

2

2

2

2

D

2

2

Thermal

Expansion

Factor (Table 9)

Factor

(Table 8)

Supercomp

Factor

Gravity

Specific

Factor

Flowing

Temperature

Base

Factor

Temperature

Base

Factor

Pressure

Factor

Annubar

Expansion

Diameter

Internal Pipe

.

Flow

Annubar

Coefficient

Unit

Factor

Conversion

Flow

Rate of

Table 2-4. Volume Rate of Flow at STD Conditions - Gas

K

.

na

F

=

/D 0.27234 (mm)

/H 1.1347E-02 (mm)

/M 1.8912E-04 (mm)

3

3

NM

NM

3

NM

NL/H 11.34700 (mm)

a

SCFD 8116.1 (in)

Q

SCFH 338.17 (in)

NL/M 0.18912 (mm)

SCFM 5.6362 (in)

2

3

kPa

/S 3.1520E-06 (mm)

NM

Pressure

Differential

w

0 @ 68° F

2

H

0 @ 68° F

0 @ 68° F

2

2

H

H

kPa

kPa

.

f

l

---- h

Gravity

Flowing

Specific

Thermal

Expansion

Factor (Table 9)

ρ

aa

F

. .

I

a

Factor

Annubar

Expansion

Y

.

2

2

2

Diameter

Internal Pipe

Annubar Flow Constant C

2

2

2

D

2

.

Annubar

Flow Coefficient

K

.

na

Factor

Unit Conversion

F

=

a

Q

ACFD 8614.56 (in)

ACFH 358.94 (in)

Rate of Flow

Table 2-5. Volume Rate of Flow at Act Conditions

ACFM 5.9823 (in)

AL/H 126.4434 (mm)

AL/M 2.10739 (mm)

3

kPa

/D 3.03473 (mm)

Am

kPa

2

/H 0.12645 (mm)

3

Am

2

3

kPa

/M 2.1074E-03 (mm)

Am

kPa

2

/S 3.5124E-05 (mm)

3

Am

2-5

Rosemount 485 Annubar

NOMENCLATURE

D Internal diameter of pipe, inches (mm)

F

aa

F

g

F

na

F

pb

Thermal Expansion Factor. This factor corrects for the flowing area change of the pipe at the Annubar location due
to temperature effects. For 316 stainless steel Annubar primary elements mounted in carbon steel pipe, Faa =

1.0000 for temperatures between 31 and 106 °F. See Table B-1 on page B-3 which includes thermal expansion
factors for various pipe materials at several temperatures.

Specific Gravity Factor. This factor corrects the flow equation whenever the gas is not air. The factor can be
calculated as:

1

----=

F

g

G

where, G = specific gravity of flowing gas, air = 1.000. For a more complete description of specific gravity, see
“Density, Specific Weight, Specific Gravity” on page 1-4 and Appendix D: Related Calculations.

Units Conversion Factor. This factor is used to convert the flow rate to the desired set of units. Appendix D: Related
Calculations shows an example of how the numerical value of Fna is derived from the hydraulic equation for a given
set of input units.

Pressure Base Factor. The Pressure Base Factors are calculated to give gas volumes at a pressure base of 14.73
psia (101.325 kPa abs). The pressure base factor can be calculated as:

F

pb

14.73

-- -=

base pressure, psia

OR

F

-- -=

pb

base pressure, kPa abs

Reference Manual

00809-0100-1191, Rev CB

May 2006

101.325

F

pv

Supercompressibility Factor. The Supercompressibility Factor accounts for the deviation from the “ideal gas” laws. In
the flow equations, gas volumes are assumed to vary with pressure and temperature in accordance with Boyle’s and
Charles' laws (the “ideal gas” laws). Actually, the volume occupied by individual gases deviate, by a slight degree,
from the volumes which the “ideal gas” laws indicate. The amount of deviation is a function of the composition of the
gas and varies primarily with static pressure and temperature. The actual deviation may be obtained by a laboratory
test conducted on a sample of the gas, carefully taken at line conditions of pressure and temperature.

The National Bureau of Standards, Circular 564, gives the compressibility factor (Z) of air and other pure gases. The
relationship between supercompressibility factor and compressibility factor is as follows:

1

F

---=

pv

Z

Table A-9 on page A-12 gives an abbreviated listing of the supercompressibility factors for air. Practical relationships
have been established by which this deviation can be calculated and tabulated for natural gases containing normal
mixtures of hydrocarbon components, considering the presence of small quantities of carbon dioxide and nitrogen
and also relating the deviation to the heating value of gas. The A.G.A. manual (NX-19), “Determination of
Supercompressibility Factors for Natural Gas”, should be used for determination of F

F

tb

Temperature Base Factor. The Temperature Base Factors are calculated to give gas volumes at a base temperature
of 60 °F (520°R) for English Units. In order to adapt the flow equation for use in SI units, the factor is calculated

.

pv

similarly at 16 °C (289.15 K). The factor can be calculated as:

temperature base (°F) + 460

Ftb-- -=

F

tf

Flowing Temperature Factor. The units conversion factor (FNA) for volumetric flow of gases at standard conditions
has been calculated assuming that the gas temperature flowing around the Annubar primary element is 60 °F (520

520

OR

temperature base (°C) + 273.15

F

-- -=

tb

288.15

°R) or 16 °C (289 K). If measurement is made at any other flowing temperature, then the flowing temperature factor
must be applied. The factor can be found in Table A-8 on page A-11 or calculated as:

520

F

--------- -=

tf

flowing temperature (°F) + 460

520

OR

520

F

--------- -=

tf

273.15 + flowing temperature (°C)

288.15

G Specific Gravity of Flowing Liquid. Ratio of the density of the flowing fluid to the density of water at 60°F which is

63.3707 lbm/ft

h

w

Differential pressure produced by the Annubar primary element. For this handbook, the differential pressure is
expressed as the height, in inches, of a water column at 68 °F at standard gravity (gc = 32.174 ft/sec2). In SI Units,

3

. See Table A-4 on page A-6 for specific gravities of various liquids.

the differential pressure is expressed in kPa.

h

= inches H2O at 68 °F (kPa)

w

K Flow Coefficient. Equation 2-8 on page 2-9 defines the flow coefficient of an Annubar primary element. It is related to

the diameter of the pipe and is generally expressed as a function of Reynolds Number. See “Reynolds Number” on
page 1-8 for an explanation of Reynolds Number.

2-6

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

P

f

Q

a

Q

s

Flowing Pressure. This is the static pressure, in absolute units, existing in the pipe. For this handbook, the pressures
are expressed in psia (kPa abs).

Actual Volumetric Flow Rate. This term is the flow rate of the fluid passing the Annubar primary element in actual
volume units per units of time. Examples are actual cubic feet per hour (ACFH), GPM, Am

3

/h, etc.

Standard (Normal) Volumetric Flow Rate. This term is the flow rate of the fluid passing the Annubar primary element
in standard volume units per unit of time. For some gases, especially fuel gases, the cubic foot is the unit of
measurement. However, a cubic foot of gas has no absolute or comparative value unless the pressure and
temperature of the gas are specified. A common unit used for evaluating rates of flow is standard cubic foot per hour
(SCFH). This unit states how many cubic feet of gas per hour would be flowing around the Annubar primary element
if the flowing pressure and temperature were equal to the base pressure and temperature. For this handbook, the
base pressure is 14.73 psia (101.56 kPa abs) and the base temperature is 60 °F (520 °R) or 0 °C (273 K).

ρ

f

Y

A

Flowing Density. For this handbook, the densities are expressed in lbm/ft (kg/m3). Appendix A: Fluid Properties and
Pipe Data gives densities of various fluids.

Expansion Factor. When a gas flows around an Annubar primary element, the change in velocity is accompanied by
a change in density. The expansion factor must be applied to correct for this change. The expansion factor also
accounts for small changes in the internal energy of the molecules due to the temperature difference between the
upstream and downstream pressure ports of the Annubar primary element. The variation of the expansion factor is
small and the ratio of specific heats for commercial gases is sufficiently constant to warrant using a constant ratio of
specific heat. Use the following algorithm to calculate the value of the gas expansion factor. This equation adjusts for
density and internal energy effects of the gas as it flows around the Annubar primary element.

Equation 2-6. : Gas Expansion Factor

h

w

Ya1Y11B–()2Y2–()

---------–=

Pfϒ

where:

Equation 2-7. : Blockage Equation

4d

------- -

B = = Blockage

πD

D = Internal Pipe Diameter in inches (cm)
d = See Table 2-7 on page 2-10
h

= Differential pressure in inches (mm) of water column

w

Pf = Flowing line pressure in psia (kPa abs)
γ = Ratio of specific heats
Y

= 0.011332 in English Units (0.31424 SI Units)

1

Y2= 0.00342 in English Units (0.09484 SI Units)

Examples of gases with a specific heat ratio of 1.4 are: air, CO, H
specific heat ratio of 1.3 are: natural gas, ammonia, CO

Y

is needed in all gas flow equations and requires the differential pressure be calculated first. If the differential

a

pressure is not known, Y
necessary to determine a final value.

is assumed to be 1.000 and the differential pressure is calculated. Iteration is then

a

, Cl2, H2S, N2O, SO2, and steam.

2

W Mass Rate of Flow. This term is the flow rate of the fluid passing the Annubar primary element in mass units per unit

time.

, NO, N2 and O2. Examples of gases with a

2

2-7

Rosemount 485 Annubar

Figure 2-1. Typical Cross
Section

Reference Manual

00809-0100-1191, Rev CB

May 2006

D

d

a = Annubar projected area = d . D

2

πD

A = Pipe inside area =

a

4d

--- -

a

A

A

B = =

------- -

A

πD

---------- -

4

Flow Coefficient
Reynolds Number
Dependency

When the 485 Annubar primary element is used within the acceptable
Reynolds Number range defined by Rosemount in Table 2-7 on page 2-10,
the Annubar Primary element's flow coefficient will be independent of
changing Reynolds Number. Any variations in the K-value with changing
Reynolds Number are due to scatter and fall within ±0.75% of the published
K-value.

A 485 Annubar primary element’s K-factor independence of Reynolds number
allows the user to measure a large range of Reynolds Numbers without need
of a correction factor for changing Reynolds Numbers. The 485 Annubar
primary element K-factor independence can be attributed to a constant
separation point along the edges of its T-shaped sensor and the probe's
ability to take a proper average of its sensing slots.

Flow Coefficient Theory Rosemount was the first company to identify and utilize the theoretical

equations linking self-averaging pitot tube flow coefficients to pipe blockage.
This K-to-Blockage theoretical link establishes a higher degree of confidence
in 485 Annubar K-factors than in flow meters that use only an empirical data
base for determining their flow coefficients.

Signal The signal generated by an Annubar can be divided into two major parts:

• the differential pressure contribution due to the Annubar 's shape (H

• the differential pressure contribution due to the Annubar’s blockage in

the pipe (H

).

b

Shape Differential An Annubar primary element placed in an infinitely large pipe (with no

confining walls) will still produce a differential pressure. This differential
pressure is nearly twice that of a standard pitot tube, and is the result of a
reduced low pressure on the downstream side. The upstream, or high
pressure is caused by the fluid impacting the front of the Annubar primary
element and is known as the stagnation pressure. The downstream, or low
pressure is caused by the fluid traveling past the Annubar primary element,
creating suction on the rear side. This suction phenomenon can be attributed
to boundary layer flow separation.

)

S

2-8

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Blockage Differential An Annubar primary element is an obstruction in the pipe and therefore,

reduces the cross-sectional area through which the fluid can pass. This
reduced area causes the fluid to accelerate and hence, reduces its pressure.
Therefore, the downstream pressure measurement of an Annubar primary
element will be affected by the Annubar's blockage in the pipe.

Since an Annubar primary element uses the internal diameter of the pipe it is
being inserted into as a throat diameter in its calculation of a flow rate, the
Annubar primary element K-factor must compensate for the amount of
obstructed area the sensor itself causes in the pipe. This is analogous to the
velocity of approach factor for an orifice plate or a venturi meter.

By writing a mass balance and an energy balance around the Annubar
primary element, and by dividing the differential pressure produced by the
Annubar primary element into H
between the Annubar primary element K-factor and the Annubar primary
element's blockage in the pipe. The derivation involves partial differential
pressure components, and the integration of a K-blockage equation. The
result is the following K vs. Blockage equation:

Equation 2-8. : K vs. Blockage

K

A

1C2B–()

------------------------------------------------- -=

1C

1C2B–()

–

1

2

and Hb, one can derive the relationship

s

Table 2-6. 485 Sensor
Constants

The Importance of the
Flow Coefficient, or K vs.
B Theory

The constants C

are determined, the equation above becomes the theoretical link between

C

2

and C2 must be determined experimentally. Once C1 and

1

the Annubar primary element K-factor (K) and the Annubar primary element's
blockage in the pipe (B). The values for constants C

and C2 are shown in the

1

table below:

Coefficient Sensor Size 1 Sensor Size 2 Sensor Size 3

C

1

C

2

– 1.515 – 1.492 – 1.5856

1.4229 1.4179 1.3318

As with any other meter, the 485 Annubar primary element's accuracy is only
as good as its flow coefficient (K-factor). Rosemount has tested a
representative sample of flowmeters and empirically determined flow
coefficients. For Annubars, these flow coefficients are plotted against the
meter's blockage. Curve fitting techniques combined with flow coefficient
theory are applied to the base line data to generate equations that predict flow
coefficients in untested line sizes and untested Reynolds Number ranges.
Please see the 485 Annubar Flow Test Data Book (document number
00821-0100-4809, Rev AA) for a more detailed discussion of this topic.

Provided the theory is based on the proper physics, these relationships are
immune to minor variation in test data. Using a theoretical basis (in addition to
empirical testing) for the prediction of untested flow coefficients provides a
much higher degree of confidence in the untested values. The graphs in
Figure 2-2 show that empirical data agree with a plot of the K vs. Blockage
Equation.

2-9

Reference Manual

00809-0100-1191, Rev CB

Rosemount 485 Annubar

May 2006

Figure 2-2. K vs. BLOCKAGE

Sensor Size 2 Sensor Size 3Sensor Size 1

Operating Limitations For an Annubar primary element to operate accurately, the flowing fluid must

separate from the probe at the same location (along the edges of the T-shape
sensor). Drag coefficients, lift coefficients, separation points, and pressure
distributions around bluff bodies are best compared by calculating the “rod”
Reynolds Number. There is a minimum rod Reynolds Number at which the
flowing fluid will not properly separate from the edges of a T-shape sensor.
The minimum rod Reynolds Numbers for the Rosemount 485 are:

Table 2-7. Reynolds Number
and Probe Width

Sensor Size Probe Width (d) Minimum Reynolds Number

1 0.590-in. (1.4986 cm) 6000
2 1.060-in (2.6924 cm) 12500
3 1.935-in (4.915 cm) 25000

Above these rod Reynolds Numbers 485 Annubar primary elements will
operate accurately.

To determine the rod Reynolds Number at any given flowrate, use the
following relationship:

where,
ρ = fluid density in lbm/ft

Re

3

(kg/m3)

rod

dVρ

-----------=

12μ

OR

Re

rod

dVρ

-------------=

100μ

d = probe width in inches (cm)
V = velocity of fluid in feet per second (m/s)
µ = fluid viscosity in lbm/ft-sec (kg/m-s)

When determining the minimum operating flow rate for an Annubar primary
element, one should also consider the capability of the secondary
instrumentation (differential pressure transmitters, manometers, etc.).

The upper operating limit for 485 Annubar primary elements is reached when
any one of the following criteria is met:

1. The fluid velocity reaches the structural limit of the Annubar.

2. The fluid velocity reaches a choked flow condition at the Annubar (gas).

3. Cavitation occurs on the downstream side of the Annubar.

2-10

Reference Manual

)

)

)

)

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Flow Calculation
Examples:

Problem:

Oil with a specific gravity of 0.825 is flowing at a rate of 6000 GPM. The 20-in.
standard wall (ID = 19.26-in.) carbon steel pipeline has a pressure of 75 psig
and a temperature of 100°F. What is the differential pressure (h

) that a

w

Sensor Size 2 485 Annubar primary element would measure?

Solution:

2

Q

a

⎛⎞

-------

h

=

w

⎝⎠

C′

Qa = 600 GPM

C′ F

na

KD2F

aa

1

----- -⋅⋅ ⋅ ⋅=

G

f

(from Equation 2-1 on page 2-1)

(from Equation 2-1 on page 2-1)

where:

Fna = 5.6664

1C

B–()

------------------------------------------------- -=

K

1C

2

1C2B–()

–

1

2

(from Equation 2-8 on page 2-9

where:

B

πD

C

C

19.25π

1.492–=

1

1.4179=

2

4 1.060()

4d

----------------------- 0.0701== =

------- -

(from Equation 2-7 on page 2-7

(from Table 2-6 on page 2-9

(from Table 2-6 on page 2-9

so:

------------------------------------------------------------------------------------------------------ - 0.6058==

K

D219.262370.9476==

Faa = 1.000

1

----- -

G

f

1 1.4179 0.0701×–()

11.492–()1 1.4179 0.0701×–()

-------------- - 1.101==

0.825

×–

1

2

so:

C 5.6664 0.6058 370.9476 1.000 1.101⋅⋅ ⋅⋅ 1401.9625==

and:

6000

⎛⎞

--------------------------- -

h

w

⎝⎠

1401.9625

2

18.316==inchH2O

2-11

Rosemount 485 Annubar

Problem:

Oil with a specific gravity of 0.825 is flowing at a rate of 22,700 LPM. The 50
cm inside diameter carbon steel pipeline has a pressure of 517 kPa and a
temperature of 38 °C. What is the differential pressure (h
2 485 Annubar primary element would measure?

Solution:

Q

⎛⎞

-------

h

=

w

⎝⎠

C′

Qa = 22700 LPM

Reference Manual

00809-0100-1191, Rev CB

May 2006

) that a Sensor Size

w

2

a

(from Equation 2-1 on page 2-1)

C′ F

na

KD2F

aa

1

----- -⋅⋅ ⋅ ⋅=

G

f

(from Table 2-2 on page 2-4)

(from Equation 2-1 on page 2-1)

where:

Fna = 0.066673

B–()

1C

------------------------------------------------- -=

K

1C

2

1C2B–()

–

1

2

(from Equation 2-8 on page 2-9)

where:

4d

B

4 2.6924()

------- -

-------------------------- - 0.0686== =

πD

C

1.492–=

1

C

1.4179=

2

50π

(from Table 2-6 on page 2-9)

(from Table 2-6 on page 2-9)

(from Table 2-6 on page 2-9)

so:

K

------------------------------------------------------------------------------------------------------------ - 0.6065==

1 1.492–()1 1.4179 0.0686⋅()–()

D25002250000==

Faa = 1.000

1

----- -

G

f

1 1.4179 0.0686⋅()–()

⋅()–

1

-------------- - 1.101==

0.825

2

2-12

so:

C′ 0.066673 0.6065 250000 1.000 1.101⋅⋅ ⋅⋅ 11130.33==

and:

22700

⎛⎞

------------------------ -

h

w

⎝⎠

11130.33

2

4.159==kPa

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Problem:

Steam at 500 psia and 620 °F is flowing in a 24-in. ID carbon steel pipe. The
measured differential pressure on a Sensor Size 3 485 Annubar primary
element is 15-in H

Solution:

WC′ hw⋅=

C′ FnaKD2YaFaaρ

⋅⋅ ⋅ ⋅ ⋅=

where:

Fna = 358.94

K

------------------------------------------------- -=

1C

where:

O. What is the flowrate in PPH?

2

f

B–()

1C

2

1C2B–()

–

1

4d

------- -

B

πD

2

4 1.920()

----------------------- 0.1019== =

24π

(from Equation 2-2 on page 2-1)

(from Equation 2-3 on page 2-1)

(from Table 2-2 on page 2-4)

(from Equation 2-8 on page 2-9)

(from Equation 2-7 on page 2-7)

C

1

C

2

so:

K

---------------------------------------------------------------------------------------------------------------- 0.5848==

1 1.5856–()1 1.3318 0.1019⋅()–()

D2242576==

1 0.011332 1 B–()20.00342–()

Y

a

where:

B

H

w

P

f

ϒ 1.3=

1.5856–()=

1.3318=

1 1.3318 0.1019⋅()–()

⋅()–

4 1.920()

4d

----------------------- 0.1019== =

------- -

πD

500p si a=

24π

15i nH2O=

(from Table 2-6 on page 2-9)

(from Table 2-6 on page 2-9)

2

h

w

---------–= (from Equation 2-6 on page 2-7)

Pfϒ

(from Equation 2-7 on page 2-7)

so:

1 0.011332 1 0.1019–()

Y

a

1.008=

F

aa

0.8413 0.9172==

ρ

f

2

0.00342–()

15

----------------------– 0.9999==
500 1.3⋅

ρ

per ASME steam tables

f

2-13

Rosemount 485 Annubar

so

C′ 358.94 0.5848 576 0.9999 1.008 0.9172⋅⋅⋅⋅⋅ 111771.96==

W 111771.96 15⋅ 432890.93==PPH

Problem:

Steam at 3500 kPa abs and 350 °C is flowing in a 60.96 cm ID carbon steel
pipe. The measured differential pressure on a Sensor Size 3 485 Annubar
primary element is 7.5 kPa. What is the flowrate in kg/hr?

Solution:)

WC′ hw⋅=

C′ FnaKD2YaFaaρ

where:

Fna = 0.12645

K

------------------------------------------------- -=

1C

⋅⋅ ⋅ ⋅ ⋅=

1C

B–()

2

1C2B–()

–

1

Reference Manual

00809-0100-1191, Rev CB

May 2006

(from Equation 2-2 on page 2-1)

f

2

(from Equation 2-3 on page 2-1)

(from Equation 2-8 on page 2-9)

where:

B

C

1

C

2

πD

60.96π

1.5856–=

1.3318=

44.9149()

4d

-------------------------- - 0.1027== =

------- -

(from Equation 2-7 on page 2-7)

(from Table 2-6 on page 2-9)

(from Table 2-6 on page 2-9)

(from Table 2-6 on page 2-9)

so:

K

---------------------------------------------------------------------------------------------------------------- 0.5845==

1 1.5856–()1 1.3318 0.1027⋅()–()

D2609.62371612.16==

1 0.31424 1 B–()20.09484–()

Y

a

1 1.3318 0.1027×–()

h

---------–=

Pfϒ

2

w

⋅()–

(from Equation 2-6 on page 2-7)

where:

B

H

P

ϒ 1.3=

4d

-------------------------- - 0.1027== =

------- -

60.96π

πD

7.5k Pa=

w

3500k Pa A=

f

(from Equation 2-7 on page 2-7)

4 4.9149()

so:

Y

1 0.31424 1 0.1027–()

a

F

1.009=

aa

ρ

13.0249 3.609==

f

2

0.09484–()

7.5

--------------------------- -– 0.9997==
3500 1.3×

(from Table B-1 on page B-1)

ρ

per ASME steam tables

f

2-14

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

so

C′ 0.12645 0.5845 371612.16 0.9997 1.009 3.609⋅⋅ ⋅⋅⋅ 99986.42==

W 99986.42 7.5⋅ 273824.1==kg h⁄

Problem:

Natural gas with a specific gravity of 0.63 is flowing in a 12-in. schedule 80
carbon steel pipe. the operating pressure is 1264 psia. The operating
temperature is 120 °F. For a Sensor Size 2 485 Annubar primary element,
determine the differential pressure (h
temperature of 60 °F and a pressure of 14.73 psia.

Solution:

2

Q

1

s

⎛⎞

h

w

Q

s

P

f

C′ F

------ -

-----

⋅=

⎝⎠

C′

P

f

6000000S CF H=

1264p si a=

KD2YaFpbFtbFtfFgFpvF⋅⋅⋅⋅⋅⋅

⋅⋅ ⋅=

na

) for a flowrate of 6 MM SCFH at a base

w

aa

(from Equation 2-4 on page 2-1)

where:

Fna = 338.17

1C

B–()

------------------------------------------------- -=

K

1C

2

1C2B–()

–

1

2

(from Equation 2-8 on page 2-9)

where:

4d

B

C

1

C

2

4 1.060()

------- -

----------------------- 0.1186== =

πD

11.37π

1.492–=

1.4179=

(from Equation 2-7 on page 2-7)

(from Table 2-4 on page 2-5)

(from Table 2-4 on page 2-5)

so:

------------------------------------------------------------------------------------------------------------ - 0.5835==

K

11.492–()1 1.4179 0.1186⋅()–()

D211.3762129.41==

1 1.4179 0.1186⋅()–()

⋅()–

2

2-15

Rosemount 485 Annubar

l

)

The differential pressure hw is required to calculate Ya. Since hw is not

Fpb=

base pressure, psia

temperature base (°F) + 460

Ftb-- -=

known, assume Y

14.73

F

520

pb

-- -=

= 1 and verify the results

a

14.73

-------------- -= 1=

14.73

60 460+

---------------------- -= 1=
520

Reference Manual

00809-0100-1191, Rev CB

May 2006

F

-- -=

tf

flowing temperature (°F) + 460

1

F

----

g

G

pv

aa

1

---

Z

1.001=

F

F

520

1

----------- 1.2599== =

0.63

1

----------------- - 1.0637== =

0.8838

520

------------------------- -= 0.9469=
120 460+

(Compressibility factor for natura

gas from A.G.A Report No. 3

so:

C 338.17 1.5835 129.411110.9469 1.2599 1.0637 1.001××××××××× 32436.74= =

2

Q

1

s

⎛⎞

-----

------ -

h

⋅

w

P

⎝⎠

f

------------ -

I

1264

C

Now the value of Y

Y

1 0.011332 1 B–()20.00342–()

a

1

6000000

⎛⎞

------------------------ -

⋅ 27.07i nH2O== =

⎝⎠

32436.74

, assumed above, can be checked:

a

2

h

---------–=

Pfϒ

w

(from Equation 2-6 on page 2-7)

2-16

where:

B

H

P

ϒ 1.3=

4d

----------------------- 0.1186== =

------- -

11.37π

πD

27.07inchH2O=

w

1264p si a=

f

(from Equation 2-7 on page 2-7)

4 1.060()

so:

Y

1 0.011332 1 1186–()20.00342–()

a

27.07

--------------------------- -– 1==
1264 1.3×

The assumed and calculated value are the same. therefore, the value of

= 24.27 inch H2O is the correct answer.

h

w

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Problem:

Natural gas with a specific gravity of 0.63 is flowing in a 300 mm ID carbon
steel pipe. The operating pressure is 8700 kPA abs and the operating
temperature is 50 °C. For a Sensor Size 2 485 Annubar primary element,
determine the differential pressure (h
base temperature of 0 °C and a pressure of 101.325 kPa.

Solution:

2

Q

1

s

⎛⎞

h

w

Q

s

P

f

C′ F

------ -

-----

⋅=

⎝⎠

C′

P

f

1700N m3m⁄=

8700k Pa=

KD2YaFpbFtbFtfFgFpvF⋅⋅⋅⋅⋅⋅

⋅⋅ ⋅=

na

where:

Fna = 0.00018912

1C

B–()

------------------------------------------------- -=

K

1C

2

1C2B–()

–

1

2

) for a flowrate of 1700 Nm3/m at a

w

(from Equation 2-4 on page 2-1)

aa

(from Equation 2-4 on page 2-1)

(from Equation 2-8 on page 2-9)

where:

4d

B

C

1

C

2

4 26.924()

------- -

-------------------------- - 0.1143== =

πD

1.492–=

1.4179=

300π

(from Equation 2-7 on page 2-7)

(from Table 2-6 on page 2-9)

(from Table 2-6 on page 2-9)

so:

------------------------------------------------------------------------------------------------------------ - 0.5856==

K

D2300290000==

F

pb

temperature base (°C) + 273.15

F

pb

F

tf

F

g

1 1.4179 0.1143⋅()–

1 1.492–()1 1.4179 0.1143⋅()–()

⋅()–

The differential pressure h

known, assume Y

101.325

-- -=

base pressure, kPa abs

-- -=

-- -=

273.15 + flowing temperature (°C)

----

G

1

288.15

288.15

1

----------- 1.2599== =

0.63

= 1 and verify the results.

a

101.325

---------------------= 1=

101.325

2

is required to calculate Ya. Since hw is not

w

0 273.15+

--------------------------- -= 0.9479=

288.15

288.15

------------------------------ -= 0.9443=

273.15 50+

pv

aa

1

---

Z

1.001=

F

F

1

-------------- - 1.0684== =

0.876

2-17

Rosemount 485 Annubar

so:

C′0.00018912 0.5856 90000 1 0.9479 1 0.9443 1.2599 1.0684 1.001⋅⋅⋅⋅⋅⋅⋅⋅⋅ 12.0215= =

1

h

-----

w

P

f

Q

⎛⎞

------ -

⋅

⎝⎠

C'

Reference Manual

00809-0100-1191, Rev CB

May 2006

2

s

1

⎛⎞

------------ -

---------------------

⋅ 2.2986 kP a== =

⎝⎠

8700

12.0215

1700

2

Now the value of Y

Y

1Y11B–()2Y2–()

a

, assumed above, can be checked:

a

h

w

---------–=

Pfϒ

(from Equation 2-6 on page 2-7)

where:

4d

B

H

P

ϒ 1.3=

4 26.924()

------- -

-------------------------- - 0.1143== =

πD

w

f

300π

2.2986k Pa=

8700k Pa=

(from Equation 2-7 on page 2-7)

so:

Y

1 0.31424 1 0.1143–()

a

⋅ 0.09484–()

2

2.2986

------------------------- -– 1==
8700 1.3⋅

The assumed and calculated value are the same. therefore, the value of

= 2.2986kPa is the correct answer.

h

w

2-18

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Section 3 Installation and Operational

Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 3-1

Upstream Flow Disturbance . . . . . . . . . . . . . . . . . . . . . . . page 3-2

Instrument Lines and Connections Leakage . . . . . . . . . . page 3-4

Flow Parameter Changes . . . . . . . . . . . . . . . . . . . . . . . . . . page 3-4

Dirt Accumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 3-4

Gas Entrapment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 3-6

Flow Parameter Limitations . . . . . . . . . . . . . . . . . . . . . . . . page 3-6

ERRORS

Alignment The Annubar probe senses a total pressure (impact and static pressure)

through the upstream slots and a low pressure through the downstream ports.
The impact pressure and the downstream low pressure are affected by the
alignment of the sensing slots/ports. A deviation from perpendicular to the
axis of the pipe in any direction will affect either or both of the sensed
pressures. The published Flow Coefficients were determined experimentally
with a carefully aligned Annubar primary element. Changes within the 3° limits
will have insignificant effects on the pressures and consequently on the Flow
Coefficients. Further changes will cause a shift in the Flow Coefficient.

Figure 3-1. Acceptable Alignment

If, for some reason, an Annubar primary element is not or cannot be installed
within the recommended limits the output signal will be repeatable and stable
but will be shifted by some unknown amount. This shift can be accounted for
by performing an in-line calibration. An in-line calibration entails determining
the installed Annubar flow coefficient typically by performing a pitot-traverse of
the flow point. After determining a new Flow Coefficient, the Annubar primary
element will perform within its normal accuracy specifications.

3°

3° 3°

www.rosemount.com

Reference Manual

00809-0100-1191, Rev CB

Rosemount 485 Annubar

May 2006

Sizing For accurate measurement, the design of the Annubar probe requires that the

flow sensing slots/ports be located at specific points in the flow stream. The
Annubar primary element is manufactured to ensure proper slot/hole location
based on customer-supplied pipe ID and wall dimensions. When the Annubar
primary element is installed in the line using the proper fittings, the sensing
ports end up at the proper locations. If an Annubar primary element is used in
a line which has a different inside diameter or wall thickness than for which it
was manufactured, the ports will not be properly located. Using the wrong
mounting fittings may also cause a location error.

The result of having the sensing ports improperly located could be an
incorrect flow measurement. The reading may be either high or low
depending on the individual application.

An Annubar primary element that is installed in an incorrect line size will
generate a repeatable signal. A calibration factor can be determined to correct
flow measurement allowing normal use of the Annubar primary element.

UPSTREAM FLOW
DISTURBANCE

The Annubar flow sensor is an averaging head type device. The location of
the sensing ports has been mathematically determined using fully developed
turbulent flow characteristics. This implies that the flow velocity profile is
symmetrical across the pipe in all directions. The averaging functions of the
Annubar primary element will not take place if the flow profile is not
symmetrical. This will cause a change in the Flow Coefficient from the
published information.

The flow profile can be influenced by any upstream device which disturbs the
flow. Examples would be valves, elbows, diameter changes, etc. Sufficient
length of straight run of pipe upstream of the Annubar primary element will
allow the turbulent flow profile to develop. A flow straightener or straightening
vanes may be used to reduce the length of straight run required. These are
available in several configurations from piping supply houses. Table 3-1
shows minimum straight run requirements with and without the use of flow
straighteners.

The Annubar primary element will produce a repeatable signal even if the
straight run requirements have not been met. In many control situations, it is
necessary to monitor changes in flow rather than to measure flow rate. Here it
would not be necessary to have the full amount of straight run. Where flow
measurement is necessary without sufficient straight run, an in-line calibration
may be necessary to determine the correct Flow Coefficient.

3-2

Reference Manual

00809-0100-1191, Rev CB
May 2006

Table 3-1. Straight Run
Requirements

Rosemount 485 Annubar

Upstream Dimensions

Without Vanes With Vanes

In Plane A

1

Out of

Plane A

A’ C C’

Dimensions

Downstream

8

—

2

11

—

3

23

—

4

12

—

10

—

16

—

28

—

12

—

—8—4—

—8—4—

—8—4—

—8—4—

4

4

4

4

4

4

4

4

4

4

4

4

5

18

—

6

30

—

18

—

30

—

—8—4—

—8—4—

4

4

4

4

4

4

3-3

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

INSTRUMENT LINES
AND CONNECTIONS
LEAKAGE

FLOW PARAMETER
CHANGES

Flow measurement using an Annubar primary element or any other type of
head device depends on comparing two pressures generated by the flow past
the device. This difference is called a differential pressure or DP The
magnitude of this DP is small and quite often less than one (1) psi. Any leaks
in the instrument lines or connections will change the DP output of the
Annubar primary element. In applications with static pressure above
atmospheric pressure a leak in the pressure lines will cause a low DP to be
seen by the secondary instrumentation.

The Annubar primary element will function over an extremely wide range of
flow conditions. Measuring flow with an Annubar primary element requires
care in determining the flowing conditions so that the secondary
instrumentation provides usable readings.

A precise flow calculation is performed as part of the application of an
Annubar primary element and secondary instrumentation. If any of the
following parameters change, the flow calculation is no longer valid.
Significant changes in fluid temperature, density, specific gravity, velocity and
pressure are some of the parameters that will cause errors in flow
measurement unless a new flow calculation is done. A new flow calculation
can then provide necessary information for calibrating the secondary
instrumentation.

DIRT ACCUMULATION One inherent advantage of an Annubar primary element over devices such as

an orifice plate is its ability to function in flows carrying dirt and grease. The
shape of the Annubar primary element causes most foreign material to flow
around the probe rather than accumulate on it. The material that does impact
on the probe does not significantly affect performance unless, under extreme
cases, some of the sensing ports are completely obstructed or the outside
shape is drastically changed by buildup.

Figure 3-2. Particulate Deflection

3-4

There are two methods of cleaning the Annubar primary element to restore
performance. Mechanical cleaning is the more certain method, but does
require removal of the Annubar primary element. Purging the Annubar
primary element is effective if the accumulation covers the sensing ports or
blocks the inner passages of the Annubar primary element.

In applications where a large amount of foreign material exists, it may be
necessary to perform a routine preventative maintenance removal of the
Annubar primary element for cleaning. The outer surfaces should be cleaned
with a soft wire brush. The outer internal passages should be cleaned with a
soft wire brush and compressed air. If necessary, a solvent for dissolving
foreign material may be appropriate.

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Purging the Annubar primary element with an external fluid source under a
higher pressure is an effective means of retaining clear pressure pathways in
the Annubar primary element.

The following precautions should be taken:

1. The purging fluid must be compatible with the process fluid and
shouldn't cause other problems such as contamination.

2. The purging fluid should be preheated or pre-cooled if the
temperature difference of the fluid and the process exceeds 150°F
(66°C).

3. The differential pressure transmitter or meter should be isolated from
the purge fluid to prevent over-ranging.

4. Continuous purging is not recommended.

The length of time between purges, or the cycle time as well as the length of
the purge cycle must be determined experimentally. There are no general
guidelines as conditions, fluids, and systems affect the specific function of a
purge system.

Purging may be done in several ways. One is to provide an external source of
fluid pressure which can be valved into the instrument lines.

Blow-down of the Annubar primary element is a method of purging. This
method uses process line pressure to clean the Annubar primary element.
Some means of opening the instrument lines are required. During blow-down,
the process fluid flows out of the Annubar primary element, carrying any
debris with it.

Care must be taken to protect the secondary instrumentation from high
pressures and temperatures when purging an Annubar primary element.

Figure 3-3. Impulse Tube Arrangement for Purge

To High Side of
Secondary Element

To Low Side of
Secondary Element

To External Source of Fluid Pressure

3-5

Reference Manual

00809-0100-1191, Rev CB

Rosemount 485 Annubar

May 2006

GAS ENTRAPMENT Flow measurement with an Annubar primary element or any head type device

involves measuring and comparing pressures of very low magnitude or very
little differences. Problems causes by leaks and liquid legs have been
previously mentioned. Problems may also be caused by gas entrapment
while measuring flow in a liquid line.

The effect of having air entrapped in an instrument line is that of building in a
shock absorber. In all flow situations the Annubar DP signal fluctuates
because of flow turbulence. The entrapped gas is compressible and therefore
absorbs a portion of the signal at the secondary instrumentation. A liquid filled
line would not have any tendency to absorb part of the signal.

Entrained air in impulse lines also leads to head errors. Low density gas in
impulse lines diplaces liquid creating measurement offset.

It is important to follow the installation recommendations for placement of the
Annubar primary element and instrumentation to minimize gas entrapment.
Periodic bleeding of the secondary instrumentation and lines may be
necessary.

FLOW PARAMETER
LIMITATIONS

The Annubar primary element will function in a wide variety of fluid flow
situations. There are two specific situations in which the Annubar primary
element should not be used. The first is in flows where the viscosity
approaches or exceeds 50 centipoise. The second is in a situation with two
phase flow. This is true of liquid/gas, liquid/solid and gas/solid situations.
Examples would be quality steam, slurries and foam. If there is doubt about
any application, consult an Emerson Process Management representative.

3-6

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Appendix A Fluid Properties and Pipe Data

FLUID PROPERTIES

Table A-1. Density of Superheated Steam and Compressed Water Density, ρ, lbm/ft

Tem p 1 2 5 10 20 50 100 200 500 750 1000

°F psia psia psia psia psia psia psia psia psia psia psia
32 62.42 62.42 62.42 62.42 62.42 62.42 62.42 62.46 62.54 62.58 62.62
40 62.42 62.42 62.42 62.42 62.42 62.42 62.42 62.46 62.54 62.58 62.62
60 62.37 62.37 62.37 62.37 62.37 62.37 62.37 62.42 62.46 62.50 62.58

80 62.23 62.23 62.23 62.23 62.23 62.23 62.23 62.27 62.31 62.38 62.42
100 62.00 62.00 62.00 62.00 62.00 62.00 62.00 62.04 62.07 62.15 62.19
120 .002901 61.73 61.73 61.73 61.73 61.73 61.73 61.77 61.81 61.84 61.88
140 .002804 .005619 61.39 61.39 61.39 61.39 61.39 61.43 61.46 61.50 61.58
160 .002713 .005435 60.98 60.98 61.01 61.01 61.01 61.01 61.09 61.13 61.20
180 .002628 .005263 .01321 60.55 60.57 60.57 60.57 0.61 60.68 60.72 60.75
200 .002548 .005101 .01280 .02575 60.10 60.13 60.13 60.13 60.21 60.24 60.31
220 .002472 .004950 .01241 .02495 59.59 59.60 59.60 59.67 59.70 59.77 59.81
240 .002402 .004807 .01205 .02420 .04885 59.10 59.10 59.10 59.17 59.24 59.28
260 .002334 .004672 .01171 .02351 .04738 58.51 58.55 58.55 58.62 58.69 58.72
280 .002271 .004545 .01139 .02285 .04602 57.94 57.94 59.97 58.04 58.07 58.14
300 .002211 .004425 .01108 .02223 .04473 .1140 57.31 57.34 57.41 57.47 57.54
320 .002154 .004311 .01079 .02165 .04352 .1107 56.63 56.66 56.75 56.82 56.88
340 .002100 .004203 .01052 .02109 .04239 .176 .2213 55.96 56.05 56.12 56.18
360 .002149 .004100 .01026 .02057 .04131 .1047 .2146 55.22 55.31 55.40 55.46
380 .002000 .004002 .01002 .02007 .04029 .1019 .2084 54.47 54.56 54.65 54.71
400 .001954 .003908 .009781 .01960 .03933 .09938 .2026 .4238 53.74 53.82 53.91
420 .001909 .003819 .009557 .0914 .03841 .09696 .1973 .4104 52.88 52.97 53.08
440 .001866 .003734 .009343 .01871 .03753 .09466 .1923 .3982 51.98 52.08 52.17
460 .001826 .003653 .009139 .01830 .03670 .09249 .1876 .3870 50.99 51.13 51.23
480 .001787 .003575 .008944 .01791 .03590 .09042 .1832 .3766 1.049 50.08 50.20
500 .001750 .003500 .008756 .01753 .03514 .08845 .1790 .3670 1.008 48.97 49.12
520 .001714 .003429 .008576 .01717 .03441 .08657 .1750 .3580 .9728 1.603 47.94
540 .001680 .003360 .008405 .01682 .03371 .08477 .1712 .3496 .9413 1.530 46.64
560 .001647 .003294 .008239 .01649 .03304 .08305 .1676 .3416 .9128 1.468 2.142
580 .001615 .003230 .008080 .01617 .03240 .08140 .1642 .3341 .8870 1.415 2.035
600 .001585 .003169 .007927 .01587 .03178 .07982 .1609 .3270 .8633 1.367 1.947
620 .001555 . 003 111 .007780 .01557 .03119 .07830 .1577 .3202 .8413 1.325 1.871
640 .001527 .003054 .007638 .01529 .03061 .07683 .1547 .3137 .8209 1.287 1.804
660 .001499 .002999 .007501 .01501 .03006 .07543 .1518 .3076 .8010 1.252 1.746
680 .001473 .002947 .007369 .01475 .02953 .07408 .1490 .3017 .7840 1.219 1.693
700 .001446 .002896 .007242 .01449 .02902 .07278 .1464 .2960 .7671 1.189 1.645
720 .001423 .002847 .007119 .01425 .02852 .07152 .1438 .2906 .7510 1.161 1.601
740 .001400 .002799 .007000 .01401 .02804 .07030 .1413 .2854 .7359 1.135 1.560
760 .001376 .002753 .006885 .01378 .02758 .06913 .1389 .2804 .7215 1.111 1.523
780 .001354 .002709 .006774 .01335 .02713 .06800 .1366 .2755 .7077 1.087 1.488
800 .001333 .002666 .006666 .01334 .02670 .06690 .1344 .2709 .6946 1.065 1.455
820 .001312 .002624 .006562 .01313 .02628 .06584 .1322 .2664 .6820 1.045 1.424
840 .001292 .002584 .006461 .01293 .02587 .06482 .1301 .2521 .6700 1.025 1.394
860 .001272 .002454 .006363 .01273 .02548 .06382 .1281 .2579 .6584 1.006 1.367
880 .001253 .002507 .006268 .01254 .02509 .06286 .1261 .2539 .6473 .9877 1.340
900 .001235 .002470 .006175 .01235 .02472 .06192 .1242 .2500 .6366 .9703 1.315
920 .001217 .002434 .006086 .01217 .02436 .06101 .1224 .2462 .6263 .9537 1.291
940 .001199 .002399 .005998 .01200 .02401 .06013 .1206 .2425 .6163 .9377 1.269
960 .001182 .002365 .005914 .01183 .02367 .05928 .1187 .2389 .6068 .9223 1.247
980 .001166 .002332 .005832 .01167 .02334 .05845 .1172 .2355 .5975 .9075 1.266

1000 .001150 .002300 .005752 0.1151 .02302 .05764 .1155 .2321 .5885 .8933 2.061

Sat Steam
Sat. Water

T

°F

sat

.002998

61.96

101.74

.005755

61.61

126.07

.01360

60.94

162.24

.02603

60.28

193.21

.04978

59.42

227.96

.1175

57.90

281.02

.2257

56.37

327.82

.4372

54.38

381.80

3

1.078

50.63

467.01

1.641

48.33

510.84

2.242

46.32

544.58

www.rosemount.com

Reference Manual

00809-0100-1191, Rev CB

Rosemount 485 Annubar

Table A-2. Properties of Saturated Water

Tem p Density Specific Viscosity Tem p Density Specific Viscosity Te mp Density Specific Viscosity Te mp Density Specific Viscosity

°F lbm/ft

32 62.4140 1.007 1.75 66 62.3344 .9994 1.03 160 60.9932 .9779 .394 330 56.2960 .9026 .163
33 62.4167 1.007 1.72 67 62.3275 .9993 1.02 165 60.8909 .9763 .380 335 56.1220 .8998 .160
34 62.4191 1.008 1.69 68 62.3205 .9992 1.00 170 60.7862 .9746 .366 340 55.9458 .8970 .157
35 62.4212 1.008 1.66 69 62.3132 .9991 .988 175 30.6789 .9729 .353 345 55.7674 .8941 .155
36 62.4229 1.008 1.63 70 62.3058 .9990 .975 180 60.5693 .9717 .341 350 55.5859 .8912 .152
37 62.4242 1.009 1.61 71 62.2981 .9988 .962 185 60.4573 .9693 .330 355 55.4042 .8883 .150
38 62.4252 1.009 1.58 72 62.2902 .9987 .950 190 60.3430 .9675 .319 360 55.2192 .8853 .147
39 62.4258 1.009 1.55 73 62.2822 .9986 .937 195 60.2265 .9656 .309 365 55.0320 .8823 .145
40 62.4261 1.009 1.53 74 62.2739 .9984 .925 200 30.1076 .9637 .300 370 54.8424 .8793 .143
41 62.4261 1.009 1.50 75 62.2654 .9983 .913 205 59.9866 .9618 .291 375 54.6506 .8762 .141
42 62.4257 1.009 1.48 76 62.2568 .9982 .902 210 59.8635 .9598 .282 380 54.4563 .8731 .139
43 62.4251 1.009 1.45 77 62.2479 .9980 .890 215 59.7382 .9578 .274 385 54.2597 .8700 .137
44 62.4241 1.009 1.43 78 62.2389 .9979 .879 220 59.6108 .9558 .267 390 54.0606 .8668 .135
45 62.4229 1.008 1.41 79 62.2297 .9977 .868 225 59.4813 .9537 .259 395 53.8590 .8635 .133
46 62.4213 1.008 1.38 80 62.2203 .9976 .857 230 59.3497 .9416 .252 400 53.6548 .8603 .131
47 62.4194 1.008 1.36 81 62.2107 .9974 .847 235 58.2161 .9494 .246 405 53.4481 .8569 .129
48 62.4173 1.007 1.34 82 62.2009 .9973 .837 240 58.0804 .9472 .239 410 53.2387 .8536 .127
49 62.4149 1.007 1.32 83 62.1910 .9971 .826 245 58.9428 .9450 .233 415 53.0267 .8502 .126
50 62.4122 1.007 1.30 84 62.1809 .9970 .816 250 58.8031 .9428 .228 420 52.8119 .8467 .124
51 62.4092 1.006 1.28 85 62.1706 .9968 .807 255 58.6614 .9405 .222 425 52.5942 .8433 .122
52 62.4059 1.006 1.26 90 62.1166 .9959 .761 260 58.5177 .9382 .217 430 52.3737 .8397 .121
53 62.4024 1.005 1.24 95 61.0585 .9950 .718 265 57.3720 .9359 .212 435 52.1503 .8361 .119
54 62.3986 1.004 1.22 100 61.9964 .9940 .680 270 57.2244 .9335 .207 440 51.9238 .8325 .118
55 62.3946 1.004 1.20 105 61.9307 .9929 .645 275 57.0747 .9311 .203 445 51.6942 .8288 .116
56 62.3903 1.003 1.19 110 61.8612 .9918 .612 280 57.9231 .9287 .198 450 51.4615 .8251 .115
57 62.3858 1.002 1.17 115 61.7884 .9907 .582 285 57.7695 .9262 .194 455 51.2255 .8213 .114
58 62.3810 1.002 1.15 120 61.7121 .9894 .555 290 57.6139 .9237 .190 460 50.9862 .8175 .112
59 62.3760 1.001 1.14 125 61.6326 .9882 .529 295 57.4563 .9212 .186 465 50.7434 .8136 .111
60 62.3707 1.000 1.12 130 61.5500 .9868 .505 300 56.2966 .9186 .183 470 50.4971 .8096 .110
61 62.3652 .9999 1.10 135 61.4643 .9855 .483 305 56.1350 .9161 .179 475 50.2472 .8056 .109
62 62.3595 .9998 1.09 140 61.3757 .9840 .463 310 56.9713 .9134 .176 480 49.9935 .8016 .108
63 62.3535 .9997 1.07 145 61.2842 .9826 .444 315 56.8056 .9108 .172 485 49.7359 .7974 .106
64 62.3474 .9996 1.06 150 61.1899 .9811 .426 320 56.6378 .9081 .169 490 49.4744 .7932 .105
65 62.3410 .9995 1.04 155 61.0928 .9795 .410 325 56.4680 .9054 .166 495 49.2087 .7890 .104

3

GfCentipoise °F lbm/ft

3

GfCentipoise °F lbm/ft

3

GfCentipoise °F lbm/ft

3

May 2006

GfCentipoise

.225
.012

(1)

.197
.013

.164
.014

.138
.015

.111
.017

Table A-3. Viscosity of Water and Steam, in Centipoise (μ)

Tem p 1 2 5 10 20 50 100 200 500 1000

°F psia psia psia psia psia psia psia psia psia psia

Sat Steam
Sat. Water

1000 .030 .030 .030 .030 .030 .030 .030 .030 .030 .031

950 .029 .029 .029 .029 .029 .029 .029 .029 .029 .030

900 .028 .028 .028 .028 .028 .028 .028 .028 .027 .027

850 .026 .026 .026 .026 .026 .026 .026 .026 .025 .056

800 .025 .025 .025 .025 .025 .025 .025 .025 .026 .026

750 .024 .024 .024 .024 .024 .024 .024 .024 .025 .025

700 .023 .023 .023 .023 .023 .023 .023 .023 .023 .024

650 .022 .022 .022 .022 .022 .022 .022 .022 .023 .023

600 .021 .021 .021 .021 .021 .021 .021 .021 .021 .021

550 .020 .020 .020 .020 .020 .020 .020 .020 .020 .019

500 .019 .019 .019 .019 .019 .019 .019 .018 .018 .0103

450 .018 .018 .018 .018 .018 .018 .018 .017 .115 .116

400 .016 .016 .016 .016 .016 .016 .016 .016 .131 .132

350 .015 .015 .015 .015 .015 .015 .015 .152 .153 .154

300 .014 .014 .014 .014 .014 .014 .182 .183 .183 .184

350 .013 .013 .013 .013 .013 .228 .228 .228 .228 .229

200 .012 .012 .012 .012 .300 .300 .300 .300 .300 .301

150 .011 .011 .427 .427 .427 .427 .427 .427 .427 .428

100 .680 .680 .680 .680 .680 .680 .680 .680 .680 .680

50 1.299 1.299 1.299 1.299 1.299 1.299 1.299 1.299 1.299 1.299
32 1.753 1.753 1.753 1.753 1.753 1.753 1.753 1.753 1.753 1.753

(1) Values below line are for water.

.677
.010

.524
.010

.368

.011

.313
.012

A-2

.094
.019

Reference Manual

00809-0100-1191, Rev CB
May 2006

Figure A-1. Viscosity of Water and Liquid Petroleum Products

Rosemount 485 Annubar

Specific Gravity 60/60

1

2

Specific Gravity of
Oil (Referenced
to Water at
60 Deg. F)

21

20

19

18

17

16

13

12

11

15

14

10

8

9

7

6

5

4

3

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

1

2

Temperature (Deg. F)

Example

The viscosity of water at 125 °F is 0.52 Centipoise (curve number 6).

NOTE

Consult factory whenever viscosity of fluid exceeds 300 centipoise.

(From Crane, Technical Paper 1410. Used by permission)

19

20

21

A-3

Rosemount 485 Annubar

Figure A-2. Viscosity of Various Liquids

19

17

18

16

4

10

11

15

9

6

2

1

8

7

5

14

12

3

13

Reference Manual

00809-0100-1191, Rev CB

May 2006

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

Example

The viscosity of water at 125 °F is 0.52 Centipoise (curve number 6).

(From Crane, Technical Paper 1410. Used by permission)

A-4

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Figure A-3. Specific Gravity – Temperature Relationship for Petroleum Oils

Reprinted with permission from the Oil and Gas Journal

1

2

3

4

5

6

7

8

9

14

25

24

20

23

21

22

10

19

18

11

12

13

15

16

17

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

1

2

3

4

5

6

7

8

9

1.04

1.02

1.00

0.98

0.96

0.94

0.92

0.90

0.88

0.86

0.84

0.82

0.80

0.78

0.74

0.72

0.70

0.68

0.66

0.64

0.624

0.584

0.564

0.509

0.376

To find the weight density of a petroleum oil at its flowing temperature when the specific gravity at 60 x F is knows,
multiply the specific gravity of the oil at flowing temperature (see Figure A-3) by 62.4, the density of water at 60 x F.

A-5

Reference Manual

00809-0100-1191, Rev CB

Rosemount 485 Annubar

Figure A-4. Chart for Specific Gravity vs. API Gravity – for Hydrocarbon-based Products and Water Gravity °A.P.I

May 2006

Table A-4. Properties of Selected Liquids

Liquid Tem p Density

°F lb/ft

Acetaldehyde 64 48.9 0.784 Gasoline, Natural 60 42.4 0.680

Acetone 60 49.4 0.792 Glycerol 122 78.6 1.261

Acetic Anhydride 68 67.5 1.083 Heptane 68 42.7 0.685

Acid Benzoic 59 79.0 1.267 Kerosene 60 50.8 0.815

Acid, Acetic Conc. 68 65.5 1.050 M. C. Residuum 60 58.3 0.935

Acid, Butyric, Conc. 68 60.2 0.965 Mercury 20 849.7 13.623

Acid, Hydrochloric, 42.5% 64 92.3 1.400 Mercury 40 848.0 13.596

Acid, Hydrochloric 64 43.5 0.697 Mercury 60 846.3 13.568

Acid, Nitric, Conc. Boil 64 93.7 1.502 Mercury 80 844.6 13.541

Acid, Ortho-phosphoric 65 114.4 1.834 Mercury 100 842.9 13.514

Ammonia, Saturated 10 40.9 0.656 Methylene Chloride 68 83.4 1.337

Aniline 68 63.8 1.023 Milk -- 64.2 - 64.6 --

Benzene 32 56.1 0.899 Oil, Olive 59 57.3 0.919
Brine, 10% CaCl 32 68.1 1.091 Pentane 59 38.9 0.624
Brine, 10% NaCl 32 67.2 1.078 Phenol 77 66.8 1.072

Bunker C Fuel Max 60 63.3 1.014 Pyridine 68 61.3 0.983

Carbon Disulphide 32 80.6 1.292 SAE 10 Lube 60 54.6 0.876

Carbon Tetrchloride 68 99.6 1.597 SAE 30 Lube 60 56.0 0.898

Chlororobenzene 68 69.1 1.108 SAE 70 Lube 60 57.1 0.916

Cresol, Meta 68 64.5 1.035 Salt Creek Crude 60 52.6 0.843

Diphenyl 163 61.9 0.993 32.6° API Crude 60 53.8 0.862

Distillate 60 53.0 0.850 35.2° API Crude 60 52.8 0.847

Fuel 3 Max 60 56.0 0.898 40° API 60 51.4 0.825

Fuel 3 Min 60 60.2 0.966 48° API 60 49.2 0.788

Fuel 5 Max 60 61.9 0.993 Toulene (Toluol) 68 54.1 0.867

Fuel 6 Min 60 61.9 0.993 Trichloroethylene 68 91.5 1.468

Furfural 68 72.3 1.160 Water 60 62.3707 1.000

Gasoline 60 46.8 0.751 Xylol (Xylene) 68 55.0 0.882

(1) Density is shown for the temperature listed.
(2) Specific gravity uses water at 60 °F as base conditions.

(1)

3

Specific Gravity

psia °F lb/ft

(2)

Liquid Tem p Density

(1)

3

Specific Gravity

(2)

psia

A-6

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Table A-5. Air Density, lbm/ft

Tem p 14.73 100 200 300 400 500 600 700 800 900 1000 11 00

°F psia psia psia psia psia psia psia psia psia psia psia psia
– 40 0.0949 0.6488 1.3087 1.9796 2.661 3.3525 4.0533 4.7628 5.4798 6.2031 6.9315 7.6632
– 20 0.0905 0.6182 1.245 1.8799 2.5227 3.1728 3.8295 4.492 5.1594 5.8308 6.5051 7.1811

0 0.0866 0.5905 1.1875 1.7906 2.3995 3.0135 3.6321 4.2547 4.8805 5.5086 6.1382 6.7684
20 0.0830 0.5652 1.1353 1.71 2.2887 2.8711 3.4567 4.0447 4.6347 5.2258 5.8175 6.409
40 0.0797 0.5421 1.0878 1.6368 2.1886 2.7429 3.2992 3.857 4.4157 4.9748 5.5338 6.092
60 0.0765 0.5208 1.0442 1.5699 2.0974 2.6266 3.1569 3.6879 4.2191 4.7502 5.2805 5.8098
80 0.0737 0.5012 1.0041 1.5085 2.0141 2.5205 3.0275 3.5347 4.0416 4.5478 5.0529 5.5567

100 0.0711 0.4829 0.9670 1.4519 1.9375 2.4234 2.9093 3.3949 3.8798 4.3637 4.8464 5.3274
120 0.0687 0.4660 0.9327 1.3997 1.8668 2.3339 2.8006 3.2666 3.7316 4.1954 4.6577 5.1184
140 0.0644 0.4503 0.9007 1.3511 1.8013 2.2511 2.7001 3.1482 3.5951 4.0406 4.4845 4.9265
160 0.0641 0.4356 0.871 1.3061 1.7406 2.1744 2.6073 3.0391 3.4695 3.8985 4.3257 4.7509
180 0.0621 0.4218 0.8432 1.264 1.684 2.103 2.521 2.938 3.3529 3.7665 4.1783 4.5882
200 0.0602 0.4089 0.8171 1.2246 1.6311 2.0364 2.4405 2.8432 3.2444 3.6439 4.0417 4.4375
220 0.0585 0.3967 0.7927 1.1877 1.5815 1.9741 2.3654 2.7551 3.1432 3.5296 3.9144 4.2972
240 0.0568 0.3853 0.7697 1.1529 1.5349 1.9156 2.2948 2.6725 3.0485 3.4228 3.7953 4.1658
260 0.0552 0.3745 0.7480 1.1202 1.4911 1.8606 2.2288 2.5956 2.9608 3.3239 3.6846 4.0424
280 0.0537 0.3644 0.7275 1.0893 1.4497 1.8088 2.1666 2.5231 2.8779 3.2306 3.5803 3.9264
300 0.0523 0.3547 0.7081 1.0601 1.4107 1.7599 2.1078 2.4546 2.7997 3.1424 3.4819 3.8174
320 0.0510 0.3456 0.6898 1.0325 1.3737 1.7136 2.0523 2.3897 2.7356 3.059 3.389 3.7147
340 0.0497 0.3369 0.6724 1.0063 1.3388 1.6698 1.9997 2.3283 2.7553 2.98 3.3013 3.6184

3

A-7

Reference Manual

00809-0100-1191, Rev CB

Rosemount 485 Annubar

Table A-6. Properties of Selected Gases

Molecular

Gas Chemical Formula

Acetylene C2H

Air --- 28.9644 .07649 .897 59.348 1.40

Ammonia NH

Argon A 39.9480 .10553 1.379 38.683 1.67

Butane-N C

Carbon Dioxide CO

Carbon Monoxide CO 28.0106 .07397 0.967 55.169 1.41

Chlorine C

Ethane C

Ethylene C2H

Helium He 4.00260 .01056 .138 368.07 1.66

Heptane, Average C7H

Hexane, Average C
Hydrochloric acid HCl 36.4610 .09606 1.256 42.383 1.40

Hydrogen H

Hydrogen Sulfide H2S 34.0799 .09024 1.177 45.344 1.32

Methane CH

Methyl Chloride CH3Cl 50.4881 .13292 1.738 30.606 1.20

2

3

4H10

2

12

2H6

4

16

6H14

2

4

Weight

26.0382 .06858 .897 59.348 1.28

17.0306 .04488 .587 90.738 1.29

58.1243 .15873 2.075 26.586 1.09

44.0100 .11684 1.528 35.113 1.28

70.9060 .19046 0 °C 2.490 0 °C 21.794 1.36

30.0701 .08005 1.047 51.391 1.19

28.0542 .07392 .967 55.083 1.22

100.2060 .26451 3.458 15.421 ---

86.1785 .22748 2.974 17.932 1.08

2.01594 .00532 .070 766.55 1.40

16.0430 .04243 .555 96.324 1.31

Density

(1)

Specific Gravity

Neon Ne 20.1830 .05155 .674 76.565 1.64

Nitric Oxide NO 30.0061 .07908 1.034 51.500 1.40

Nitrogen N

Nitrous Oxide N2O 44.0128 .11606 1.518 3 5.111 1.26

Octane Average C

Oxygen O

Penatane, ISO C

Propane C3H

Propylene C

Sulphur Dioxide SO

(1) Density is given for gas at 14.73 psia and 60 °F unless noted.
(2) Specific gravity used air at 14.73 psia and 60 °F as base conditions.

2

8H18

2

5H12

8

3H6

2

28.0130 .07397 .967 55.164 1.40

114.2330 .30153 3.942 13.528 ---

31.9988 .08453 1.105 48.293 1.40

72.1514 .19045 2.490 21.418 1.06

44.0972 .11854 1.550 35.044 1.33

42.081 .04842 –47 °C .634 –47 °C 36.722 1.14

64.0630 .16886 2.208 24.122 1.25

(2)

Individual gas

Constant R

May 2006

Ration of Specific

head = C

p/Cv

A-8

Reference Manual

00809-0100-1191, Rev CB
May 2006

Figure A-5. Viscosity of Various Gases

Rosemount 485 Annubar

1

Viscosity (Cp)

2

3

4

7

5

6

9

8

10

11

12

1

2

3

4

5

6

7

8

9

10

11

12

Temperature (Deg. F)

Figure A-5 Example: The viscosity of sulphur dioxide gas (SO

The curves for hydrocarbon vapors and natural gases in Figure A-5 are taken from Maxwell. The curves for all
other gases (except helium) in the chart are based upon Sutherland’s formula, as follows:

3

-- -

⎛⎞

μμ

=

0

⎝⎠

T0C+

---------------- -

TC+

2

T

⎛⎞

------

⎝⎠

T

0

where:
μ = viscosity, in centipoise at temperature T

= viscosity, in centipoise at temperature To

μ

o

T = absolute temperature, in °Rankine, for which viscosity is desired

= absolute temperature, in °Rankine, for which viscosity is known

T

o

C = Sutherland’s constant

) at 200 °F is 0.016 centipoise.

2

NOTE

The variation of viscosity with pressure is small for most gases. For the gases in Figure A-5 and Figure A-6, the
correction of viscosity for pressure is less than 10% for pressures up to 500 lb/in.2 (3447 kPa).

A-9

Rosemount 485 Annubar

Figure A-6. Viscosity of Refrigerant Vapors (saturated and superheated vapors)

Reference Manual

00809-0100-1191, Rev CB

May 2006

Viscosity (Cp)

1

2

3

4

6

5

8

7

1

2

3

4

5

6

7

8

Temperature (Deg. F)

Figure A-6 Example: The viscosity of carbon dioxide gas (CO

) at 80 °F is 0.016 centipoise.

2

Table A-7. Factors to Change from a Temperature Base of 60 °F to Other Temperature Bases

Temperature

(°F)

40 0.9615 50 0.9808 60 1.0000 70 1.0192 80 1.0385
41 0.9635 51 0.9827 61 1.0019 71 1.0212 81 1.0404
42 0.9654 52 0.9846 62 1.0038 72 1.0231 82 1.0462
43 0.9673 53 0.9865 63 1.0058 73 1.0250 83 1.0442
44 0.9692 54 0.9885 64 1.0077 74 1.0269 84 1.0462
45 0.9712 55 0.9904 65 1.0096 75 1.0288 85 1.0481
46 0.9731 56 0.9923 66 1.0115 76 1.0308 86 1.0500
47 0.9750 57 0.9942 67 1.0135 77 1.0327 87 1.0519
48 0.9769 58 0.9962 68 1.0154 78 1.0246 88 1.0538
49 0.9788 59 0.9981 69 1.0173 79 1.0365 89 1.0558

F

tb

Temperature

(°F)

F

tb

Tem perat ure

(°F)

F

tb

Temperature

(°F)

F

tb

Temperature

(°F)

90 1.0577

F

tb

A-10

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Table A-8. Flowing Temperature Factors - F

Temperature

(°F)

1 1.0621 31 1.0291 61 0.9990 91 0.9715
2 1.0609 32 1.0281 62 0.9981 92 0.9706
3 1.0598 33 1.0270 63 0.9971 93 0.9697
4 1.0586 34 1.0260 64 0.9962 94 0.9688
5 1.0575 35 1.0249 65 0.9952 95 0.9680
6 1.0564 36 1.0239 66 0.9943 96 0.9671
7 1.0552 37 1.0229 67 0.9933 97 0.9662
8 1.0541 38 1.0219 68 0.9924 98 0.9653
9 1.0530 39 1.0208 69 0.9915 99 0.9645

10 1.0518 40 1.0198 70 0.9905 100 0.9636

11 1.0507 41 1.0188 71 0.9896 110 0.9551
12 1.0496 42 1.0178 72 0.9887 120 0.9469
13 1.0485 43 1.0168 73 0.9877 130 0.9388
14 1.0474 44 1.0157 74 0.9868 140 0.9309
15 1.0463 45 1.0147 75 0.9856 150 0.9233
16 1.0452 46 1.0137 76 0.9850 160 0.9158
17 1.0441 47 1.0127 77 0.9840 170 0.9085
18 1.0430 48 1.0117 78 0.9831 180 0.9014
19 1.0419 49 1.0107 79 0.9822 190 0.8944
20 1.0408 50 1.0098 80 0.9813 200 0.8876
21 1.0392 51 1.0089 81 0.9804 210 0.8810
22 1.0387 52 1.0078 82 0.9795 220 0.8745
23 1.0376 53 1.0068 83 0.9786 230 0.8681
24 1.0365 54 1.0058 84 0.9777 240 0.8619
25 1.0355 55 1.0048 85 0.9768 250 0.8558
26 1.0344 56 1.0039 86 0.9759 260 0.8498
27 1.0333 57 1.0029 87 0.9750 270 0.8440
28 1.0323 58 1.0019 88 0.9741 280 0.8383
29 1.0312 59 1.0010 89 0.9732 290 0.8327
30 1.0302 60 1.000 90 0.9723 300 0.8275

Factor Temperature (°F) Factor Temperature (°F) Factor Temperature (°F) Factor

tf

A-11

Rosemount 485 Annubar

Table A-9. Supercompressibility Factor – Fpv, Air Flowing Temperature

Reference Manual

00809-0100-1191, Rev CB

May 2006

Pressure

psia

14.7 1.0092 1.0077 1.0065 1.0056 1.0048 1.0041 1.0035 1.0031 1.0027 1.0024 1.0021 1.0019 1.0016 1.0015
100 1.0613 1.0516 1.0437 1.0372 1.0319 1.0275 1.0239 1.0208 1.0182 1.0160 1.0141 1.0125 1.0112 1.0100
200 1.1193 1.1007 1.0856 1.0732 1.0629 1.0544 1.0472 1.0412 1.0361 1.0318 1.0281 1.0249 1.0222 1.0198
300 1.1744 1.1477 1.1259 1.1079 1.0930 1.0805 1.0700 1.0612 1.0537 1.0473 1.0419 1.0372 1.0331 1.0296
400 1.2270 1.1929 1.1649 1.1416 1.1223 1.1060 1.0924 1.0808 1.0710 1.0626 1.0554 1.0493 1.0439 1.0392
500 1.2774 1.2365 1.2026 1.1744 1.1508 1.1310 1.1143 1.1001 1.0880 1.0777 1.0689 1.0612 1.0546 1.0488
600 1.3260 1.2785 1.2391 1.2062 1.1786 1.1554 1.1358 1.1191 1.1048 1.0926 1.0821 1.0730 1.0652 1.0583
700 1.3728 1.3192 1.2746 1.2373 1.2058 1.1793 1.1568 1.1377 1.1213 1.1073 1.0952 1.0847 1.0756 1.0677
800 1.4181 1.3587 1.3091 1.2675 1.2324 1.2028 1.1775 1.1560 1.1376 1.1218 1.1081 1.0963 1.0860 1.0771
900 1.4620 1.3971 1.3428 1.2971 1.2585 1.2258 1.1979 1.1741 1.1537 1.1361 1.1209 1.1077 1.0963 1.0863

1000 1.5046 1.4345 1.3756 1.3260 1.2840 1.2483 1.2179 1.1918 1.1695 1.1502 1.1335 1.1191 1.1065 1.0955

110 0 1.5460 1.4709 1.4077 1.3543 1.3090 1.2705 1.2376 1.2094 1.1851 1.1642 1.1460 1.1303 1.1166 1.1046
1200 1.5863 1.5064 1.4390 1.3820 1.3336 1.2923 1.2569 1.2266 1.2005 1.1779 1.1584 1.1414 1.1266 1.1136
1300 1.6257 1.5411 1.4697 1.4092 1.3577 1.3137 1.2760 1.2436 1.2157 1.1916 1.1706 1.1524 1.1365 1.1226
1400 1.6641 1.5751 1.4998 1.4358 1.3814 1.3348 1.2948 1.2604 1.2308 1.2051 1.1827 1.1633 1.1463 1.1314
1470 1.6905 1.5984 1.5204 1.4542 1.3977 1.3493 1.3078 1.2721 1.2412 1.2144 1.1911 1.1709 1.1531 1.1376

–40 °F –20 °F 0 °F 20 °F 40 °F 60 °F 80 °F 100 °F 120 °F 140 °F 160 °F 180 °F 200 °F 220 °F

Temperature

A-12

Reference Manual

00809-0100-1191, Rev CB
May 2006

Appendix B Pipe Data

350 psig

Class 350

300 psig

Class 300

250 psig

Class 250

Rosemount 485 Annubar

200 psig

Class 200

150 psig

Class 150

100 psig

Class 100

50 psig

Class 50

Wall I.D. Wall I.D. Wall I.D. Wall I.D. Wall I.D. Wall I.D. Wall I.D.

Pipe

O.D.

Class A

100 ft. 43 psig Class B Class C Class D Class E Class F Class G Class H

O.D. Wall I.D. O.D. Wall I.D. O.D. Wall I.D. O.D. Wall I.D. O.D. Wall I.D. O.D. Wall I.D. O.D. Wall I.D. O.D. Wall I.D.

/2 4 5 6 8 10 12 14 16 18 20 22 24

1

/2 3 3

(1)

1

/2 2 2

1

/4 1

1

C and Titanium Pipe

®

/4 1 1

3

/2

.840 1.050 1.315 1.660 1.900 2.375 2.875 3.500 4.000 4.500 5.563 6.625 8.625 10.750 12.750 14.000 16.000 18.000 20.000 22.000 24.000

1

Out.

Dia.

I.D. .710 .920 1.185 1.530 1.770 2.245 2.709 3.334 3.834 4.334 5.345 6.407 8.407 10.482 12.438 13.668 15.670 17.670 19.634 21.624 23.563

Wall .065 .065 .065 .065 .065 .065 .083 .083 .083 .083 .109 .109 .109 .134 .156 .156 .165 .165 .188 .188 .218

I.D. .674 .884 1.097 1.442 1.682 2.157 2.635 3.260 3.760 4.260 5.295 6.357 8.329 10.420 12.390 13.624 15.624 17.624 19.564 21.564 23.50

Wall .083 .083 .109 .109 .109 .109 .120 .120 .120 .120 .134 .134 .148 .165 .180 .188 .188 .188 .218 .218 .250

I.D. .622 .824 1.049 1.380 1.610 2.067 2.469 3.068 3.548 4.026 5.047 6.065 7.981 1.020 12.00

Wall ★.109 ★.113 ★.133 ★.140 ★.145 ★.154 ★.203 ★.216 ★.226 ★.237 ★.258 ★.280 ★.322 ★.365 ■.375

▲.147 ▲.154 ▲.179 ▲.191 ▲.200 ▲.218 ▲.276 ▲.300 ▲.318 ▲.337 ▲.375 ▲.432 ▲.500 ▲.500 ▲.500

I.D. .546 .742 .957 1.278 1.500 1.939 2.323 2.900 3.364 3.826 4.813 5.761 7.625 9.750 11.7 5

Wall

Pipe

Size

Table B-1. Pipe Data

Cast iron Pipe – ASA Standard

2 3.96 0.32 3.32 0.32 3.32 0.32 3.32 0.32 3.32 0.32 3.32 0.32 3.32 0.32 3.32

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3 4.800.354.100.354.100.354.100.354.100.354.100.354.100.354.10

4 6.90 0.38 6.14 0.38 6.14 0.38 6.14 0.38 6.14 0.38 6.14 0.38 6.14 0.38 6.14

5 9.050.418.230.418.230.418.230.418.230.418.230.418.230.418.23

10 11. 10 0.44 10.22 0.44 10.22 0.44 10.22 0.44 10.22 0.44 10.22 0.48 10.14 0.52 10.06

12 13.20 0.48 12.24 0.48 12.24 0.48 12.24 0.48 12.24 0.52 12.16 0.52 12.16 0.56 12.08

16 17.40 0.54 16.32 0.54 16.32 0.54 16.32 0.58 16.24 0.63 16.14 0.68 16.04 0.68 16.04

14 15.30 0.48 14.34 0.51 14.28 0.51 14.28 0.55 14.20 0.59 14.12 0.59 14.12 0.64 14.02

18 19.50 0.54 18.42 0.58 18.34 0.58 18.34 0.63 18.24 0.68 18.14 0.73 18.04 0.79 17.92

20 21.60 0.57 20.46 0.62 21.36 0.62 20.36 0.67 20.26 0.72 20.16 0.78 20.04 0.84 19.92

24 25.80 0.63 24.54 0.68 24.44 0.73 24.34 0.79 24.22 0.79 24.22 0.85 24.10 0.92 23.96

Pipe

Size

Cast iron Pipe – AWWA Standard

2 3.80 0.39 3.02 3.95 0.42 3.12 3.96 0.45 3.06 3.96 0.48 3.00 --- --- --- --- --- --- --- --- --- --- --- ---

3 4.800.423.965.000.454.105.000.484.045.000.52 3.96 --- --- --- --- --- --- --- --- --- --- --- ---

4 6.90 0.44 6.02 7.10 0.48 6.14 7.10 0.51 6.08 7.10 0.55 6.00 7.22 0.58 6.06 7.22 0.61 6.00 7.38 0.65 6.08 7.38 0.69 6.00

5 9.050.468.139.050.518.039.300.568.189.300.608.109.420.668.109.420.718.009.600.758.109.600.808.00

10 11.1 0 0.50 10.10 11 .10 0.57 9.96 11 .40 0.62 10.16 11. 40 0.68 10.04 11. 60 0.74 10.12 11. 60 0.80 10.00 11. 84 0.86 10.12 11 .84 0.92 10.00

12 13.20 0.54 12.12 13.20 0.62 11.96 13.50 0.68 12.14 13.50 0.75 12.00 13.78 0.82 12.14 13.78 0.89 12.00 14.08 0.97 12.14 14.08 1.04 12.00

14 15.30 0.57 14.16 15.30 0.66 13.98 15.65 0.74 14.17 15.65 0.82 14.01 15.98 0.90 14.18 15.98 0.99 14.00 16.32 1.07 14.18 16.32 1.16 14.00

16 17.40 0.60 16.20 17.40 0.70 16.00 17.80 0.80 16.20 17.80 0.89 16.02 18.16 0.98 16.20 18.16 1.08 16.00 18.54 1.18 16.18 18.54 1.27 16.00

18 19.50 0.64 18.22 19.50 0.75 18.00 19.92 0.87 18.18 19.92 0.96 18.00 20.34 1.07 18.20 20.34 1.17 18.00 20.78 1.28 18.22 20.78 1.39 18.00

20 21.60 0.67 20.26 21.60 0.80 21.00 22.06 0.92 20.22 22.06 1.03 21.00 22.54 1.15 20.24 22.54 1.27 20.00 23.02 1.39 20.24 23.02 1.51 20.00

24 25.80 0.76 24.28 25.80 0.89 24.02 26.32 1.04 24.22 26.32 1.16 24.00 26.90 1.31 24.28 26.90 1.45 24.00 27.76 1.75 24.26 27.76 1.88 24.00

30 31.74 0.88 29.98 32.00 1.03 29.94 32.40 1.20 30.00 32.74 1.37 30.00 33.10 1.55 30.00 33.46 1.73 30.00

36 37.96 0.99 35.98 38.30 1.15 36.00 38.70 1.36 39.98 39.16 1.58 36.00 39.60 1.80 36.00 40.04 2.02 36.00

42 44.20 1.10 42.00 44.50 1.28 41.94 45.10 1.54 42.02 45.58 1.78 42.02

48 50.50 1.26 47.98 50.80 1.42 47.96 51.40 1.71 47.98 51.98 1.96 48.06

54 56.66 1.35 53.96 57.10 1.55 54.00 57.80 1.90 54.00 58.40 2.23 53.94

60 62.80 1.39 60.02 63.40 1.67 60.06 64.20 2.00 60.20 64.82 2.38 60.06

72 75.34 1.62 72.10 76.00 1.95 72.10 76.88 2.39 72.10

84 87.54 1.72 84.10 88.54 2.22 84.10

Stainless Steel, Hastelloy

Pipe Size

Sched

(2)

5S

10S

40S

80S

(1) These materials are generally available in schedules 40 and 80 only.

(2) Wall thickness of Schedule 5S and 10S does not permit threading in accordance with the American Standard for Pipe Threads (ASA No. B2.1).

Rosemount 485 Annubar

■.500

Reference Manual

00809-0100-1191, Rev CB

May 2006

Pipe

(1)

★.375 ★.375 .438 ▲.500 ▲.500 .562 --- .625 .625 .625 .625 .625 ■.625

/2 4 5 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42

1

/2 3 3

1

/2 2 2

1

/4 1

1

/4 1 1

3

/2

1

.840 1.050 1.315 1.660 1.900 2.375 2.875 3.500 4.000 4.500 5.563 6.625 8.625 10.750 12.750 14.000 16.000 18.000 20.000 22.000 24.000 26.000 28.000 30.000 32.000 34.0 00 36.000 42.000

Out.

Dia.

Wall .109 .113 .133 .140 .145 .154 .203 .216 .226 .237 .258 .280 .322 .365 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 ■.375

I.D. .252 .434 .599 .895 1.100 1.503 1.771 2.300 2.728 3.1 52 4.063 6.065 7.981 1.020 12.00 --- --- --- --- --- --- --- --- --- --- --- --- ---

Wall .294 .308 .358 .382 .400 .436 .552 .600 .636 .674 .750 ★.280 ★.322 ★.365 ■.375 --- --- --- --- --- --- --- --- --- --- --- --- ---

I.D. .546 .742 .957 1.278 1.500 1.939 2.323 2.900 3.364 3.826 4.813 5.761 7.625 9.750 11.750 13.000 15.000 17.000 19.000 21.000 23.000 25.000 27.000 29.000 31.000 33.000 35.000 41.000

Wall .147 .154 .179 .191 .200 .218 .276 .300 .318 .377 .375 .432 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500 .500

I.D. --- --- --- --- --- --- --- --- --- --- --- --- 8.071 10.136 12.090 13.250 15.250 17.124 19.000 21.000 22.876 --- 26.750 28.750 30.750 32.750 34.750 40.750

Wall --- --- --- --- --- --- --- --- --- --- --- --- .277 .307 .330

I.D. --- --- --- --- --- --- --- --- --- --- --- --- 7.813 9.750 11.626 12.814 14.688 16.500 18.376 20.250 22.064

Wall --- --- --- --- --- --- --- --- --- --- --- --- .406 s.500 .562 .59 3 .656 .750 .812 .875 .968

I.D. --- --- --- --- --- --- --- --- --- --- --- --- 7.439 9.314 11.064 12.126 13.938 15.688 17.438 19.250 20.938

Wall --- --- --- --- --- --- --- --- --- --- --- --- .593 .718 .843 .937 1.031 1.156 1.281 1.375 1.531

I.D. --- --- --- --- --- --- --- --- --- --- --- --- 7.001 8.750 10.500 11.500 13.124 14.876 16.500 18.250 19.876

I.D. --- --- --- --- --- --- --- --- --- --- --- 8.125 10.250 12.250 13.376 15.376 17.376 19.250 21.250 23.250 25.000 27.000 29.000 31.000 33.000 35.000 41.000

Wall --- --- --- --- --- --- --- --- --- --- --- .250 .250 .250 .312 .312 .312 ★.375 ★.375 ★.375 ▲.500 ▲.500 ▲.500 ▲.500 ▲.500 ▲.50 0 ▲.500

I.D. .622 .824 1.049 1.380 1.610 2.067 2.469 3.068 3.548 4.026 5.047 6.065 7.981 10.020 11.9 38 13.124 15.000 16.976 18.814 --- 22.626

Wall ★.109 ★.133 ★.133 ★.140 ★.145 ★.154 ★.203 ★.216 ★.226 ★.237 ★.258 ★.280 ★.322 ★.365 .406 .438 ▲.500 .562 .593 --- .687

I.D. .546 .742 .957 1.278 1.500 1.939 2.323 2.900 3.364 3.826 4.813 5.761 7.625 9.564 11. 37 6 12.500 14.314 16.126 17.938 19.750 21.564

I.D. --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- 13.500 15.500 17.500 19.500 21.500 23.500 25.376 27.376 29.376 31.376 33.376 35.376 ---

Wall --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- .250 .250 .250 .250 .250 .250 .312 .312 .312 .312 .312 .312 ---

Wall .147 ▲.154 ▲.179 ▲.191 ▲.200 ▲.218 ▲.276 ▲.300 ▲.318 ▲.337 ▲.375 ▲.432 ▲.500 .593 .687 .750 .843 .937 1.031 1.125 1.218

Wall --- --- --- --- --- --- --- --- --- --- --- --- .812 1.000 1.125 1.250 1.438 1.562 1.750 1.875 2.062

I.D. --- --- --- --- --- --- --- --- --- 3.624 4.563 5.501 7.189 9.064 10.750 11.8 14 13.564 15.250 17.000 18.75 0 20.376

Wall --- --- --- --- --- --- --- --- --- .438 .500 .562 .718 8.43 1.000 1.093 1.218 1.375 1.500 1.625 1.812

I.D. .466 .614 .815 1.160 1.338 1.689 2.125 2.624 --- 3.438 4.313 5.189 6.813 8.500 10.1 26 11.1 88 12.814 14.438 16.064 17.750 19.314

Wall .187 .218 .250 .250 .281 .343 .375 .438 --- .531 .625 .718 .906 1.125 1.312 1.406 1.593 1.781 1.968 2.125 2.343

B-2

Pipe Size

Std I.D. .622 .824 1.049 1.380 1.610 2.067 2.469 3.068 3.548 4.026 5.047 6.065 7.981 10.20 12.000 13.250 15.250 17.250 19.250 21.250 23.250 25.250 27.250 29.250 31.250 33.250 35.250 41.250

Double

Extra

Heavy

Extra

Carbon Steel and PVC

Heavy

Sched

Sched

30

Sched

60

Sched

Sched

20

Sched

10

40

Sched

100

80

Sched

120

Sched

(1) These materials are generally available in schedules 40 and 80 only.

140

Sched

160

Character Description

▲ = Wall thicknes is identical with the thickness of “Extra Heavy” pipe.

★ = Wall thicknes is identical with the thickness of “Standard Weight” pipe.

■ = These do not conform to the American Standard B36.10.

Pipe Weight Formula for Steel Pipe (pounds per foot):

10.68 (D-t)t

where:

D = Outside Diameter

t = Wall Thickness

Reference Manual

00809-0100-1191, Rev CB
May 2006

aa

Correction

Factor, F

Typ e 3 16

Typ e 3 04

Rosemount 485 Annubar

Temperature (°F) of Piping Material

Thermal Expansion Factor

aa

– 155 – 230 – 190 – 276 0.995

– 264 – 317 0.993

– 204 – 322 – 245 0.994

Aluminum Copper Type 430 2% CRMO 5% CRMO Bronze Carbon Steel

Table B-2. F

– 63 – 102 – 86 – 119 0.997

– 108 – 163 – 137 – 189 0.996

– 19 – 44 – 34 – 55 0.998

25 19 44 – 13 – 14 17 – 6 7 0.999

68 68 68 68 68 68 68 68 1.000

113 127 157 146 151 122 144 130 1.001

332 296 312 225 289 240 1.003

246 222 232 175 218 186 1.002

494 434 460 321 425 343 1.005

415 366 389 273 358 292 1.004

641 566 594 417 551 439 1.007

568 501 527 369 489 391 1.006

783 690 730 675 536 1.009

713 629 662 613 488 1.008

918 811 858 794 631 1.011

851 750 795 735 584 1.010

956 871 918 851 674 1.012

1054 928 979 907 727 1.013

1121 984 1040 961 777 1.014

1189 1038 1102 1015 799 1.015

B-3

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

B-4

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Appendix C Unit and Conversion Factors

Table C-1. Equivalents of
Absolute Viscosity

Absolute or

Dynamic Viscosity

Centipoise (m) 1 0.01 2.09 (10
Poise gram/cm-sec

dyne-second/cm
slugs/ft-second

second/ft2 (μ’ε)

pound

f

pounds/ft-second
pounds-second/ft

f

Pound
Pound

= Pound of Force

m

3

(100 μ)

2

(με)

= Pound of Mass

Centipoise

(μ)

100 1 2.09 (10-3) 0.0672

47900 479 1 g or 32.3

1487 14.87 1/g or .0311 1

To convert absolute or dynamic viscosity from one set of units to another
using Table C-1, locate the given set of units in the left hand column and
multiply the numerical value by the factor shown horizontally to the right under
the set of units desired.

Poise

gram/cm-sec

dyne-sec/cm

(100 μ)

slugs/ft-sec

3

pound

2

sec/ft

f

(μ'ε)

-3

)6.72 (10-3)

pounds/ft-sec

pounds-sec/ft

2

(με)

Table C-2. Equivalents of
Kinematic Viscosity

As an example, suppose a given absolute viscosity of 2 poise is to be
converted to slugs/foot-second. By referring to Table C-1, we find the
conversion factor to be 2.09 (10-3). Then, 2 (poise) times 2.09 (10-3) = 4.18
(10-3) = 0.00418 slugs/foot-second.

Kinematic Viscosity Centipoise (υ) Strokes cm2/second (100 υ) fm2/second (υ')

Centipoise (υ) 1 0.01 1.076 (10
Strokes cm2/second

(100 υ)

2

/second (υ') 92900 929 1

fm

100 1 2.09 (10-3)

-3

)

To convert kinematic viscosity from one set of units to another using
Table C-2, locate the given set of units in the left hand column and multiply the
numerical value by the factor shown horizontally to the right under the set of
units desired.

2

As an example, suppose a given kinematic viscosity of 0.5 ft
converted to centistokes. By referring to Table C-2, we find the conversion
factor to be 92900. Then, 0.5 ft

2

/second times 92900 = 46450 centistokes.

/second is to be

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Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

Table C-3. Equivalents of Kinematic Viscosity and
Saybolt Universal Viscosity

Kinematic

Viscosity

Centistokes (υ) At 100 °F Basic Values at 210 °F Centistokes (υ) At 122 °F at 210 °F

1.83 32.01 32.23 48 25.3 ---

2.0 32.62 32.85 50 26.1 25.2

4.0 39.14 39.41 60 30.6 29.8

6.0 45.56 45.88 70 35.1 34.4

8.0 52.09 52.45 80 39.6 39.0

10.0 58.91 59.32 90 44.1 43.7

15.0 77.39 77.93 100 48.6 48.3

20.0 97.77 98.45 125 60.1 60.1

25.0 119.3 120.1 150 71.7 71.8

30.0 141.3 142.3 175 83.8 83.7

35.5 163.7 164.9 200 95.0 95.6

40.0 186.3 187.6 225 106.7 107.5

45.0 209.1 210.5 250 11 8. 4 119. 4

50.0 232.1 233.8 275 130.1 131.4

55.0 255.2 257.0 300 141.8 143.5

60.0 278.3 280.2 325 153.6 155.5

65.0 301.4 303.5 350 165.3 167.6

70.0 324.4 326.7 375 177.0 179.7

75.0 347.6 350.0 400 188.8 191.8

80.0 370.8 373.4 425 200.6 204.0

85.0 393.9 396.7 450 212.4 216.1

90.0 417.1 420.0 475 224.1 228.3

95.0 440.3 443.4 500 235.9 240.5

100.0 463.5 466.7 525 247.7 252.8

120.0 556.2 560.1 550 259.5 265.0

140.0 648.9 653.4 575 271.3 277.2

160.0 741.6 --- 600 283.1 289.5

180.0 834.2 --- 625 294.9 301.8

200.0 926.9 --- 650 306.7 314.1

220.0 1019.6 --- 675 318.4 326.4

240.0 1112 .3 --- 700 330.2 338.7

260.0 1205.0 --- 725 342.0 351.0

280.0 1297.7 --- 750 353.8 363.4

300.0 1390.4 --- 775 365.5 375.7

320.0 1483.1 --- 800 377.4 388.1

340.0 1575.8 --- 825 389.2 400.5

360.0 1668.5 --- 850 400.9 412.9

380.0 1761.2 --- 875 412.7 425.3

400.0 1853.9 --- 900 424.5 437.7

420.0 1946.6 --- 925 483.5 450.1

440.0 2039.3 --- 950 488.1 462.5

460.0 2132.0 --- 975 459.9 474.9

480.0 2224.7 --- 1000 471.7 487.4

500.0 2317.4 --- 1025 483.5 499.8

Over 500 Saybolt seconds =

Equivalent Saybolt Universal Viscosity, sec.

Centistokes x 4.6347

Saybolt seconds =

Centistokes x 4.6673

NOTE:

To obtain the Saybolt Universal viscosity equivalent to
a kinematic viscosity determined at t, multiply the
equivalent Saybolt Universal viscosity at 100 °F by
1+(t - 100) 0.000 064.

Example: 10υ at 210 °F are equivalent to 58.91
multiplied by 1.0070 or 59.32 seconds Saybolt
Universal at 210 °F.

Table C-4. Equivalents of Kinematic Viscosity and Saybolt
Furol Viscosity

Kinematic

Viscosity

1050 495.2 512.3
1075 507.0 524.8
110 0 518.8 537.2
1125 530.6 549.7
115 0 542.4 562.2
1175 554.2 574.7
1200 566.0 587.2
1225 577.8 599.7
1250 589.5 612.2
1275 601.3 624.8
1300 613.1 637.3

Over 1300 Saybolt fluid seconds =

Equivalent Saybolt Furol Viscosity, sec.

Centistokes x 0.4717

Log (Saybolt Furol

seconds - 2.87) = 0.4717

[Log (Centistokes)] - 0.3975

Tables C-3 (abstracted from Table 1, D2161-63T) and C-4 (abstracted from Table 3, D2161-63T) are reprinted with their permission of the America Society for Testing Materials
(ASTM).

C-2

Reference Manual

00809-0100-1191, Rev CB
May 2006

Table C-5. Equivalents of Degrees API, Degrees Baume, Specific Gravity,
Weight Density, and Pounds per Gallon at 60 °F/60 °F.

Values for API Scale Values for Baume Scale

Degrees on

API or

Baume

Scale

0 --- --- --- --- --- --- 1.0000 62.36 8.337
2 --- --- --- --- --- --- 1.0140 63.24 8.454
4 --- --- --- --- --- --- 1.0284 64.14 8.574
6 --- --- --- --- --- --- 1.0432 65.06 8.697

8 --- --- --- --- --- --- 1.0584 66.01 8.824
10 1.0000 62.36 8.337 1.0000 62.36 8.337 1.0741 66.99 8.955
12 0.9861 61.50 8.221 0.9859 61.49 8.219 1.0902 67.99 9.089
14 0.9725 60.65 8.108 0.9722 60.63 8.105 1.1069 69.03 9.228
16 0.9593 59.83 7.998 0.9589 59.80 7.994 1.1240 70.10 9.371
18 0.9465 59.03 7.891 0.9459 58.99 7.886 1.1417 71.20 9.518
20 0.9340 58.25 7.787 0.9333 58.20 7.781 1.1600 72.34 9.671
22 0.9218 57.87 7.736 0.9211 57.44 7.679 1.1789 73.52 9.828
24 0.9100 56.75 7.587 0.9091 56.70 7.579 1.1983 74.73 9.990
26 0.8984 56.03 7.490 0.8974 55.97 7.482 1.2185 75.99 10.159
28 0.8871 55.32 7.396 0.8861 55.26 7.387 1.2393 77.29 10.332
30 0.8762 54.64 7.305 0.8750 54.57 7.295 1.2609 78.64 10.512
32 0.8654 53.97 7.215 0.8642 53.90 7.205 1.2832 80.03 10.698
34 0.8550 53.32 7.128 0.8537 53.24 7.117 1.3063 81.47 10.891
36 0.8448 52.69 7.043 0.8434 52.60 7.031 1.3303 82.96 11.091
38 0.8348 52.06 6.960 0.8333 51.97 6.497 1.3551 84.51 11. 297
40 0.8251 51.46 6.879 0.8235 51.36 6.865 1.3810 86.13 11.513
42 0.8155 50.86 6.799 0.8140 50.76 6.786 1.4078 87.80 11. 737
44 0.8063 50.28 6.722 0.8046 50.18 6.708 1.4356 89.53 11.969
46 0.7972 49.72 6.646 0.7955 49.61 6.632 1.4646 91.34 12.210
48 0.7883 49.16 6.572 0.7865 49.05 6.557 1.4948 93.22 12.462
50 0.7796 48.62 6.499 0.7778 48.51 6.484 1.5263 95.19 12.725
52 0.7711 48.09 6.429 0.7692 47.97 6.413 1.5591 97.23 12.998
54 0.7628 47.57 6.359 0.7609 47.45 6.344 1.5934 99.37 13.284
56 0.7547 47.07 6.292 0.7527 46.94 6.275 1.6292 101.60 13.583
58 0.7467 46.57 6.225 0.7447 46.44 6.209 1.6667 103.94 13.895
60 0.7389 46.08 6.160 0.7368 45.95 6.143 1.7059 106.39 14.222
62 0.7313 45.61 6.097 0.7292 45.48 6.079 1.7470 108.95 14.565
64 0.7238 45.14 6.034 0.7216 45.00 6.016 1.7901 111.64 14.924
66 0.7165 44.68 5.973 0.7143 44.55 5.955 1.8354 114 .46 15.302
68 0.7093 44.23 5.913 0.7071 44.10 5.895 11.8831 117.44 15.699
70 0.7022 43.79 5.854 0.7000 43.66 5.836 1.9333 120.57 16.118
72 0.6953 43.36 5.797 0.6931 43.22 5.778 --- --- --­74 0.6886 42.94 5.741 0.6863 42.80 5.722 --- --- --­76 0.6819 42.53 5.685 0.6796 42.38 5.666 --- --- --­78 0.6754 42.12 5.631 0.6731 41.98 5.612 --- --- --­80 0.6690 41.72 5.577 0.6667 41.58 5.558 --- --- --­82 0.6628 41.33 5.526 0.6604 41.19 5.506 --- --- --­84 0.6566 40.95 5.474 0.6542 40.80 5.454 --- --- --­86 0.6506 40.57 5.424 0.6482 40.42 5.404 --- --- --­88 0.6446 40.20 5.374 0.6422 40.05 5.354 --- --- --­90 0.6388 39.84 5.326 0.6364 39.69 5.306 --- --- --­92 0.6331 39.48 5.278 0.6306 39.33 5.257 --- --- --­94 0.6275 39.13 5.231 0.6250 38.98 5.211 --- --- --­96 0.6220 38.79 5.186 0.6195 38.63 5.165 --- --- --­98 0.6166 38.45 5.141 0.6140 38.29 5.119 --- --- ---

100 0.6112 38.12 5.096 0.6087 37.96 5.075 --- --- ---

Tables C-5 are reprinted with their permission of the America Society for Testing Materials (ASTM).

Specific

gravity

(S)

Oil Liquids lighter than water Liquids heavier than water

Weight

Density lb/ft

(ρ)

3

Pounds

per

Gallon

Specific

gravity

(S)

Weight

Density lb/ft

(ρ)

Rosemount 485 Annubar

3

Pounds

per

Gallon

Specific

gravity

(S)

Weight

Density lb/ft

(ρ)

3

Pounds

per

Gallon

C-3

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

Table C-6. Equivalents

Weight

1 kg = 2.205 lb
1 cubic inch of water (60 °F) = 0.073551 cubic inch of mercury (32 °F)
1 cubic inch of mercury (32 °F) = 13.596 cubic inch of water (60 °F)
1 cubic inch of mercury (32 °F) = 0.4905 lb

Velocity

1 foot per second = 0.3048 meter per second
1 meter per second = 3.208 foot per second

Density

1 pound per cubic inch = 27.68 gram per cubic centimeter
1 gram per cubic centimeter = 0.03613 pound per cubic inch
1 pound per cubic foot = 16.0184 kg per cubic meter
1 kilogram per cubic meter = 0.06243 pound per cubic foot

Physical Constants

Base of natural logarithms (e) = 2.7182818285
Acceleration of gravity (g) = 32.174 foot/second

2

= (980.665 centimeter/second2)

Pi (π) = 3.1415926536

Measure

1-in. = 25.4 millimeter 1 ft = 304.8 millimeter
1-in. = 2.54 centimeter 1 ft = 30.48 centimeter
1 millimeter = 0.03937-inch 1-in.

2

= 6.4516 centimeter

2

1 millimeter = 0.00328 foot 1centimeter2 = 0.0008 foot2
1 micron = 0.000001 meter 1 foot

2

= 929.03 centimeter2

1 torr = 1 millimeter mercury Circumference of a circle = 2πr = πd

2

10

= 1 atom mercury Area of a circle = πr

° Kelvin ° Rankine ° Celsius

2 = πd2

(1)

/4

° Fahrenheit

Absolute Zero 0 0 –273.15 –459.67
Water Freezing Point

273.15 491.67 0 32

(14.696 psia)
Water Boiling Point

373.15 671.67 100 212

(14.696 psia)

(1) To convert degree Celsius (tc) to degrees Fahrenheit: t = 1.8tc = 32
(2) To convert degree Fahrenheit to degree Celsius (tc): tc = (t - 32)/1.8.

(2)

C-4

Prefixes

atto (a) = one-quintillionth = 0.000 000 000 000 000 001 = 10
femto (f) = one-quadrilliointh = 0.000 000 000 000 001 = 10
pico (p) = one-trillionth = 0.000 000 000 001 = 10
nano (n) = one-billionth = 0.000 000 001 = 10
micro (m) = one-millionth = 0.000 001 =
milli (m) = one-thousandth = 0.001= 10
centi (c) = one-hundredth = 0.01 =
deci (d) = one-tenth = 0.1 =
uni (one) = 1.0 = 10
deka (da) = ten = 10.0 = 10

-1

-0

1

hecto (h) = one-hundred = 100.0 = 10
kilo (k) = one-thousand = 1 000.0 = 10

-6

-3

-2

2

3

mega (M) = one-million = 1 000 000.0 = 10
giga (G) = one-billion = 1 000 000 000.0 = 10
teta (T) = one-trillion = 1 000 000 000 000.0 = 10

-12

-9

6

9

12

-18

-15

Reference Manual

00809-0100-1191, Rev CB
May 2006

Table C-7. Equivalents of Liquid Measures and Weights

To Obtain Multiply

Column X Row

U.S. Gallon 1 0.833 8 8.337 0.13368 231 3.78533 0.003785

Imperial Gallon 1.2009 1 9.60752 10 0.16054 277.42 4.54596 0.004546

U.S. Pint 0.125 0.1041 1 1.042 0.01671 28.875 0.473166 0.000473

U.S. Pound Water 0.11995 0.1 0.9596 1 0.016035 27.708 0.45405 0.000454

U.S. Cubic Foot 7.48052 6.22888 59.8442 62.365 1 1728 28.31702 0.028317

U.S. Cubic Inch 0.004329 0.00361 0.034632 0.03609 0.0005787 1 0.016387 0.0000164

Liter 0.2641779 0.2199756 2.113423 2.202 0.0353154 61.02509 1 0.001000

Cubic Meter 264.170 219.969 2113.34 2202 35.31446 61023.38 999.972 1

Water at 60 °F (15.6 °C) 1 Barrel = 42 gallons (petroleum measure).

U.S.

Gallon

Imperial

Gallon

U.S.

Pint

U.S. Pound

Water

Example:

Suppose a given absolute viscosity of 2 pose is to be converted to slugs/foot-second. By referring to Table C-7, we
find the conversion factor to be 2.09 (10-3). Then, 2 (poise) times 2.09 (10-3) = 4.18 (10-3) = 0.00418
slugs/foot-second.

Rosemount 485 Annubar

U.S. Cubic

Foot

U.S. Cubic

Inch

Liter

Cubic

Meter

Table C-8. Equivalents of Liquid Measures and Weights

To Obtain

Multiply

Column X Row

2

lb/in

2

lb/ft

atmospheres 14.696 2116.22 1 1.0332 1.0332 407.520 33.9600 29.921 760.00 1.01325 0.101325 101.325 10351.0

2

kg/cm

2

kg/m

inch water

inch mercury

mm mercury

mm water

Water at 60 °F (15.6 °C) 1 Barrel = 42 gallons (petroleum measure).

(1) 68 °F (20 °C)

(1)

(1)

foot water

(1)

(1)

bars 14.5038 2088.54 0.98692 1.01972 10197.2 402.190 33.5158 29.5300 750.061 1 0.10 100 10215.6

MPa 145.038 20885.4 9.8692 10.1972 101972.0 4021.90 335.158 295.300 7500.61 10.0 1 1000 102156

KPa 0.145038 20.8854 0.0098692 0.0101972 101.972 4.02190 0.33516 0.2953 7.50061 0.01 0.001 1 102.156

(1)

2

lb/in

1 .144 0.068046 0.070307 703.070 27.7300 2.3108 2.03602 51.7149 0.068948 0.0068948 6.8948 704.342

0.006944 1 0.000473 0.0004888 4.88243 0.19257 0.016048 0.014139 0.35913 0.004788 0.0000479 0.04788 4.89127

14.2233 2048.16 .096784 1 1000 394.41 32.868 28.959 735.558 0.98066 0.098066 98.066 10018.1

0.001422 0.204816 0.0000968 0.001 1 0.3944 0.003287 0.002896 0.073556 0.000098 0.0000098 0.0098 1.00181

0.036062 5.1929 0.002454 0.00253 29.354 1 0.08333 0.073423 1.8649 0.002486 0.000249 0.24864 25.24

0.432744 62.315 0.29446 0.030425 304.249 12 1 0.88108 22.3793 0.029837 0.0029837 2.9837 304.800

0.491154 70.7262 0.033420 0.03453 345.319 13.6197 1.1350 1 25.4 0.033864 0.0033864 3.3864 345.94

0.0193368 2.78450 0.0013158 0.0013595 13.595 0.53621 0.044684 0.03937 1 0.001333 0.0001333 0.13332 13.6197

.0014198 .20445 .0000966 .0000998 .99819 .039370 .003281 .002891 .073423 .0000979 .0000098 .0097889 1

lb/ft2atmospheres kg/cm

2

kg/m

inch

2

water

foot

(1)

water

(1)

inch

mercury

(1)

mm

mercury

(1)

bars MPa KPa

water

Example:

(8 Imperial gallons)(4.454596) = 36.36768 liters

To convert from one set of units to another, locate the given units in the left column and multiply the numerical value
by the factor shown horizontally to the right under the set of units desired.

mm

(1)

C-5

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

Table C-9. Temperature Conversion

–459.4 ° to 0° 1 ° to 60 ° 61 ° to 290 ° 300 ° to 890 ° 900 ° to 3000 °

C F/C F C F/C F C F. C F C F/C F C F/C F

–273 –459.4 --- –17.2 1 33.8 16.1 61 141.8 149 300 572 482 900 1652
–268 –450 --- –16.7 2 35.6 16.7 62 143.6 154 310 590 488 910 1670
–262 –440 --- –16.1 3 37.4 17.2 63 145.4 160 620 608 493 920 1688
–257 –430 --- –15.6 4 39.2 17.8 64 147.2 166 330 626 499 930 1706
–251 –420 --- –15.0 5 41.0 18.3 65 149.0 171 340 644 504 940 1724
–246 –410 --- –14.4 6 42.8 18.9 66 150.8 177 350 662 510 950 1742
–240 –400 --- –13.9 7 44.6 19.4 67 152.6 182 360 680 516 960 1760
–234 –390 --- –13.3 8 46.4 20.0 68 154.4 188 370 698 521 970 1778
–229 –380 --- –12.8 9 48.2 20.6 69 156.2 193 380 716 527 980 1796
–223 –370 --- –12.2 10 50.0 21.1 70 158.0 199 390 734 532 990 1814
–218 –360 --- –11.7 11 51.8 21.7 71 159.8 204 400 752 538 1000 1832
–212 –350 --- –11.1 12 53.6 22.2 72 161.6 210 410 770 549 1020 1868
–207 –340 --- –10.6 13 55.4 22.8 73 163.4 216 420 788 560 1040 1904
–201 –330 --- –10.0 14 57.2 23.3 74 165.2 221 430 806 571 1060 1940
–196 –320 --- –9.4 15 59.0 23.9 75 167.0 227 440 824 582 1080 1976
–190 –310 --- –8.9 16 60.8 24.4 76 168.8 232 450 842 593 11 00 2012
–184 –300 --- –8.3 17 62.6 25.0 77 170.6 238 460 860 604 1120 2048
–173 –280 --- –7.2 19 66.2 26.1 79 174.2 249 480 896 627 11 60 2120
–169 –273 –459.4 –6.7 20 68.0 26.7 80 176.0 254 490 914 638 1180 2156
–168 –270 –454 –6.1 21 69.8 27.2 81 177.8 260 500 932 649 1200 2192
–162 –260 –436 –5.6 22 71.6 27.8 82 179.6 266 510 950 660 1220 2228
–157 –250 –418 –5.0 23 73.4 28.3 83 181.4 271 520 968 671 1240 2264
–151 –240 –400 –4.4 24 75.2 28.9 84 183.2 277 530 986 682 1260 2300
–146 –230 –382 –3.9 25 77.0 29.4 85 185.0 282 540 1004 693 1260 2300
–140 –220 –364 –3.3 26 78.8 30.0 86 186.8 288 550 1022 693 1280 2336
–134 –210 –346 –2.8 27 80.6 30.6 87 188.6 288 550 1022 704 1300 2372
–129 –200 –328 –2.2 28 82.4 31.1 88 190.4 293 560 1040 732 1350 2462
–123 –190 –310 –1.7 29 84.2 31.7 89 192.2 299 570 1058 760 1400 2552
–118 –180 –292 –1.1 30 86.0 32.2 90 194.0 304 580 1076 788 1450 2642
–112 –170 –274 –0.6 31 87.8 32.8 91 195.8 310 590 1094 816 1500 2732
–107 –160 –256 0.0 32 89.6 33.3 92 197.6 316 600 1112 843 1550 2822
–101 –150 –238 0.6 33 91.4 33.9 93 199.4 321 610 1130 871 1600 2912

–96 –140 –220 1.1 34 93.2 34.4 94 201.2 327 620 1148 899 1650 3002
–90 –130 –202 1.7 35 95.0 35.0 95 203.0 332 630 116 6 927 1700 3092
–84 –120 –184 2.2 36 96.8 35.6 96 204.8 338 640 1184 954 1750 3182
–79 –110 –166 2.8 37 98.6 36.1 97 206.6 343 650 1202 982 1800 3272
–73 –100 –148 3.3 38 100.4 36.7 98 208.4 349 660 1220 1010 1850 3362
–68 –90 –130 3.9 39 102.2 37.2 99 210.2 354 670 1238 1038 1900 3452
–62 –80 –112 4.4 40 104.0 37.8 100 212.0 360 680 1256 1066 1950 3542
–57 –70 –94 5.0 41 105.8 43 110 230 366 690 1274 1093 2000 3632
–51 –60 –76 5.6 42 107.6 49 120 248 371 700 1292 1121 2050 3722
–46 –50 –58 6.1 43 109.4 54 130 266 377 710 1310 1177 2150 3902
–40 –40 –40 6.7 44 111.2 60 140 284 388 730 1346 1204 2200 3992
–34 –30 –22 7.2 45 11 3.0 66 150 302 393 740 1364 1232 2250 4082
–29 –20 –4 7.8 46 114.8 71 160 320 399 750 1682 1260 2300 4172
–23 –10 14 8.3 47 11 6.6 77 170 338 404 760 1400 1288 2350 4262

–17.8 0 32 8.9 48 118.4 82 180 356 410 770 1418 1316 2400 4352

– – – 9.4 49 120.2 88 190 374 416 780 1436 1343 2450 4442
– – – 10.0 50 122.0 93 200 392 421 790 1454 1371 2500 4532
– – – 10.6 51 123.8 99 210 410 427 800 1472 1399 2550 4622
– – – 11.1 52 125.6 100 212 413.6 432 810 1490 1427 2600 4712
– – – 11 .7 53 127.4 104 220 428 438 820 1508 1454 2650 4802
– – – 12.2 54 129.2 110 230 446 443 830 1526 1482 2700 4892
– – – 12.8 55 131.0 116 240 464 449 840 1544 1510 2750 4982
– – – 13.3 56 132.8 121 250 482 454 850 1562 1538 2800 5072
– – – 13.9 57 134.6 127 260 500 460 860 1580 1566 2850 5162
– – – 14.4 58 136.4 132 270 518 466 870 1598 1593 2900 5252
– – – 15.0 59 138.2 138 280 536 471 880 1616 1621 2950 5342
– – – 15.6 60 140.0 143 290 554 477 890 1634 1649 3000 5432

(1) Locate temperature in the middle column. If in degree Celsius, read degree Fahrenheit equivalent in right hand column. Of in degree Fahrenheit, read

degree Celsius equivalent in left hand column.

(1)

C-6

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Appendix D Related Calculations

Ideal and Real Specific Gravity . . . . . . . . . . . . . . . . . . . . . . . . .page D-1

Derivation of Annubar primary element flow equations . . . . . page D-3

IDEAL AND REAL
SPECIFIC GRAVITY

The real specific gravity of a gas is defined as the ratio of the density of the
gas to the density of air while both gas and air are the same pressure and
temperature. The fact that the temperature and pressure are not stated
results in small variances in specific gravity determination. It has been
common practice to determine the specific gravity at near atmospheric
pressure and temperature and assume that this specific gravity holds true for
all other pressure and temperatures. This assumption neglects
compressibility effects.

Compressibility effects lead to defining the term “ideal specific gravity,” which
is the ratio of the molecular weight of the gas to the molecular weight of air. As
long as no chemical reactions occur which would change the composition
(molecular weight) of the gas, the ideal specific gravity remains constant
regardless of the pressure and temperature. The molecular weight of air is

28.9644.

The relationship between ideal specific gravity and real specific gravity is
established as follows:

PV = MZRT

or

WZRT⋅⋅⋅⋅

g

c

---------------------------------------- -=

Equation D-1.

where

M

PV

g

W

c

----------- -=

g

or

g

g

WZRT⋅⋅⋅

c

------------------------------⋅=

----- -

P

g

V

www.rosemount.com

Equation D-2.

where

Since

ϒ

ρg

g

------ -=

g

Equation D-3.

Equation D-4.

W

-----=

V

c

g

ZRT⋅⋅ ⋅

P ϒ

then

P

c

------------------------------ -⋅=

g

Equation D-2 can be written:

ZRT⋅⋅

ρg

--------------------⋅ρZRT⋅⋅⋅==

------ -

g

g

c

P

ρ

--------------------=

ZRT⋅⋅

Rosemount 485 Annubar

Now since the real specific gravity is defined as:

It can be written as:

or

Equation D-5.

The gas constant R is defined as the Universal Gas Constant divided by the
molecular weight

Equation D-5 can be written as

G

G

R

ρ

g

---------------------------- -

ZgRgT

⋅⋅

-----------------------------=

ρ

a

---------------------------- -

ZaRaT

⋅⋅

P

⋅⋅⋅

gZaRaTa

----------------------------------------=

⋅⋅⋅

P

aZgRgTg

1545.32

---------------------=

Mol. Wt.

Reference Manual

00809-0100-1191, Rev CB

May 2006

ρ

s

G

----- -=

ρ

a

g

a

1545.32

G

P

aZg

1545.32

----------------------------------------------------------------- Tg⋅

Molecular Weight of Gas

MolecularWeightofAir

----------------------------------------------------------------- T

P

gZa

MolecularrWeight rofrAir

-------------------------------------------------------------------------------------------=

⋅

a

or

P

⋅⋅

gZaTa

---------------------------- -

Equation D-6.

G

P

⋅⋅

aZgTg

Now since the ideal specific gravity is

MolecularrWeight rofrGas

------------------------------------------------------------------- -×=

Molecular

rWeight rofrAir

MolecularrWeight rofrGas

G

------------------------------------------------------------------- -=

f

Molecular

rWeight rofrAir

Equation D-6 can be written as:

P

⋅⋅

gZaTa

---------------------------- - G

Equation D-7.

G

⋅⋅

P

aZgTg

⋅=

f

Equation D-7 gives the relationship between real specific gravity and ideal
specific gravity. As can be seen, if both the gas and air are at the same
pressure and temperature, the difference between real and ideal specific
gravities depends upon the respective compressibility factors.

The following nomenclature applies to the above equations:

P = Pressure in psia
V = Volume in cubic feet
M = Mass
R = Universal gas Constant =

G

1545.32

-------------------------------------------------- -=

MolecularWeight

T = temperature in degree Rankine
Z = Compressibility factor (deviation from Boyle’s Law)
W = Weight

= Standard gravitational constant, 32.1740 ft/second

g

c

2

g = Actual gravitational constant for location

γ = Specific Weight
ρ = Density

G = Real specific gravity
G

= Ideal specific gravity

f

D-2

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

DERIVATION OF
ANNUBAR PRIMARY
ELEMENT FLOW
EQUATIONS

The Annubar primary element flow equations listed in Section 2: Annubar
Primary Element Flow Calculations are all derived from the hydraulic
equation. The hydraulic equation for volumetric flow and mass flow is given
on page 1-11. The following shows how the Annubar primary element flow
equations are developed from the hydraulic equations.

Problem

Derive the volumetric flow rate in GPM for liquids where the differential
pressure is measured in inches of water at 68 °F, the pipe diameter is
measured in inches.

Solution

1 Gallon = 231-in.

3

= 0.13368 ft

3

1 ft3 = 7.48052 gallons
1-in. water at 68 °F (h

) at standard gravity = 0.036065 lbf/in.2 (psi)

w

g = local gravity constant

= standard gravity constant, 32.1740 ft/sec

g

c

ρ = Density lbm/ft

3

dP = P1 – P2 = differential pressure, lbf/ft

2

2

D = Diameter of pipe, inch
A = Area of pipe, ft

2

K = Annubar Flow Coefficient
Q = Volumetric Flow, GPM

Beginning with Equation D-8

–()

2g P

1P2

Equation D-8.

QKA

------------------------------- -⋅ KA2g
ρ

The units can be checked as follows:

QFt

2

----------------------

s

dP

-------⋅==
ρ

lbf

⎛⎞

ft

------ -

⎝⎠

2

ft

2

lbm

⎛⎞

----------

⎝⎠

3

ft

3

ft

------==

s

NOTE

In the above units conversion, lbf is set equal to lbm. This is only true at
standard gravity. The gage location factor described later corrects for
locations where the local gravity does not equal the standard gravity.

Substituting units leads to:

2 32.1740

---------------------------------------------------------------------------------------------------------------------------------------- -

----------------------- - h

sec

QK

ft

2

ond

60S ec

----------------- -

Min

0.036065

w

lbm

----------

ρ

3

ft

7.48052G al

------------------------------- -

3

Ft

lbf

-------------- -·144

2

inch

-------------------------

144inch

inch

-------------- -

2

ft

3

Ft

2

2in2

πD

-------------------=

2

4

D-3

Rosemount 485 Annubar

Equation D-9.

We can now define the density of any fluid by referencing that fluid to
water at 60 °F.

G G PM 44.751K D

ρρ60Gf⋅=

Reference Manual

00809-0100-1191, Rev CB

May 2006

h

2

w

------ -==

ρ

where:

ρ

60

= density of water at 60 °F = 62.3707 lbm/ft

3

gf = flowing specific gravity of the fluid

h

Equation D-10.

G G PM 44.751 K D

GP M 5.6664 K D

2

2

h

------ -⋅⋅ ⋅=

G

--------------------------- -⋅⋅ ⋅==

62.3707G

w

f

w

f

If the pipe temperature is different from the temperature at which the internal
diameter (D) was measured, a factor (F

) must be applied to account for the

AA

area change. With these four factors applied, Equation D-10 becomes:

h

Equation D-11.

GP M 5.6664 K D2F

AA

w

------ -⋅⋅ ⋅ ⋅=

G

f

This equation is identical to the first Annubar primary element flow equation
for volume rate of flow in liquids.

D-4

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

Appendix E Flow Turndown and Differential

Pressure Requirements

Flow Turndown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page E-1

Differential Pressure (DP Turndown) . . . . . . . . . . . . . . . . . . . . page E-2

Flow Measurement System Turndown . . . . . . . . . . . . . . . . . . .page E-2

Percent of Value and Percent of Full Scale accuracy . . . . . . . page E-2

Annubar Turndown Limitations . . . . . . . . . . . . . . . . . . . . . . . . .page E-3

Minimum measurable differential pressure . . . . . . . . . . . . . . .page E-4

Putting it all together: The flow system turndown . . . . . . . . . page E-4

The Annubar primary element is the latest in averaging pitot tube technology
and provides the highest accuracy over the widest range or turndown of any
flow sensor of its kind. Like any measurement device, it must be applied
properly to obtain the performance it is capable of. The definition and
application of turndown to a flow system is often misunderstood, but plays a
major role in the determination of proper flow system specification.

The concept of turndown and how it applies to an Annubar primary element
and DP transmitter will be covered in this appendix.

FLOW TURNDOWN The ability to measure the flowrate accurately over a wide range is dependent

on several factors any of which can impose a limitation that may restrict the
operation of a flow measurement system. The flow turndown is the ratio of the
highest flowrate expected to be accurately measured by the flow
measurement system to the lowest accurate flowrate. This quantity is
expressed typically on one line with a colon. For example, if a turndown ratio
is 10, the turndown is written “10:1” and is read as ten-to-one. The flow
turndown is abbreviated “TD.”

It is important that the actual operating flowrates be estimated as closely as
possible prior to buying a flow measurement system. To some flow
measurement system users, this seems like a contradiction because they are
buying the flow measurement system to tell them exactly that. However, a
good estimate of the flowrate can be made by using simple devices and
methods. Some problems can be avoided by doing this before buying a flow
measurement system.

In many actual field service cases, the flow measurement system was
apparently not functioning. The user realized, after a lot of time and effort was
expended, that the flow in the pipe was so small relative to the capacity of the
measurement system, that the flow could not be measured.

www.rosemount.com

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

DIFFERENTIAL
PRESSURE (DP
TURNDOWN)

ACCURACY AND FLOW
TURNDOWN

Because the DP transmitter or secondary meter must cover the range of
signals from the flow measurement primary sensor, a “DP turndown”,
or TD

can be defined as the ratio of the highest DP to be measured to the

h

lowest. Due to the square root relationship, the DP turndown will be equal to
the square of the flow turndown, or TD:

Equation E-1.

It is this relationship that restricts the ability of the DP-type flow measurement
system to measure wide ranges. For example, for a 10:1 flow turndown, the
DP turndown is 100:1. This means that a high flowrate that generates 50-in.
water column (50-in. WC) will have a DP of approximately 0.50-in. WC at the
minimum flowrate for a 10:1 flow turndown.

Before turndown can be determined, the accuracy of the flow system over the
range of operation must be determined. In order to extend the turndown
capability of this measurement, the accuracy (error) statement must be
increased. This is true for most simple types of flow measurement systems.

Another method of improving the accuracy over a higher turndown is to
calibrate the actual meter and incorporate this calibration information into the
computation of the measured value.

TDhTD[]

2

=

or

TD TD

=

h

FLOW MEASUREMENT
SYSTEM TURNDOWN

PERCENT OF VALUE
AND PERCENT OF FULL
SCALE ACCURACY

Each flow measurement component should be examined for suitability to the
application. Although some flow measurement systems can have up to six
components, turndown most greatly affects the Annubar sensor and the DP
transmitters or meters that read the DP signal. This section will focus on the
Annubar and DP transmitters. To calculate true system accuracy and
turndown, the performance of all components must be included.

When determining accuracy of measuring devices, the performance
statements must be carefully read. There are two methods of expressing
accuracy which are very different and affect the performance of the device
over its operating range. It is important to note that error statements and
representative curves actually represent the probability that the true error is
somewhere within the indicated limit.

A “percent of value” accuracy is the error at a specific value, but in measuring
devices typically implies that the device has a consistent error statement over
the entire operating range. A “percent of full scale” accuracy relates the error
of the device when it is measuring a quantity that represents 100% of the
output signal. The actual or value error for a device with this type of accuracy
statement is calculated using the following equation.

Equation E-2.

% Value Error =

% Full Scale Error

% of Scale

.

100%

E-2

The difference between these two methods is not obvious until they are
plotted. Figure E-1 shows the two methods for expressing value error. Type
“A” shows a 1% of value error, and type “B” a 1% of full scale error statement.
Both are plotted over a 10:1 turndown.

Reference Manual

00809-0100-1191, Rev CB
May 2006

Figure E-1. Percent of Value and
Full Scale Error

Rosemount 485 Annubar

DP transmitters and meters are typically “B” devices. Annubars and other
primary flow sensor devices are typically “A” type.

10

Typ e B

0.75% of Full Scale

Typ e A

0.75% of Value

0

ANNUBAR TURNDOWN
LIMITATIONS

-10
0100908070605040302010

-0.75% of Value

-0.75% of Full Scale

% of Full Scale

% of Reading Error

The design of the Annubar provides a consistent, linear calibration
characteristic over a wide turndown range (see Figure E-1). The limitation at
“high end” flows is structural and not functional. The low end limitations are
due to practical limitations of the flow lab calibration facilities, the limit of
turbulent flow, or the limitation of measuring the low differential pressures.

Turbulent flow exists above pipe Reynolds numbers from 4000 to 13000.
Turbulent flow characterizes the velocity profile and exists in nearly all
industrial pipe and ducting. Annubar sensors are calibrated for turbulent flows
only.

The functional limitations for low flows are summarized in Table E-1. All
calibration data for each sensor was used to determine a minimum “rod”
Reynolds number, Rd. These limitations may be above or below the minimum
practical differential pressure signal.

Other types of DP flow sensors such as orifice plates and venturi tubes have
similar limitations, but are slightly more Reynolds number dependent which
reduces their turndown at the lower ranges of their calibrations.

E-3

Rosemount 485 Annubar

Table E-1. Annubar Minimum
Functional Velocity and DP for
Typical Process Fluids

Sensor Minimum Rd Water Gas Steam

1 6000 0.5 (12.7) 0.25 (6.35) 1 (25.4)
2 12500 0.5 (12.7) 0.25 (6.35) 1.5 (38.1)
3 25000 0.5 (12.7) 0.25 (6.35) 2 (50.8)

Reference Manual

00809-0100-1191, Rev CB

May 2006

Minimum DP, in. H2O (mm H2O)

MINIMUM MEASURABLE
DIFFERENTIAL
PRESSURE

PUTTING IT ALL
TOGETHER: THE FLOW
SYSTEM TURNDOWN

The low end limitations, due to the Annubar primary element calibration, may
also be due to the ability to measure the differential pressure. This limit may
be reached before the functional limit explained above and typically occurs in
gas and low pressure stream flows.

The minimum measurable DP for the Annubar is based on the type of fluid
measured and for liquids and gases is due to the level of DP fluctuations or
noise in the signal.

For steam flows, the minimum DP is due to the method of DP transmitter to
Annubar sensor hookup. The DP signal is conveyed through two water
(condensate) legs. An additional error in measurement will occur if these
water legs are not equal in height. Because of this inherent error, the
minimum recommended DP must be higher.

The flow system (flow primary or Annubar primary and secondary transmitter
or meter) performance is determined over the selected operating range.
Because the DP transmitter or meter is a type “B” accuracy device, the
system accuracy will be type “B” or the error will increase at the lower scale.
The combined error over the selected operating range is determined by using
the “square root of the sum of the squares” rule, or

2

Equation E-3.

% System Error

E

2

E

+=

p

s

where:

E-4

= percent error in flow due to primary

E

p

E

= percent error in flow due to secondary

s

At this point, things get a little complicated because each device contributes
errors to the calculated flowrate through its relationship in the flow equation.
An Annubar or other flow primary sensor will contribute directly to the error in
flow, whereas a secondary device (DP transmitter or meter) contributes to the
error in DP which is the square of the error in flow. For a DP transmitter or
meter, the contribution to the flow calculation error is:

Equation E-4.

EfDP()o1

%

±

-------------- -+ 1– 100⋅=

DP

100

%

%

oE

where:

(DP) = percent error in flowrate due to DP

%E

f

%E

= percent error in DP

DP

Reference Manual

00809-0100-1191, Rev CB
May 2006

Rosemount 485 Annubar

The percent error in DP will depend on the percent scale, so that:

%

oE

Equation E-5.

EfDP()o1

%

±

-------------- -+ 1– 100⋅=

%

oDP

DP

where:

= percent of full scale error (accuracy) of the DP transmitter

%E

FS

%DP = percent of scale at which the DP transmitter is operating

Since the largest contributor to system error is due to the DP transmitter at the
minimum scale, the turndown that is possible for the system will be
determined by how large of an error statement can be tolerated at the
minimum flowrate. This relationship can be turned around so that the error at
minimum scale is calculated for the desired flow turndown. From
Equation E-1

%

100

---------- -=

TD

--------------------------- -==

%

2

100

DP

min

or

Equation E-6.

TD TD

%

DP

min

h

When Equation E-6 is combined with Equation E-5, the percent error in flow
due to the DP transmitter or meter at minimum scale is determined

Equation E-7.

%

EfDP()\=

···

±

jjj 1

E

--------------------- TD()

+ 1– 100⋅

100

DP

2

%

%

Equation E-7 must be put into Equation E-3 to determine the error in flow at
the minimum scale for the desired flow turndown. This relationship should be
the deciding factor when determining the available flow turndown for any DP
type flow measurement system.

Example

A Sensor Size 2 485 Annubar primary element and a DP transmitter are to be
used to measure water flow (μ = 1 cP) between 3000 and 1000 GPM in a
10-in. sch 40 (10.02-in. I.D. line). The DP at maximum flow is approximately

84.02-in.H

O. If the transmitter has an reference accuracy of 0.04% at that

2

span, determine the error in flowrate due to the Annubar flow sensor and DP
transmitter at 1000 GPM.

Solution

Calculate DP at minimum flowrate

TDhTD

=

2

(from Equation E-1)

3000

TD

------------ - 3==
1000

93()=

TD

h

h

h

-------------

min

max

TD

h

84.02

-------------- - 9.34== =
9

-in.H2O

Now, the minimum Reynolds number is this application must be checked
against the minimum allowable Reynolds number per Table E-1.

3160 G PM G⋅⋅

R

-----------------------------------------

D

D μ

⋅

cp

3160 1000 1⋅⋅

-------------------------------------- - 315369===

10.02 1⋅

E-5

Rosemount 485 Annubar

This value exceeds the minimum Reynolds number of 12500 from Table E-1
so the discharge coefficient uncertainty of the Annubar will be the published

0.75%.

Calculated Percent System Error:

where:

E

so:

%

SystemError E

= 0.75%

p

%

E

EfDP() 1

s

SystemError 0.7520.36

2

+=

p

%

⎛⎞

-------------- - TD

+ 1–

⎝⎠

+= 0.832=

E

E

100

2

(from Equation E-5)

s

2

fs

2

Reference Manual

00809-0100-1191, Rev CB

2

%

0.04

⎛⎞

100⋅ 1

%%

------------------ 3

+ 1–

⎝⎠

100

May 2006

100 0.36=⋅== =

%

E-6

Reference Manual

00809-0100-1191, Rev CB
May 2006

Appendix F References

“ASME Steam Tables,” American Society of Mechanical Engineers, New York,

1967.

“Air Conditioning Refrigerating Data Book - Design,” American Society of
Refrigerating Engineers, 9th Edition, New York, 1955.

“Bureau of Standards Bulletin 14,” pages 58 to 86; E.C. Bingham and R.F.
Jackson, (S.P. 298, August, 1916) (1919).

“Chemical Engineers Handbook,” R.H. Perry, C.H. Chilton, and S.D.
Kirkpatrick; McGraw-Hill Book Co., Inc., New York, 4th Edition.

“Data Book on Hydrocarbons,” J.B. Maxwell; D. Van Nostrand Company, Inc.,
New York, 1950.

“Dowtherm Handbook,” Dow Chemical Co., Midland, Michigan, 1954.

“Flow of Fluids Through Valves, Fittings, and Pipe, Technical Paper No. 410;”
16th Printing, Crane Co., New York, 1985.

Rosemount 485 Annubar

“Manual for the Determination of Supercompressibility Factors for Natural
Gas,” American Gas Association Par Research Project NX-19., December,

1962.

“Flow Measurement with Orifice Meters,” R.F. Stearns, R.M. Jackson, R.R.
Johnson and Others; D. Van Nostrand Company, Inc., New York, 1951.

“Fluid Meter,” American Society of Mechanical Engineers, Par 1 - 6th Edition,
New York, 1971.

“Handbook of Chemistry and Physics,” 55th Edition, 1974 - 1975, Chemical
Rubber Publishing Co., Cleveland, Ohio.

“Orifice Metering of Natural Gas,” Gas Measurement Committee Report No.
3; American Gas Association, Arlington, 1972.

“Petroleum Refinery Engineering,” W.L. Nelson; McGraw-Hill Book Co., New
York, 1949.

“Standard Handbook for Mechanical Engineers,” Theodore Baumeister and
Lionel Marks; 7th Edition, McGraw-Hill Book Co., New York.

“Tables of Thermal Properties of Gases,” National Bureau of Standards
Circular 564, November 1955.

www.rosemount.com

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

F-2

Reference Manual

00809-0100-1191, Rev CB
May 2006

Appendix G Variable List

Variable Description Unit

V Velocity ft/sec
W Mass flow rate lbm/sec
R

D

R

d

D Pipe diameter in.
d Probe width in.

ρ Density lb/ft3
μ Absolute viscosity cP

Q Volumetric flow rate ft3/sec
G

f

P

f

A Area in2
G Specific gravity Dimensionless
h

w

h Head ft. of flowing fluid
B Blockage Dimensionless
Y

A

F

pb

F

tb

F

tf

F

g

F

pv

F

m

F

AA

F

L

Υ Ratio of Specific Heats Dimensionless
P Pressure psia
g Local gravitational constant ft/s2
g

c

υ Kinematic viscosity ft/s2
υ

cs

D

ft

Q

s

Q

A

G

s

F

NA

F

RA

T Temperature °F
T

f

K Flow coefficient Dimensionless

1

C

μ

cP

Pipe Reynolds # Dimensionless
Rod Reynolds # Dimensionless

Specific gravity of flowing fluid Dimensionless
Pressure, flowing psia

Head or differential pressure in H2O at 60 °F

Gas Expansion Factor Dimensionless
Base pressure factor Dimensionless
Base temperature factor Dimensionless
Flowing temperature factor Dimensionless
Specific gravity factor Dimensionless
Supercompressability factor
Manometer factors
Thermal expansion factor
Gage location factor Dimensionless

Standard gravitational constant ft/s2

Kinematic viscosity centistokes
Pipe diameter ft
Flowing density lbm.ft3
Volumetric flowrate at standard conditions SCFM
Volumetric flowrate at actual conditions ACFM
Specific gravity at standard conditions Dimensionless
Units conversion factor Dimensionless
Reynolds number factor

Flowing temperature °F

Calculations constant Dimensionless
Absolute viscosity centiPoise

Rosemount 485 Annubar

www.rosemount.com

Rosemount 485 Annubar

Reference Manual

00809-0100-1191, Rev CB

May 2006

G-2

Reference Manual

00809-0100-1191, Rev CB
May 2006

Index

Rosemount 485 Annubar

A

Accuracy

Scale

. . . . . . . . . . . . . . . . . E-2

Alignment

Errors

. . . . . . . . . . . . . . . . . 3-1

Annubar

Primary Element
Turndown

. . . . . . . . 2-1

. . . . . . . . . . . . . . E-3

B

Bernoulli’s Theorem . . . . . . . . . 1-9

C

Connections

Leakage . . . . . . . . . . . . . . . 3-4

Conversion Factors

. . . . . . . . . . C-1

D

Density . . . . . . . . . . . . . . . . . . . 1-4

Derivation

Flow Equations

Differential Pressure

Measurable
Physical Fluid Properties
Turndown

Dirt Accumulation . . . . . . . . . . . 3-4

. . . . . . . . .D-3

. . . . . . . . . . . .E-4

. . 1-3

. . . . . . . . . . . . . . E-2

E

Errors . . . . . . . . . . . . . . . . . . . . 3-1

Alignment
Dirt Accumulation

Gas Entrapment . . . . . . . . 3-6

Sizing

. . . . . . . . . . . . . . 3-1

. . . . . . . 3-4

. . . . . . . . . . . . . . . . . 3-2

F

Factors

Conversion . . . . . . . . . . . .C-1

Unit

. . . . . . . . . . . . . . . . . . C-1

Flow Calculation
Flow Coefficient

Reynolds Number
Theory

Flow Disturbance

Upstream

Flow Equations

. . . . . . . . . . . 2-12

. . . . . . . 2-9

. . . . . . . . . . . . . . . . 2-9

. . . . . . . . . . . . . . 3-2

. . . . . . . . . . . . . 2-1

Derivation . . . . . . . . . . . . . .D-3

Flow Measurement System

Turndown

Flow Parameter

Changes

Limitations . . . . . . . . . . . . . 3-6

Flow Patterns
Flow System

Turndown

Flow Turndown . . . . . . . . . . . . .E-1

Flowrate

Gases

Liquids . . . . . . . . . . . . . . . 1-15

Fluid Properties

Saturated Water

Selected Gases . . . . . . . . .A-8

Various Liquids
Viscosity

Water and Liquid Petroleum

. . . . . . . . . . . . . .E-2

. . . . . . . . . . . . . . . 3-4

. . . . . . . . . . . . . . 1-6

. . . . . . . . . . . . . .E-4

. . . . . . . . . . . . . . . . 1-12

. . . . . . . . . . . . .A-1

. . . . . . . . .A-2

. . . . . . . . . .A-4

Water and Steam

. . . .A-2

A-3

G

Gas

Location Factors . . . . . . .A-12

Gas Entrapment
Gases

Flowrate

. . . . . . . . . . . . 3-6

. . . . . . . . . . . . . . 1-12

I

Ideal

Specific Gravity

. . . . . . . . .D-1

L

Laminar . . . . . . . . . . . . . . . . . . . 1-7

Leakage

Connections

Limitations

Liquids . . . . . . . . . . . . . . . . . . . . 1-4

Flowrate

. . . . . . . . . . . . 3-4

. . . . . . . . . . . . . . . . . 3-6

. . . . . . . . . . . . . . 1-15

N

Nomenclature . . . . . . . . . . . . . . 2-7

O

Operating Limitations . . . . . . . 2-11

P

Physical Fluid Properties . . . . . .1-1

Differential Pressure

Pressure . . . . . . . . . . . . . . .1-1

Temperature

Pipe Blockage

Pipe Data . . . . . . . . . . . . . . . . . B-1

Pressure

Physical Fluid Properties

. . . . . . . . . . . .1-4

. . . . . . . . . . . . .2-10

. . . . . .1-3

. . 1-1

R

Real

Specific Gravity . . . . . . . . D-1

References
Reynolds Number

. . . . . . . . . . . . . . . .F-1

. . . . . . . 1-8, 2-9

Probe Width . . . . . . . . . . . 2-11

S

Saturated Water

Fluid Properties

Scale Accuracy . . . . . . . . . . . . E-2

Sensor Constants

485

. . . . . . . . . . . . . . . . . . 2-10

Sensor Shape . . . . . . . . . . . . . . 2-9

Signal

. . . . . . . . . . . . . . . . . . . .2-9

Sizing

Errors

. . . . . . . . . . . . . . . . .3-2

Specific Gravity

Ideal

. . . . . . . . . . . . . . . . . D-1

Real

. . . . . . . . . . . . . . . . . D-1

Specific Weight . . . . . . . . . . . . . 1-4

. . . . . . . . A-2

. . . . . . . . . . . . . 1-4

T

Temperature

Physical Fluid Properties

Theory

Flow Coefficient

Transition

Turbulent . . . . . . . . . . . . . . . . . .1-7

Turndown

. . . . . . . . . . . . . . . . . .1-7

Annubar

DP . . . . . . . . . . . . . . . . . . E-2

Flow
Flow Measurement System

Flow System . . . . . . . . . . . E-4

. . . . . . . . . . . . . . E-3

. . . . . . . . . . . . . . . . . E-1

. . . . . . . . . 2-9

. . 1-4

E-2

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Rosemount 485 Annubar

U

Unit Factors . . . . . . . . . . . . . . .C-1

Upstream

Flow Disturbance

V

Variable List . . . . . . . . . . . . . . .G-1

Velocity

Average

Viscosity

Absolute . . . . . . . . . . . . . . . 1-5

Kinetic

. . . . . . . . . . . . . . . 1-7

. . . . . . . . . . . . . . . . . . 1-5

. . . . . . . . . . . . . . . . 1-6

W

Water and Steam

Fluid Properties

. . . . . . . . 3-2

. . . . . . . . . A-2

Reference Manual

00809-0100-1191, Rev CB

May 2006

Index-2

Reference Manual

00809-0100-1191, Rev CB

May 2006

Rosemount, the Rosemount logotype, and Annubar are registered trademarks of Rosemount Inc.
PlantWeb is a registered trademark of one of the Emerson Process Management group of companies.
All other marks are the property of their respective owners.

Emerson Process Management

Rosemount Inc.

8200 Market Boulevard
Chanhassen, MN 55317 USA
T (U.S.) 1-800-999-9307
T (International) [phone]
F [phone]

www.rosemount.com

¢00809-XXXX-XXXX ¤

© 2006 Rosemount Inc. All rights reserved.