This product complies with the requirements concerning electromagnetic compatibility (EMC) stipulated in Council directive no.
89/336/EEC of 3rd May 1989, altered at directive no. 92/31/EEC,
on the approximation of the laws of the Member States relating to
electromagnetic compatibility.
MJK Automation A/S declare that the product complies to the
values stipulated in EN 50081-1 and EN 50082-1.
2
Flow converter 713
Thank you for choosing Flow converter 713. Flow converter 713 is a modern construction, in which the relation
between functions, and "userfriendliness“ and precision
is optimum. In order to gain full use from the equipment,
we recommend that you read the instructions very thoroughly. Should any problems occur during installation or
operation, our technicians will be at your disposal.
Flow converter 713 is for the measurement of ow in
open umes and weirs. The method of measurement
and linearization complies with the norm ISO 1438. This
norm indicates how the head over the weir and umes
are constructed, and how the calculations for linearization are to be arrived at. The owrate is generaly speeking determined by using the following mathematical
function:
Flow Q = f(level
x
· constant)
where the exponent x and the constant depends on the
weir or the ume.
The ow converter has 3 different linearization systems
depending on how the volume of water is measured.
• One choose between a number of predened umes and
weirs, e.g. Parshall umes and V-notch weirs.
• If the ume or weir differ from the normal types of umes
and weirs, the formula Q(h)=k x hn can be applied, where
k and n are keyed in directly.
• Some times it can be desirable to linearizate a levelsignal
which does not follow a mathematical expression. As an
example a ow can be measured in a partly lled pipe,
where the menu point-linearization can be applied.
Technical section with the principles of measuring
Flowconverter 713 converts the level to ow from these
examples. Some of the examples are simplied. The ISO
1438 norm indicates a number af calculation methods
for umes and weirs. The Flowconverter 713 uses these
methods where it is possible.
Rectangular sharp edged weir
according to ISO 1438
Rectangular sharp edged weir is supplied in two types:
- with side contraction
where the opening has a smaller width than the feeder
and
- without side contraction
where the width of the opening corresponds to the width
of the channel (B = b).
Rectangular sharp edged weir
with side contraction:
Universal formula: (Kindsvater/Carter)
Q = 3600 × Ce × 2/3 × 2g × be × h
where: Q = ow in m3/hb = width of weir in [m]
be = effective width of weir in [m]
be = b + k
ha = height in [m]
b
he = effective height in [m]
he = ha+kh, kh = 0,001
hb = depth below edge in [m]
B = ume width in [m]
L = distance to sensor,
4 - 5 × h
g = acc. due to gravity = 9,81 m/s2
a max.
kb is a correction factor in meter.
For determination of k
b/B = 0 kb = 0,0024 m
b/B = 0,2 kb = 0,0024 m
b
b/B = 0,4 kb = 0,0027 m
b/B = 0,6 kb = 0,0036 m
b/B = 0,8 kb = 0,0042 m
b/B = 1,0 kb = -0,0090 m
1,5
e
d
β
ß = minimum 45°
d ~ 1-2 mm
Edge
Ce is a contraction coefcient (no unit) depending on the
ratio of b/B and ha/h
b.
For determination of Ce
b/B = 1,0 Ce = 0,602+0,075 ha/h
b/B = 0,9 Ce = 0,598+0,064 ha/h
b/B = 0,8 Ce = 0,596+0,045 ha/h
b/B = 0,7 Ce = 0,594+0,030 ha/h
b/B = 0,6 Ce = 0,593+0,018 ha/h
b/B = 0,4 Ce = 0,591+0,0058 ha/h
b/B = 0,2 Ce = 0,588-0,0018 ha/h
b/B = 0 Ce = 0,587-0,0023 ha/h
b
b
b
b
b
b
b
b
3
The following limitations apply for the values of ha/hb, ha,
hb and b:
ha/hb = max. 1,0
ha = min 0,03, max 0,75 m
hb = min 0,10 m
b = min 0,30 m
Formula: (Rehbock equation)
Determination of Ce for different values of b/B.
The following limitations apply for the values of ha/hb, ha,
hb and b:
ha/hb = max. 2,5
h
h
b = min 0,15 m
a
b
= min 0,03 m
= min 0,10 m
(B-b)/2 = min 0,10 m
Rectangular sharp edged weir without side
contraction:
Q = 3600 × Ce × 2/3 × 2g × b × h
where: Q = ow in m3/h
b = width of edge in [m]
Ce = 0,602+0,083 ha/h
ha = height in [m]
b
he = effective height in [m]
he = ha+kh, kh = 0,0012
g = acc. due to gravity = 9,81 m/s
Triangular weir
according to ISO 1438
h
a
h
b
1,5
e
2
h
a
h
b
The sides of the channel must continue at minimum 0,3
x h
after the weir.
a max.
ha = height
hb = depth below edge in [m]
B = ume width in [m]
L = distance to sensor,
4 to 5 × h
a max.
ß = minimum 45°
d = 1-2 mm
d
ha = height in [m]
hb = depth below edge in [m]
B = umewidth in [m]
L = distance to sensor,
4 to 5 × h
a max.
The following limitations apply:
α = 20° - 100°
ha/hb = max 0,4
ha/B = max 0,2
ha = min 0,06 m
hb = min 0,09 m
Formula: (Kindsvater-Shen).
Q = 3600 × Ce × 8/15 × 2g × tg(α/2) × h
where: Q = ow in m3/h
ha = height in [m]
he = the effective height in [m]
he = ha + kh, kh = 0,001
g = acc. due to gravity = 9,81 m/s
2
α = aperture angle
β
2,5
e
4
kh is set to 0,001 m and is a correction factor.
The ow is calculated from the formula:
Ce is the coefcient of discharge (no unit). For determi-
nation of Ce, look at diagram below.
0,005
0,004
0,003
0,002
0,001
Diagram for determination of k
h
Diagram for determination of Ce.
Q = k × h
n
where:
a
Q = ow in m3/h
b = width in the measuring ume in[ m]
ha = water level before the narrowing in [m]
hb = water level in the narrowing in [m]
L = distance to the sensor (use table below)
The factor k and exponent n are constants.
The formula complies to free ow, hb
< 0,7 × h
max
a max
b k n L
1" 217 1,548 0,24
2" 425 1,548 0,27
3" 630 1,548 0,30
6" 1310 1,574 0,41
9" 1851 1,528 0,58
12" 2407 1,519 0,89
24" 5142 1,55 0,99
36" 7863 1,566 1,09
Table for determination of the constants k, n and the
distance to the sensor.
12"
36"
9"
6"
3"
2"
1"
24"
Parshall ume
The most common type of ume is the Parshall ume.
The Parshall ume is a standardized Venturi ume.
h
a
h
b
At free ow, only the level ha is measured. The location
of the sensor is important and must be carried out as illustrated in the drawing and the table in the next column.
It is important to have a laminar ow (horizontal streaming calm water with no whirls) at the out- and inlet from
the ume. Upstream the measuring ume, must extend
at least ten times the width of the inlet section of the
ume.
On the outlet side the only demand is that the water
should run freely. This is the case when hb ≤ 0,7 × ha.
Q/h diagram for Parshall umes, the height ha is shown
as a function of the ow Q.
5
Ark6 Diagram 1
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
050100150200250300350400450500
8"
10"
12"
15"
24"
30"
Q [m3/h]
h
a
[m]
Palmer - Bowlus ume
The Palmer & Bowlus ume is characterized by its circular connection, which makes it easy to install in pipe-
lines. The ume is aimed at measurement in the scale of
20-100% of the prescribed ow.
where:
ha = water level before the narrowing
L = ½ × DN (the nominal diameter of the ume),
measured from the beginning of the meas. section.
No simple ow formulas can be set up for the Palmer
& Bowlus umes, the formulas are dened individually
for every ume. The Flow formulas are derived from the
continuity equation and Bernoulli’s equation:
2
2
A
x A
1
Q = 2g(h1- h2) x
where:
A1 and h1= cross section and height in the inlet of the
Table showing the size of D, and the max. ow for the
Palmer & Bowlus umes.
A2 and h2= cross section and height in the outlet of the
ume
For the Palmer & Bowlus umes with the dimensions 6'',
8", 10", 12", 15", 18'', 21'', 24" and 30", the ow formulas
are dened and incorporated in the ow converter. In
the menu „Programming of ow calculation“ the relevant
ume is chosen.
Q/h diagram for the MJK Palmer & Bowlus umes, the
height ha is shown as a function of the ow Q.
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