If you multiply the large crosssectional area (A1) by the
corresponding velocity (v1), the
product is the same as when you
multiply the small cross-sectional
area (A2) by the velocity there (v2).
Pressure in currents
Because the speed of the water increases in the narrow part of a tube,
the pressure also increases in the direction of flow. But an increase in
pressure also means an increase in force per unit of area and, thus, an
increase in the distance the narrower stream of water can shoot.
The pressure in the direction of
flow is also called dynamic
pressure, because it arises with
dynamics, or the force of
movement. In tubes, there is
always also something called
static (resting) pressure, which is
a product of the difference in
pressure between the entrance to
and exit from the tube.
Dynamic pressure is measured
against the stream, static
pressure in the stream. When the
liquid is resting, there is only
static pressure, and the dynamic
pressure is equal to zero. When
movement starts, dynamic
pressure rises and static pressure
simultaneously drops.
That also applies in reverse. In a
uniform current, in any case, the
sum of the two pressures is
always the same.
This equation is called the flow rate
equation or continuity equation:
45
Page 5
EXPERIMENT 18
Total energy
Work yielded
Friction
Toggle switch centerStop in all directions
Supply
Toggle switch
left
Toggle switch
right
= F
2
: A
2
p
1
: p
2
= V
2
: V
1
p
1
: p
2
= T
1
: T
2
or: p · V = constant
F
1
· L
1
= F
2
· L
2
p
1
· V
1
= p
2
· V
2
A
1
· v
1
= A
2
· v
2
F (Force)
A (Area)
P (power) =
W (work)
t (time)
F
d
=C
d
·
A · · v
2
2
P ==2= 2 Pa
10 N
5 m
2
Nm
2
P == 200,000 Pa
100 N
0.0005 m
2
P =
= 16,000 Pa or 16 hPa or 1.6 bar
4 N
0.00025 m
2
or= constant=
p · V
T
p
2
· V
2
T
2
F
d
= 0.4 ·
2 m
2
· 1.23 kg/m
3
· (40 m/s)
2
2
F
d
= 0.4 ·=787.2 N
3936
2
kg · m
s
2
1 N =
1 kg · m
s
2
1 Pa=
1 bar = 1,000 hPa
1 N
1 m
2
1 W =
1 J
1 s
P (Pressure) =
F
1
: A
1
= F
2
: A
2
F
1
· L
1
= F
2
· L
2
Load · Load arm = Force · Force arm
F (Force)
A (Area)
P ==2= 2 Pa
10 N5 m
2
P == 200,000 Pa
100 N
0.0005 m
P =
= 16,000 Pa or 16 hPa or 1.6 bar
0.00025 m
Compressed air
The air-filled balloon has potential
energy too. You can drive a paddle
wheel turbine with it.
1
x
23
17
YOU WILL NEED
› Axle lock
› Washer
› Short frames
› Long axle
› Medium gear wheels
› Baseplate
› Turbine blades
› 1 Balloon
2
Water, Air, and Energy
CONSERVATION OF ENERGY
Not all of the potential energy of the
water is converted into hammer beats in
our gravity hammer experiment. Part of
it is used up by friction in the axle seats,
the pulley wheels, and the hammer
shaft. In this process, it is only lost as far
as the hammering is concerned. If you
add up the work from the friction and
the hammering, it equals the energy you
started with.
Power is work divided by time
Balloon
Work is measured independent of the time it takes to do the work. If
3
you do the same amount of work in less time, then you exert more
power doing it — whether its raising your hand in school or biking.
When you calculate power, time
becomes a factor. Power is the
relationship of the work
performed to the time needed to
do it:
The unit of measure for power P
is the watt (W):
8
19
17
11
6
5
In other words, the conservation of
energy law applies:
In addition to watts, kilowatts (1
kW = 1,000 W) and megawatts (1
mW = 1,000,000 W) are also used
as units of power. The engine of a
mid-sized car handles about 60
kW. A human can perform about
200 watts of physical work over
a long period of time, while a
cyclist with a bicycle can get to
1,500 watts fairly quickly.
In a closed mechanical
system, no energy is lost.
Energy can be neither created
nor destroyed. It can only be
converted. The sum of the
mechanical energy remains
the same (constant).
Page 6
CAR WITH HYDRAULIC BRAKES
Let‘s Build Models
Every vehicle should be able to brake. As
their main braking device, passenger cars
have a hydraulically activated foot brake.
Its hydraulic mechanism consists of a
cylinder that transfers force from the
brake pedal to the main cylinder. From
there, the braking force is transferred
equally by separate pathways to the
braking cylinders on the wheels. Big and
heavy vehicles, e.g. a tour bus or dredger,
have so-called servo brakes, which
amplify the braking force through a
pump.
This model is like the racing car model
(page 89) — but without the drive spring.
Test the hydraulic brake by pushing
against the car’s brake pedal (the front
pair of rods). Push the pedal down to
activate the brake. That pulls the rear pair
of rods down onto the tires. Water will
serve as the hydraulic fluid. You will see
in Experiments 1 and 2 (on pages 10 and
11) how to fill it without air bubbles.
> See Pages 10-11 and 20-22
YOU WILL NEED
› 8 Anchor pins 1
› 4 Joint pins 2
› 2 Shaft plugs 3
› 10 Axle locks 5
› 8 Washers 6
› 1 Short frame 8
› 4 Long rods 9
› 6 Short rods 10
› 4 Long axles 11
› 3 Medium axles 12
› 2 Medium pulleys 14
› 2 Large gear wheels 16
› 2 Small gear wheels 18
› 1 XL (extra long) axle 21
› 1 Rubber band (medium) 25
› 2 Wheels 28
› 2 Tire rings for pulleys 29
› 2 Hydraulic cylinders 42
› 1 Piece of narrow tubing 43
1
2
3
1011
42
4
1
1
9
2
12
42
12
5
43
5
6
5
10
1
65
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