Equipment for Engineering Education
Instruction Manual
HM150.07 Bernoulli’s Principle
Demonstrator
G.U.N.T. Gerätebau GmbH
P.O. Box 1125
D-22881 Barsbüttel • Germany
Phone (040) 670854-0
Fax
(040) 670854-42
All rights reserved G.U.N.T. Gerätebau GmbH, Barsbüttel
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
Instruction Manual
Puplication No. 917.00007A15012
10/95
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
Contents
1 Unit description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Performance of experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
All rights reserved G.U.N.T. Gerätebau GmbH, Barsbüttel
3 Assessment of experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1
Velocity Profile Venturi Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2
Pressure Distribution Venturi Tube . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3
Determining the Flow Rate Factor . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Technical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
1
Unit description
The HM150.07 is used to investigate Bernoulli’s
law.
The measurement object is a venturi tube with 6
pressure measurement points.
The 6 static pressures are displayed on a board
with 6 water pressure gauges.
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The overall pressure can also be measured at
various locations in the venturi tube and indicated
on a second water pressure gauge.
Measurement is by way of a probe which can be
moved axially with respect to the venturi tube. The
probe is sealed by way of a compression gland.
Water is supplied either from the HM150 Fluid
Mechanics Basic Module or from the laboratory
mains.
The HM150 enables a closed water circuit to be
constructed.
Possible experiments:
1 Unit description
-
Demonstration of Bernoulli’s law
-
Pressure measurements along venturi tube
-
Determination of flow rate factor K
2
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
Components:
10
1
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2
7
8
3
9
5
6
4
1 Assembly board
6 Compression gland
2
3 Discharge pipe
7 Probe for measuring overall pressure
(can be moved axially)
4 Outlet ball cock
8 Hose connection, water supply
5 Venturi tube with
6 measurement points
9 Ball cock at water inlet
1 Unit description
Single water pressure gauge
10 6-fold water pressure gauge
(pressure distribution in venturi tube)
3
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
All rights reserved G.U.N.T. Gerätebau GmbH, Barsbüttel
2
Performance of experiment
1
-
Arrange the experimentation set-up on the
HM150 such that the discharge routes the
water into the channel
-
Make hose connection between HM150 and
unit
-
Open discharge of HM150
-
Set cap nut [1] of probe compression gland
such that slight resistance is felt on moving
probe
-
Open inlet and outlet ball cock
-
Close drain valve [2] at bottom of single water pressure gauge
-
Switch on pump and slowly open main cock
of HM150
-
Open vent valves [3] on water pressure gauges
-
Carefully close outlet cock until pressure gauges are flushed
-
By simultaneously setting inlet and outlet
cock, regulate water level in pressure gauges such that neither upper nor lower range
limit [4,5] is overshot or undershot
-
Record pressures at all measurement points.
Then move overall pressure probe to corresponding measurement level and note down
overall pressure
-
Determine volumetric flow rate. To do so,
use stopwatch to establish time t required for
raising the level in the volumetric tank of the
HM150 from 20 to 30 litres
3
2
4
5
2 Performance of experiment
4
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
ATTENTION! The experimental set-up should
be arranged absolutely plane to avoid falsification of measurement results (use of spirit level
recommended).
All rights reserved G.U.N.T. Gerätebau GmbH, Barsbüttel
For taking pressure measurements, the volumetric
tank of the HM150 must be empty and the outlet
cock open, as otherwise the delivery head of the
pump will change as the water level in the volumetric tank increases.
This results in fluctuating pressure conditions. A
constant pump delivery pressure is important with
low flow rates to prevent biasing of the measurement results.
80 mm
The zero of the single pressure gauge is 80 mm
below that of the 6-fold pressure gauge. Allowance
is to be made for this fact when reading the pressure level and performing calculations.
Both ball cocks must be reset whenever the flow
changes to ensure that the measured pressures
are within the display ranges.
2 Performance of experiment
5
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
3
Assessment of experiment
The measured values are to be compared to
Bernoulli’s equation.
Bernoulli’s equation for constant head h:
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p1 w12 p2 w22
ρ + 2 = ρ + 2 = const.
Allowance for friction losses and conversion of the
pressures p1 and p2 into static pressure heads h1
and h2 yields:
w2
w2
h1 + 2g1 = h2 + 2g2 + hv
Condition 1
Condition 2
p1:
Pressure at cross-section A1
h1:
Pressure head at cross-section A1
w1: Flow velocity at cross-section A1
p2:
Pressure at cross-section A2
h2:
Pressure head at cross-section A2
w2: Flow velocity at cross-section A2
3 Assessment of experiment
ρ:
Density of medium = constant for
incompressible fluids such as water
hv
Pressure loss head
6
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
The mass flow is constant in closed systems.
.
.
m1 = m2
Given
.
m1
.
.
m =V ⋅ρ
:
.
m2
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.
.
V1 ⋅ ρ = V2 ⋅ ρ
.
.
V1 = V2
Given
.
V =A⋅w
:
.
A1 ⋅ w1 = A2 ⋅ w2 = V = const.
3 Assessment of experiment
7
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
3.1
Velocity profile in venturi tube
The venturi tube used has 6 measurement points.
1
2 3
4
5
6
The table below shows the standardised refer__
ence velocity w . This parameter is derived from
the geometry of the venturi tube.
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__
A
wi = A1
i
Point
i
Di
[mm]
[m ⋅ 10 ]
reference
__
velocity w
1
28,4
6,33
1
2
22,5
3,97
1,59
3
14,0
1,54
4,11
4
17,2
2,32
2,72
5
24,2
4,60
1,37
6
28,4
6,33
1
A
2
−4
Multiplying the reference velocity values with a
starting value, the student can calculate the theoretical velocity values wcalc at the 6 measuring
points of the venturi tube.
At constant flow rate, the starting value for calculating the theoretical velocity is found as:
.
V
w1 = A
1
The results for the calculated velocity wcalc can be
found in the following table.
3 Assessment of experiment
8
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
All rights reserved G.U.N.T. Gerätebau GmbH, Barsbüttel
The following values were determined for various
flow rates:
i
h1
[mmWS]
h2
[mmWS]
h3
[mmWS]
h4
[mmWS]
h5
[mmWS]
h6
[mmWS]
hstat.
280
269
120
195
242
250
htotal
369
369
370
364
359
352
hdyn.
9
20
170
89
37
22
wmes.
0,420
0,626
1,826
1,320
0,852
0,594
wcalc.
0,435
0,692
1,785
1,185
0,592
0,4355
hstat.
205
196
62
128
166
173
htotal
293
294
292
288
280
276
hdyn.
8
18
150
80
34
23
wmes.
0,396
0,594
1,715
1,250
0,816
0,671
wcalc.
0,404
0,644
1,662
1,100
0,556
0,404
hstat.
195
191
130
158
173
176
htotal
276
275
273
271
268
264
hdyn.
1
4
57
33
15
8
wmes.
0,140
0,280
1,057
0,800
0,520
0,396
wcalc.
0,262
0,418
1,073
0,715
0,362
0,262
t für
10 l
.
V
[l/s]
36,29
0,275
39,0
0,256
60,0
0,166
The table makes allowance for the following relationships.
Calculation of dynamic pressure head:
hdyn. = htot.− 80mm − hstat.
80 mm must be subtracted, as there is a zero-point
difference of 80 mm between the pressure gauges.
The velocity wmeas was calculated from the dynamic pressure
wmeas. = √

2 ⋅ g ⋅hdyn
.
3 Assessment of experiment
9
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
Graphical representation
The graph below illustrates the measured and
calculated velocity profile along the venturi tube at
a flow rate of 0,275 l/s.
The deviations can be attributed to inexact
measurements.
Flow velocity
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w [m/s]
1,8
Measured
1,4
1,0
0,6
Calculated
0,2
1
2
3
4
5
6
Measurement points i on venturi tube
3 Assessment of experiment
10
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
3.2
Pressure Distribution Venturi Tube
Graphical representation
The pressure changes in the venturi tube can be
represented in a graph directly:
Pressure Distribution Venturi Tube
400
350
htotal
hstat
250
hdyn in mm WC
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300
200
150
100
hdyn
50
0
1
2
3
4
5
6
Measuring Point
The graph shows, that the equation
hdyn. = htot.− 80mm − hstat.
is fullfilled at every point in the venturi tube.
Furthermore, it becomes clear, that there is a slight
overall pressure loss in the venturi tube.
3 Assessment of experiment
11
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
3.3
Determination of Flow Rate Factor
A venturi tube can be used for flow rate measurements. In comparison with orifice or nozzle, there
is a far more smaller pressure loss during measurements of flow rate. The pressure loss ∆p between largest and smallest diameter of the tube is
used as measure for the flow rate:
∆p::
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.
V = K⋅√
∆ p
The flow rate factor K is generally made available
for the user by the manufacturer of a venturi tube.
If the flow rate factor is unknown, it can be determined from the pressure loss ∆p::
.
V
K = ∆p

√
The following table shows the pressure loss for
various flow rates as well as the flow rate factor K.
.
V =0,275 l/s
Measuring ∆p
K
l
Point
[mm WC]
[
s ⋅ bar

√
1
3
160
2,1
.
V =0,256 l/s
∆p
K
]
[mm WC]
143
[
.
V =0,166 l/s
∆p [mm WC] K
l
]
s ⋅√
bar


2,1
[
65
l
]
s ⋅√
bar


2,1
The pressure loss is read off from the six -tube
manometer in mm water column and set in the
equation as bar. The flow rate can be used with
unit l/s.
3 Assessment of experiment
12
HM150.07 Bernoulli’s Theorem
Demonstration Apparatus
4
Technical Data
Water multi tube manometer
6-fold:
300 mm H2O
Total pressure tube manometer
1-fold:
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Venturi meter
nom. diameter:
min. diameter:
Overall dimension
(L x W x H):
Weight:
4 Technical Data
530 mm H2O
28.4 mm
14 mm
1100 x 640 x 900 mm
40 kg
13