hm150.07 bernoulli's principle demonstrator
TRANSCRIPT
Equipment for Engineering Education
Instruction ManualHM150.07 Bernoulli’s Principle
Demonstrator
G.U.N.T. Gerätebau GmbHP.O. Box 1125D-22881 Barsbüttel • GermanyPhone (040) 670854-0Fax (040) 670854-42
Instruction Manual
Puplication No. 917.00007A15012 10/95
HM150.07 Bernoulli’s Theorem Demonstration Apparatus
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Contents
1 Unit description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Performance of experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
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
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1
1 Unit description
The HM150.07 is used to investigate Bernoulli’slaw.
The measurement object is a venturi tube with 6pressure measurement points.
The 6 static pressures are displayed on a boardwith 6 water pressure gauges.
The overall pressure can also be measured atvarious locations in the venturi tube and indicatedon a second water pressure gauge.
Measurement is by way of a probe which can bemoved axially with respect to the venturi tube. Theprobe is sealed by way of a compression gland.
Water is supplied either from the HM150 FluidMechanics Basic Module or from the laboratorymains.
The HM150 enables a closed water circuit to beconstructed.
Possible experiments:
- Demonstration of Bernoulli’s law
- Pressure measurements along venturi tube
- Determination of flow rate factor K
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1 Unit description 2
Components:
1
2
3
45 6
7
8
10
9
1 Assembly board
2 Single water pressure gauge
3 Discharge pipe
4 Outlet ball cock
5 Venturi tube with 6 measurement points
6 Compression gland
7 Probe for measuring overall pressure (can be moved axially)
8 Hose connection, water supply
9 Ball cock at water inlet
10 6-fold water pressure gauge (pressure distribution in venturi tube)
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1 Unit description 3
2 Performance of experiment
- Arrange the experimentation set-up on theHM150 such that the discharge routes thewater into the channel
- Make hose connection between HM150 andunit
- Open discharge of HM150
- Set cap nut [1] of probe compression glandsuch that slight resistance is felt on movingprobe
- Open inlet and outlet ball cock
- Close drain valve [2] at bottom of single wa-ter pressure gauge
- Switch on pump and slowly open main cockof HM150
- Open vent valves [3] on water pressure gau-ges
- Carefully close outlet cock until pressure gau-ges are flushed
- By simultaneously setting inlet and outletcock, regulate water level in pressure gau-ges such that neither upper nor lower rangelimit [4,5] is overshot or undershot
- Record pressures at all measurement points.Then move overall pressure probe to corre-sponding measurement level and note downoverall pressure
- Determine volumetric flow rate. To do so,use stopwatch to establish time t required forraising the level in the volumetric tank of theHM150 from 20 to 30 litres
1
2
3
4
5
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2 Performance of experiment 4
ATTENTION! The experimental set-up shouldbe arranged absolutely plane to avoid falsifica-tion of measurement results (use of spirit levelrecommended).
For taking pressure measurements, the volumetrictank of the HM150 must be empty and the outletcock open, as otherwise the delivery head of thepump will change as the water level in the volume-tric tank increases.
This results in fluctuating pressure conditions. Aconstant pump delivery pressure is important withlow flow rates to prevent biasing of the measure-ment results.
The zero of the single pressure gauge is 80 mmbelow that of the 6-fold pressure gauge. Allowanceis to be made for this fact when reading the pres-sure level and performing calculations.
Both ball cocks must be reset whenever the flowchanges to ensure that the measured pressuresare within the display ranges.
80 mm
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2 Performance of experiment 5
3 Assessment of experiment
The measured values are to be compared to Bernoulli’s equation.
Bernoulli’s equation for constant head h:
p1ρ +
w1 2
2 = p2ρ +
w2 2
2 = const.
Allowance for friction losses and conversion of thepressures p1 and p2 into static pressure heads h1and h2 yields:
h1 + w1
2
2g = h2 + w2
2
2g + hv
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
ρ: Density of medium = constant for incompressible fluids such as water
hv Pressure loss head
Condition 1 Condition 2
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3 Assessment of experiment 6
The mass flow is constant in closed systems.
m 1.
= m 2.
Given m .
= V .
⋅ ρ :
V1.
⋅ ρ = V2.
⋅ ρ
V1.
= V2.
Given V .
= A ⋅ w :
A1 ⋅ w1 = A2 ⋅ w2 = V .
= const.
m1.
m2.
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3 Assessment of experiment 7
3.1 Velocity profile in venturi tube
The venturi tube used has 6 measurement points.
The table below shows the standardised refer-ence velocity w
__ . This parameter is derived from
the geometry of the venturi tube.
w__
i = A1Ai
Point i
Di[mm]
A
[m2 ⋅ 10−4]
referencevelocity 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
Multiplying the reference velocity values with astarting value, the student can calculate the theo-retical velocity values wcalc at the 6 measuringpoints of the venturi tube.
At constant flow rate, the starting value for calcu-lating the theoretical velocity is found as:
w1 = V.
A1
The results for the calculated velocity wcalc can befound in the following table.
654321
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3 Assessment of experiment 8
The following values were determined for variousflow rates:
i h1[mmWS]
h2[mmWS]
h3[mmWS]
h4[mmWS]
h5[mmWS]
h6[mmWS]
t für10 l
V .
[l/s]
hstat. 280 269 120 195 242 250
36,29 0,275
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
39,0 0,256
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
60,0 0,166
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
The table makes allowance for the following rela-tionships.
Calculation of dynamic pressure head:
hdyn. = htot.− 80mm − hstat.
80 mm must be subtracted, as there is a zero-pointdifference of 80 mm between the pressure gau-ges.
The velocity wmeas was calculated from the dyna-mic pressure
wmeas. = √2 ⋅ g ⋅hdyn.
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3 Assessment of experiment 9
Graphical representation
The graph below illustrates the measured andcalculated velocity profile along the venturi tube ata flow rate of 0,275 l/s.
The deviations can be attributed to inexact measurements.
Measured
Calculated
0,2
0,6
1,0
1,4
1,8
w [m/s]
1 2 3 4 5 6
Measurement points i on venturi tube
Flo
w v
eloc
ity
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3 Assessment of experiment 10
3.2 Pressure Distribution Venturi Tube
Graphical representation
The pressure changes in the venturi tube can berepresented in a graph directly:
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 slightoverall pressure loss in the venturi tube.
0
50
100
150
200
250
300
350
400
1 2 3 4 5 6
Pressure Distribution Venturi Tube
Measuring Point
hdyn
in m
m W
C
htotal
hstat
hdyn
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3 Assessment of experiment 11
3.3 Determination of Flow Rate Factor
A venturi tube can be used for flow rate measure-ments. In comparison with orifice or nozzle, thereis a far more smaller pressure loss during meas-urements of flow rate. The pressure loss ∆p be-tween largest and smallest diameter of the tube isused as measure for the flow rate:
V. = K ⋅ √∆p
The flow rate factor K is generally made availablefor the user by the manufacturer of a venturi tube.If the flow rate factor is unknown, it can be deter-mined from the pressure loss ∆p::
K = V.
√∆p
The following table shows the pressure loss forvarious flow rates as well as the flow rate factor K.
The pressure loss is read off from the six -tubemanometer in mm water column and set in theequation as bar. The flow rate can be used withunit l/s.
∆p::
V. =0,275 l/s V
. =0,256 l/s V
. =0,166 l/s
MeasuringPoint
∆p [mm WC]
K
[l
s ⋅√bar ]
∆p [mm WC]
K
[l
s ⋅√bar ]
∆p [mm WC] K
[l
s ⋅√bar ]
1 160 2,1 143 2,1 65 2,13
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3 Assessment of experiment 12
4 Technical Data
Water multi tube manometer6-fold: 300 mm H2O
Total pressure tube manometer
1-fold: 530 mm H2O
Venturi meternom. diameter: 28.4 mmmin. diameter: 14 mm
Overall dimension(L x W x H): 1100 x 640 x 900 mm
Weight: 40 kg
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4 Technical Data 13