hm150.07 bernoulli's principle demonstrator

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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3.1 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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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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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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3.2 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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3.3 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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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

hm150.07 bernoulli's principle demonstrator

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