UNIVERSITY OF WINDSOR Faculty of Engineering

FLUID MECHANICS I (85-233)

Experiment B: Bernoulli’s Principle Experiment (Revised 2014F)

OBJECTIVE:

• Demonstration of Bernoulli’s law • Measurement of pressure along the Venturi tube • Determination of flow rate factor

APPARATUS: • Venturi tube: The dimensions of the Venturi tube are given in Table 1.

Table 1: Dimensions of the Venturi tube at different measurement locations

Pointi Di [mm]

Ai [m2.10-4]

P1 28.4 6.33 P2 22.5 3.97 P3 14.0 1.54 P4 17.2 2.32 P5 24.2 4.60 P6 28.4 6.33

• 6 water pressure gauges for measuring the static pressure at 6-locations (see

label 10 of Figure1) • 1 overall water pressure gauge (see label 2 of Figure 1) for measuring the total

pressure (this gauge can be moved at different locations) • Volumetric tank to measure the volume flow rate • Stop watch

PROCEDURE:

1. Check that the water supply hose is connected (label 8, Figure 1). 2. Open discharge of HM150 (label 4). 3. Adjust the overall pressure probe (label 7) to a measuring location (start with

location 1. Adjustment is made by loosening compression gland (label 6) to allow movement. Be sure to tighten the gland after adjustment of pressure probe has been done.

4. Open both the inlet and the outlet cock. 5. Switch on pump and slowly open the main cock.

EXPERIMENT B – BERNOULLI’S PRINCIPLE EXPERIMENT GROUP #_______________ DATE:_______________

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6. Simultaneously set the inlet and outlet cocks to regulate water level in the pressure gauges such that neither the upper nor the lower range overshoots or undershoots.

7. After the pressure gauge fluctuation stops, record all the pressure gauge readings.

8. Determine the volumetric flow rate by collecting approximately 10 litre of water. 9. Take similar readings at a second, third, fourth and fifth locations. 10. Repeat the experiment for one more volumetric flow rate.

Figure 1 Venturi meter apparatus (HM150).

EXPERIMENT B – BERNOULLI’S PRINCIPLE EXPERIMENT GROUP #_______________ DATE:_______________

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DATA REDUCTION: a.) Bernoulli’s theorem

212

p V gzρ+ + = constant along a streamline

p = static pressure, V = velocity g = gravitational acceleration z = vertical displacement from a reference level ρ = density of water

Applying Bernoulli’s theorem between point 1 and 2 2 2

1 1 1 2 2 21 12 2

p V gz p V gzρ ρ+ + = + +

Since z1 = z2, 2 21 1 2 21 12 2

p V p Vρ ρ+ = + or 2 2

1 1 2 2

2 2p V p V

g gγ γ+ = +

Total (overall) pressure head: 2 2

1 1

2 2totalp V p Vh

g gγ γ= + = +

Static pressure head: 1static

phγ

= gγ ρ=

Dynamic pressure head 21

2dynVhg

=

b. ) Continuity equation 1 1 2 2 3 3 4 4 5 5 6 6AV AV AV AV AV AV Q= = = = = =

SAMPLE CALCULATIONS:

Applying Bernoulli’s Principle at Point 1

ρ=1000kg/m3 (approximate)

g=9.81m/s2

Time to collect 10L of fluid,

t=____________(s) Volumetric flow rate, Q=0.01/t

=_______________(m3/s)

Static and total heads at P1,

hstat=_______________(mm)

htotal=_______________(mm

)

Dynamic head at P1,

. 80dyn total statich h mm h= − −

hdyn=_______________(m)

Velocity measured at P1,

, .2. .meas dynV g h=

Vmeas=____________________

_(m/s)

EXPERIMENT B – BERNOULLI’S PRINCIPLE EXPERIMENT GROUP #_______________ DATE:_______________

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Calculated velocity at P1, 41033.6 −==

xQ

AQVcal =_________________________________(m/s)

EXPERIMENT B – BERNOULLI’S PRINCIPLE EXPERIMENT GROUP #_______________ DATE:_______________

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RESULTS: Repeat the experiment for one more volumetric flow rate and record the data in the

table below.

DATA SHEET

EXPERIMENT B – BERNOULLI’S PRINCIPLE EXPERIMENT GROUP #_______________ DATE:_______________

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RESULTS: a. Plot calculated and measured flow velocity (y-axis) at the corresponding

measurement points along the axis of the Venturi tube on the graph below.

b. Plot different head values at the corresponding measuring points along the axis

of the Venturi tube on the graph below.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6Measurement points on Venturi tube

Flow

vel

ocity

(m/s

)

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6Measurement points on Venturi tube

hsta

t, ht

otal, h

dyn (

mm

)

EXPERIMENT B – BERNOULLI’S PRINCIPLE EXPERIMENT GROUP #_______________ DATE:_______________

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QUESTIONS: 1. How do the velocity and head vary along the length of the venturi? Are there

maximum/minimum values?

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2. How closely does the experimental data match the theoretical data?

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3. What are the possible sources of error?

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GROUP MEMBERS: Printed Name Duties Signature