Bernoulli-lab - Week3 PDF

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Faculty of Engineering Engineering Thermofluids Bernoulli’s Principle Laboratory INTRODUCTION: The Venturi meter shown in Figure 1 is used to measure the flow speed in a pipe. If the cross-sectional areas A1 and A2 and the difference in height, h, of the liquid levels in the two locations are known the flow speed, V, can be determined using Bernoulli’s equation. We are assuming that the flow is steady, incompressible and has negligible internal friction (inviscid). Hence we can use Bernoulli’s equation given by 1 Eq. (1) p+ ρV 2+ ρgz=¿ Constant 2 Here, p = pressure (Pa), V = velocity (m/s) g = gravitational acceleration (m/s2) z = vertical location (m)  = fluid density (water = 1000 kg/m3) We apply Eq. 1 to the wide section (Point 1) and narrow section (Point 2, the throat) of the pipe. 1 1 2 2 p1+ ρV 1 +ρg z 1= p2 + ρV 2 + ρg z 2 Eq. (2) 2 2 We also notice that point 1 and point 2 have the same vertical coordinates (elevation) z1 = z2 hence 1 1 1 p1 −p 2= ρ (V 22−V 12) p1   V12  p2   V22 2 2 2 or Eq. (3) Using, Continuity equation A 1 V 1=A 2 V 2 , the flow speed at point 2 is Substituting this and rearranging, we get

(( ) )

A1 2 1 p1 −p 2= ρV 21 −1 A2 2 p −p The pressure difference 1 2

is also equal to

V 2=

( )

A1 V A2 1

.

Eq. (4)

ρgΔh . Substituting this in Eq. 4 and solving

for V1 we get

V 1=

√

2 gΔh 2 ( A 1 / A 2) −1

OBJECTIVES:  To measure the of flow rate (Q)  To measure the pressure across the Venturi meter  To apply Bernoulli’s principle  To explain the likely source of any error.

Eq. (5)

DATE:______________ PROCEDURE: (should we have been face-to-face, the following steps would have been followed) 1. Check that the water supply hose is connected (label 8, Figure 2). 2. Open discharge of HM150 (label 4). 3. Open both the inlet and the outlet cock. 4. Switch on pump and slowly open the main cock. 5. Simultaneously set the inlet and outlet cocks to regulate water label in the pressure gauges such that neither the upper nor the lower range overshoots or undershoots. 6. After the pressure gauge fluctuation stops, record all the pressure gauge readings. 7. Determine the volumetric flow rate by collecting 10 litres of water.

Figure 2. Venturi meter apparatus (HM150). 8. Watch the following video from University of Texas Arlington for a better understanding: https://www.youtube.com/watch?v=Qlie8g_YYPc. The same apparatus is used at the University of Windsor. DATA SET: For a given flow rate: Time to collect 10L of water Manometer readings Manometer readings at (s) at P1(mm) P2(mm) Run 1 Run 2 Record the cross sectional areas A 1 = ____________m2 at P1 and A2 = ____________m2 at P2, respectively. Note: the data set is provided on the last page of this lab write-up 2

DATE:______________

Printed Name

Signature

For all questions listed below, write the final answers with units in the box provided. Show all of your work to get a full credit. 1. Using the manometer readings, determine the difference, 2. Record the value as the average of Run 1 and Run 2.

Δh

in meters for Runs 1 and

2. Determine the pressure difference between P1 and P2 in Pascals for Run 1 and Run 2. Record the value as the average of Run 1 and Run 2. Assume values of  = 1000kg/m3 (water) and g = 9.81m/s2

3. Apply Bernoulli’s equation to determine the velocity at station 1 (V1) in m/s of the Venturi meter for Run 1 and Run 2. Record the value as the average of Run 1 and Run 2.

3

DATE:______________ 4. Calculate the volumetric flow rate Q in m3 /s using that Q = (10 L of water)/t for Run 1 and Run 2. Record the value as the average of Run 1 and Run 2.

5. Using the mass conservation and the measured flow rate Q, calculate the velocity at station 1 for Run 1 and Run 2. Record the value as the average of Run 1 and Run 2.

6. Calculate the error between the calculated velocity in Question 3 with the actual velocity based on the volumetric flow rate, Q. Discuss the meaning of your error and the possible sources.

velocity based on Q-velocity based on Bernoulli's | % error=| velocity based on Q

4

DATE:______________ DATA COLLECTION SHEET: The following experimental data should be used to complete the lab report. Two runs are repeated for a given flow rate.

Run 1 Run 2

Time to collect 10L of water (s) 74.6 73.6

Manometer readings at P1(mm) 229 230

Manometer readings at P2(mm) 185 189

The cross sectional areas at P1 and P2 are A1 = 6.33 cm2 and A2 = 1.54 cm2, respectively. Take the density of water at 20C.

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