Fluid Mechanics Laboratory Manual

Cairo University Faculty of Engineering Irrigation and Hydraulics Department

Fluid Mechanics 2nd Year Civil Engineering 2010 - 2011

Fluid Mechanics Laboratory Manual

Irrigation and Hydraulics Department 2010 – 2011

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Table of Contents Description of the Hydraulic Bench ………………………………………………… 3 1.

Weir Experiment (Rectangular and Triangular)…………….……………………….. 5

2.

Impact of Jet ……………………..…………………………….. .……………………9

3.

Flow through Sharp Edged Orifice ………………………………………………….13

4.

Bernoulli’s Theorem Demonstration ………………………………………………..18

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The Hydraulics Bench The standard Hydraulics Bench is used for all the laboratory experiments carried out during this course. The Bench has a closed water circulating system to facilitate mobility. Water is stored in an enclosed tank at the bottom of the bench then pumped up to the experimental setup situated on top of the bench from which water flows into the upper tank. The upper tank has a drain controlled by a plug to collect and gauge the water in the upper tank after which water is drained to the bottom tank. The volume of water collected in the upper tank (in liters) can be measured using the graduated scale fixed at the side of the Hydraulics Bench. The switch of the water pump and the control valve that regulates the amount of water that flows to the experimental setup are at the front side of the Hydraulics Bench (Please see the attached photographs).

Pump Switch

Scale of the volume (liter)

Control Valve

Plug and sink to drain water to the lower tank Upper tank of the bench

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Scale of the volume (liter)

Pump Switch

Control Valve

Plug and sink to drain water to the lower tank Upper tank of the bench

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1. Weir Experiment (Rectangular and Triangular)

Objectives of the Experiment 1. To demonstrate the flow over different weir types. 2. To calculate the coefficient of discharge for different weir types. 3. To study the variation and dependence of the relevant parameters.

Theory For the rectangular weir:

For the triangular weir:

where Cd B H θ g

= = = = =

8 θ  . tan . 2 g .H 2 15 2 5

3

2 Q = C d . .B. 2g .H 2 3

Q = Cd .

Coefficient of discharge width of the rectangular weir (3 cm) head above the weir crest or apex angle of the triangular weir acceleration of gravity

Experimental Setup

Point Gauge Stilling Baffle Open Channel

Weir Plate (V-notch)

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1. The rectangular or triangular weir plate is attached to the regular Hydraulic Bench as shown in the photographs. 2. A stopwatch, a hook or a point gauge are also needed with the experiment.

Procedures and Readings 1. Make sure that the Hydraulic Bench is leveled. 2. Set the Vernier on the point gauge to a datum reading by placing the tip of the gauge on the crest or the apex of the weir. Take enough care not damage the weir plate and the point gauge. 3. Put the point gauge half way between the stilling baffle plate and the weir plate. 4. Allow water to flow into the experimental setup and adjust the minimum flow rate by means of the control valve to have atmospheric pressure all around water flowing over the weir. Increase the flow rate incrementally such that the head above the weir crest increases around 1 cm for each flow rate increment 5. For each flow rate, wait until steady condition is attained then measure and record the head (H) above the weir. 6. For each flow rate, measure and record the initial and final volumes in the collecting tank and the time required to collect that volume. For each flow rate, take 3 different readings of the volumes and time and record the averages.

Calculations and Results Interpretation A. Rectangular weir: Fill the following table of observations Reading

Crest level (C.L.) (mm)

Water level (W.L.)(mm)

Initial volume (I.V.) (liter)

1 2 3 4 5

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Final volume (F.V.) (liter)

Time (T) (sec)



Fill the following table of results Reading

Volume = F.V.-I.V. (liter)

H = C.L.W.L. (cm)

Time (sec)

Q= volume/time

Log Q

Log H

H1.5

Cd

(cm3/s)

1 2 3 4 5 Plot Q against H, Q against H1.5, log Q against log H, Cd against H, and obtain the Cd from the slopes of the two linear graphs. Compare the three obtained values of the Cd

B. Triangular weir: Fill the following table of observations Reading

Crest level (C.L.) (mm)

Water level (W.L.)(mm)



Time (T) (sec)

1 2 3 4 5 Fill the following table of results Reading


H = C.L.W.L. (cm)

Time (sec)

Q= volume/time

Log Q

Log H

H2.5

Cd

(cm3/s)

1 2 3 4 5 Plot Q against H, Q against H5/2, Log Q against Log H, Cd against H, and obtain the Cd from the slopes of the two linear graphs. Compare the three obtained values of the Cd

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Suggestions for Conclusions and Comments 1. Is Cd constant? Give comments. 2. Can the Q-H relation be described by an empirical formula? If so, assume the relation is in the form of Q = kH n and find the constants k and n.

Example (V-notch experiment)

H = C.L. - W.L. (cm) 2 2.3 2.5 2.8

volume (lit) 5 5 5 5

time (sec.) 76 53 41 32

Q (cm3/s) 65.79 94.34 121.95 156.25

2.5

H 5.66 8.02 9.88 13.12

2/5

Q 5.34 6.16 6.83 7.54

180.00 160.00

slope = 11.974

140.00 120.00 Q

100.00 80.00 60.00 40.00 20.00 0.00 0.00

2.00

4.00

6.00 H^2.5

θ  Cd = slope*15/(8* tan  . 2 g ) = 0.507 2

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8.00

10.00

12.00

14.00



2. Impact of Jet Objective of the Experiment To demonstrate and investigate the validity of theoretical expressions for the calculation of the force exerted by a jet on objects of various shapes.

Theory From momentum principle, Fy = ρQ( v − v. cos θ)

where

•

For flat plate (90º),

•

For 120º plate,

•

For hemispherical target 180º,

FLAT PLATE

90

v=

Q A

Q2 A Q2 Fy = 3ρ 2A Q2 Fy = 2ρ A

Fy = ρ

HEMISPHERE

120 DEG CONE

o

Experimental Setup 1. The impact of jet apparatus is placed above the regular Hydraulic Bench as shown in the photographs. 2. A stopwatcher.

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Weight pan Water bubble level

Pointer (spirit level)

Target Plate From Pump

Glass housing

Nozzle

Weights

Plates with different shapes

Procedures and Readings 1. Remove the stop plate and transparent casing to measure the nozzle diameter and place the flat plate (90º) on the rod attached to the weight pan. Then, reassemble the apparatus. 2. Connect the inlet pipe of the apparatus to the outlet of the Hydraulic Bench. 3. Level the base of the apparatus using the bubble balance. 4. Screw down the top plate to datum on the spirit level. 5. Adjust the level gauge to suit datum on the weight pan. 6. Add masses to the weight pan. Allow water to flow in the experiment and adjust the flow by the control valve of the Hydraulic Bench so that the pan will be re-adjacent to the level gauge. 7. Before taking readings the weight pan should be oscillated upwards and downwards and rotated to minimize the effect of friction. 8. Take the readings of the initial and final volumes and the time of accumulation. 9. Record the masses on the weight pan. 10. Repeat the experiment for different masses on the weight pan.

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11. Repeat the previous steps with different shapes of plates (120º and the hemispherical target).

Calculations and Results Interpretation For each plate, fill the following table of observations Reading

Mass on weight pan M (gm)



Time (T) (sec)

1 2 3 4 5 Nozzle Diameter = 8 mm g = 9.81 m/s2

Fill the following table of results Reading

Mass on weight pan M (gm)


Time (sec)

1 2 3 4 5 Plot mass M on weight pan with Q2 From the analysis, verify that the slope of the graphs should be: ρ Flat plate = gA ρ 120º plate = 1.5 gA ρ Hemispherical target = 2 gA Calculate the Coefficient of Impact = (Fact / Fcalculated)

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Q= volume/time

(cm3/s)

Q2



Suggestions for Conclusions and Comments 1. Comment on the coefficient of impact. 2. Comment on the results of the computed slope and the shape of the target plate.

Example (flat plate)

m (gm) 280 230 180 130

V (lit) 5 5 5 5

T (sec) 13 14 16 20

Q (cm3/s) 384.6154 357.1429 312.5 250

Q

2

147929 127551 97656.25 62500

300 250

solpe = 0.0019

m

200 150 100 50 0 0

20000

40000

60000

80000 Q^2

ρ =0.0202 gA

slope = 0.0019

12

100000

120000

140000

160000



3. Flow through Sharp Edged Orifice. Objective of the Experiment 1. To study the path of water jets issuing from orifices. 2. To determine the coefficients of discharge, velocity and contraction from a sharp-edged circular orifice. 3. To study the variation and dependence of the relevant parameters.

Theory The coefficient of discharge Cd is the ratio of the actual discharge Q act to the theoretical discharge Qth. The theoretical discharge is given by the following relationship where A is the area of the orifice and H is the total head on the orifice centerline and the actual discharge can be measured.

Q th = A 2gH

&

Cd =

Qa < 1.0 Q th

The Path of the jet from the orifice is given by the following equation where x is the horizontal distance, y is the vertical distance and v is the flow velocity from the orifice.

x = vact t

&

y = 0 . 50 g y = 0.50 g

cv =

x

y = 0.50 gt 2

2

v 2 act x2

2

c v * 2 gH x

2* y* H

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Experimental Setup

Scale

Paper

Constant head tank Pointers (thin pins)

Metal piece for over flow

Orifice

The regular Hydraulic Bench is used in this experiment 1. The orifice plate apparatus is placed above the regular Hydraulic Bench as shown in the photographs. 2. A stopwatch is needed. 3. The adjustable stainless steel overflow pipe near the top of the tank is used to adjust the level of water in the tank.

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Procedures and Readings 1. Turn on the pump of the hydraulic bench and allow water into the constant head tank to build up above the orifice. Wait until steady condition is achieved. 2. You can control the level of the water into the constant head tank by pulling up and down the adjustable stainless steel overflow pipe as shown in the photograph. 3. Measure the head (H) above the orifice using the graduated scale. 4. By setting the thin pins so that they just touch the issuing water jet, draw the path of the water jet on the given graph paper. 5. Measure and record the initial and final volumes and the time of accumulation for each reading of head (H). 6. Repeat the previous steps for at least four more different heads (H) by changing the position of the adjustable stainless steel overflow pipe.

Calculations and Results Interpretation For each reading of head (H), fill the following table of observations Initial

Final

Point(1) Point(2) Point(3) Point(4) Point(5) Point(6) H (cm) volume volume (liter) X(cm) Y(cm)

1. 2. 3. 4. 5. 6. 7. 8.

Calculate the theoretical flow rate using the measured head and the area of the orifice. Calculate the actual flow using the volume and time recorded. Calculate the coefficient of discharge Cd. draw x2-y relationship and determine the coefficient of velocity Repeat the above mentioned steps for various values of measured head Plot Qa against (H)0.5 Comment on the graphs and on the slope of each graph. Is the coefficients of the orifice is constant with change of water head

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(liter)



Example point 1 X (cm) Y (cm) 2 X 2 0.5 Cv = (X /4YH)

5 0.2 25 0.88

point 2 10 0.7 100 0.94

point 3 15 1.5 225 0.97

point 4 20 1.8 400 1.18

point 5 25 4.2 625 0.96

point 6 30 5.7 900 0.99

H (mm)

V (lit)

400

7

T (sec) 150

Dorifice = 6mm vth = (2gH)0.5 =

280.14

cm/sec

Qact = V/T = Qth = aorifice * vth =

46.67 79.17

cm3/s cm3/s

Cd = Qact/Qth =

0.589

2

0.5

Cv = (X /4YH) 2= SLOPE = 4HCv Cv = Cc = Cd/Cv =

158.28 0.995 0.592

1000 900 800

slope = 158.28 700

X^2

600 500 400 300 200 100 0 0

1

2

3

4

Y

17

5

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4. Bernoulli’s Theorem Demonstration Objective of the Experiment 1. To demonstrate the variation of the pressure along a converging-diverging pipe section. 2. To verify the Bernoulli’s Theorem.

Theory   v2 p + + Z  = constant. For ideal flow at any section on the pipe,    2 g ρg In the experimental setup, the pipe is horizontal (i.e. Z = constant). Therefore along the pipe, v2 p + = constant 2 g ρg

Experimental Setup

Air inlet Control Valve

Water Manometer

From the Pump To the Venturi Air bubble

Glass Venturimeter

The Bernoulli’s experimental setup is placed on the top of the regular Hydraulic Bench.

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Pitot Tube



Procedures 1. Level the Bernoulli’s experimental apparatus on the Hydraulic Bench by adjusting the screw legs. 2. Switch on the pump and open the flow control valve to fill the entire apparatus and manometers with water. Ensure that no air is entrapped in the apparatus or any of the manometers by opening the air valve at the right end of the air chamber connecting the top ends of the manometers. Make sure to close the air valve again. 3. Adjust the flow rate into the experiment by the flow control value in the apparatus. 4. To make visible the water levels in the manometers, connect and work the hand air pump at the air inlet (shown in the photograph) to raise the air pressure in the air chamber, thus pushing the manometer columns down into the glass tubes. 5. Carefully adjust both flow control valves in the apparatus and in the Hydraulic Bench to provide the combination of flow rate and pressure within the pipe such that the pressure difference between the highest and the lowest manometer levels is reasonable. 6. Observe the variation of the scale readings of the water levels in each manometer tube. 7. Push the stainless steel probe (pitot-tube) at the right end of the horizontal transparent section of the pipe into the tapered portion of the pipe. Position its end at stations adjacent to the manometer openings in the pipe one station at a time. For each position, observe the corresponding scale reading of the manometer to the probe. Compare the pitot-tube reading to the manometer reading connected to the same position. 8. Repeat the previous steps with different flow rates at high and low static pressure for different combinations of valve opening.

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