Fluid Prac

FLUID MECHANICS LABS 2013/2014

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F16/1334/2010 Njoroge Kagwi Maurice

DEPARTMENT OF CIVIL AND CONSTRUCTION ENGINEERING

HYDRAULICS LABORATORY

1.VENTURI FLUME EXPERIMENT

INTRODUCTION

Flumes are one of the many types of engineering hydraulic structures extensively used in

hydraulics to control, regulate and measure flow in channels.

Equations of flow are derived from the energy equation and continuity.

Objective

To confirm the expression for the discharge through venture flume

Q=Cd √

(H+

) ] n

And to obtain the values of Cd, and n

Where,

Q is discharge


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Cd is the discharge coefficient

b the throat width

g the gravitational pull

H the head of flow

V the velocity

n = 3/2

APPARATUS

Stop watch, vernier callipers, venture flumes in channels, pumps

METHOD

The pump was started filling the channel tank to overflow the gate.

This was to ensure steady and uniform flow conditions were created.

The bottom of the channel was then read using the vernier scale installed in the machine

and recorded as the datum, z.

The gate was raised to a maximum allowing maximum height of flow in channel and the

height of water surface in channel before the flume recorded as h1.

Volume collected and time taken was recorded to determine discharge.

This was repeated for 9 levels of the gate valve (hence 9 normal depths of flow.)

The width of channel, b, before the flume and after the flume were measured using the

vernier callippers and the diameter of discharge tank measured using the tape measure.

RESULTS

FLUME 1

Widths of channel, b1 and b2=6.370 cm and 6.424 cm respectively.

Average width of channel =

6.397 cm

Diameter of discharge tank =38.60 cm

DATUM: bottom of channel=5.80 cm


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initial height, h1 Time, sec y(depth)= s -5.8(datum)

height in tank,cm

6.5 9.69 0.10412 19.7

10 9.1 0.09708 16.1

9.75 7.95 0.09 10.29

8.9 10.26 0.07824 12.9

8.4 13.58 0.0715 14.6

9.2 15.21 0.06408 13.7

8.8 13.22 0.06231 11.5

8.3 14.34 0.05839 11.2

ANALYSIS AND COMPUTATION OF DATA

GRAPH OF LOG Q AGAINST LOG 2/3 (H+V2/2g)

Time, s y(depth)= s-5.8

height in tank, cm

volume, cm3

Q = Vo l/time m3/s

velocity,v, m/s

V2/2g y+v2/2g log q Log (2/3(y+v2/2g)

9.69 0.10412 19.7 23053.18 0.237906877 2.033023736 0.210662 0.314782 -0.62359 -0.6780816

9.1 0.09708 16.1 18840.41 0.207037508 1.769230769 0.15954 0.25662 -0.68395 -0.7668005

7.95 0.09 10.29 12041.48 0.151465176 1.294339623 0.085388 0.175388 -0.81969 -0.9320911

10.26 0.07824 12.9 15095.73 0.147131918 1.257309942 0.080572 0.158812 -0.83229 -0.9752072

13.58 0.0715 14.6 17085.1 0.125810716 1.075110457 0.058912 0.130412 -0.90028 -1.0607722

15.21 0.06408 13.7 16031.9 0.105403711 0.900723208 0.041351 0.105431 -0.97714 -1.1531238

13.22 0.06231 11.5 13457.44 0.101796051 0.8698941 0.038569 0.100879 -0.99227 -1.1722923

14.34 0.05839 11.2 13106.37 0.091397311 0.781032078 0.031091 0.089481 -1.03907 -1.224359


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From the graph,

Equation of line

Y=1.3225x-1.0401

Log Q= n log(2/3(H+v2 /g))+log Cdbt√

Comparing it to

Y= mx+ c

n=1.3225

log bt Cd √ =-1.1401

bt=3.276 cm

Cd =0.8887

FLUME 2 EXPERIMENT

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0lo

g Q

log 2/3(H+v2/2g)


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Dia of tank = 0.389m

Datum =5.52 cm

TIME, t Surface height s

Depth of flow

Tank initial h1

tank final h2

Head h of water

9.88 15.54 0.100 6.1 24.5 0.184

7.34 15.02 0.095 8.3 21.3 0.130

7.91 14.54 0.090 9.2 21.8 0.126

7.42 14.1 0.086 8.8 20.4 0.116

9.82 13.515 0.080 7.2 20.3 0.131

8.41 13.05 0.075 7.6 18.2 0.106

8.20 12.4 0.069 7.8 16.8 0.090

7.06 11.931 0.064 9.8 16.8 0.070

6.20 10.21 0.047 8.4 12 0.036

ANALYSIS OF DATA FOR FLUME

Head =h2-h1

Vol = /4

T in seconds

Q V= Q/A m/s

H+V2/2g Log Q log 2/3 (H+V2/2g)

0.184 0.02187 9.88 0.0022 0.3440 0.1062 -2.65495 -1.14984

0.130 0.01545 7.34 0.0021 0.3451 0.1011 -2.67676 -1.17147

0.126 0.01497 7.91 0.0019 0.3269 0.0956 -2.72282 -1.19543

0.116 0.01379 7.42 0.0019 0.3373 0.0916 -2.73096 -1.21421

0.131 0.01557 9.82 0.0016 0.3088 0.0848 -2.79985 -1.24764

0.106 0.01260 8.41 0.0015 0.3098 0.0802 -2.8245 -1.27196

0.090 0.01070 8.20 0.0013 0.2953 0.0732 -2.88458 -1.31132

0.070 0.00832 7.06 0.0012 0.2863 0.0683 -2.92872 -1.34176

0.036 0.00428 6.20 0.0007 0.2292 0.0496 -3.1611 -1.48082

GRAPH OF LOG Q AGAINST LOG 2/3 (H+V2/2g)


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Q = Cdbt√ . (

(H+

)n

Log Q= log Cdbt√ + n Log(. (

(H+

)n

From the graph, n is the gradient = 1.528

Log Cdbt√ = -0.8866, y intercept

Cdbt√ =0.1228

bt = 3.394 cm the throat width.

Solving for Cd = 0.913

DISCUSSION

-3.2

-3.1

-3

-2.9

-2.8

-2.7

-2.6

-1.7 -1.2 -0.7 -0.2 0.3 0.8

log

Q

Log 2/3(H+v2/2g)


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In this experiment the friction coefficients for the two flumes were compared.

The coefficient of discharge of each flume differs from the other and can only be

determined experimentally.

This coefficient must be multiplied with the theoretical ideal flow to get the actual discharge

of the flume.

Errors in the experiments could have resulted from erroneous recording of time and water

heights, surface depths of flow.

These were reduced by allowing more time before collecting discharge, using vernier to

measure surface heights and drawing of a line of best fit in the graph.

The theoretical value of n should be 3/2 or 1.5 compared to 1.4 and 1.51 got In the

experiment.

CONCLUSION

The expression

Q=Cd √

(H+

) ] 3/2

Was confirmed true for actual flume discharge.

The value of n were found to be 1.3 and 1.5 for the two flumes respectively with their values

of Cd being 0.88 and 0.91.

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