Orifice and Jet Flow

King faisal university College of engineering Department of mechanical & civil engineering

Experiment#5 Fluid mechanics Lab Orifice and Jet Flow

Tested by [Group (B)] Arafat . A . Ali ID# 213189413 Experiment date :- Feb 7th,2016 Submit date :- Mar 21th,2016

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Engr312

Engr312 FLUID MECHANICS Laboratory Experiment #5

Orifice and Jet Flow Objective:



Studying the flow through small orifice discharging to atmosphere.



Calculating the coefficient of discharge (Cd).



Calculating the coefficient of velocity (Cv).



Calculating the coefficient of contraction (Cc)

Introduction



An Orifice is an opening in the side or base of tank or reservoir through which fluid is discharge in the form of a jet.



The discharge will depend upon the head of the fluid (H) above the level of the orifice.



The term small orifice means that the diameter of the orifice is small compared with the head producing flow.

List of Equipment

1. Basic hydraulic bench 2. Osborne Reynolds’ Demonstration Apparatus 3. Hydrostatic pressure apparatus 4. Bernoulli’s Demonstration apparatus 5. Dead weight calibrator 6. Orifice and free jet flow apparatus 7. Orifice discharge apparatus 8. Free and Forced vortices apparatus 9. Compressible flow bench

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Theory:

 Two reasons for the difference between theoretical and actual discharge.  First: The velocity of jet is less than the velocity calculated because there is losses of energy between point A and B.

Vactual  Cv .Vtheo.  Cv 2 gH ,Cv is the coefficient of velocity  Second: The stream line of the orifice contract reducing the area of flow. (Vena Contraction)

Aactual  Cc . A Where. Cc is the coefficient of contraction.

Qactual  Cv .Cc . A 2 gH Qactual  Cd A 2 gH Cd in the range [0.6-0.65]

Measurement of Jet Trajectory

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Procedure:

1. Install the required orifice 2. adjust the overflow pipe to obtain a required level in the tank 3. Open the water supply valve to obtain a steady flow with minimum overflow 4. wait until the level in the tank and jet profile is stable before adjusting the probes tips to be in-line with the center of the jet and record the probe tip profile as well as the Y = 0 mark 5. Record the flow volume by using the stopwatch and bench-measuring tank. Data & Results: Table 1 : Parameters of the apparatus and some reading from the experiment

Water level, H

379 (mm)

Volume, Lt

5

Time, s

16.44 0.30414 * 10-3 (m3/s)

Flow rate, QA = volume/time Diameter of orifice, m

0.013

2

Area (m )

0.000133

Table 2 : Reading from the experiment

X

Y

YTHEORETICAL =

X1

4

40

Y1

1

X2 4H 1.055

2 √ YH Error % 38.93584

5.540897

X2

80

Y2

5

4.221

87.0632

77.83641

X3

120

Y3

12

9.499

134.8777

250.1319

X4

160

Y4

21.5

16.887

180.5381

461.3456

X5

200

Y5

31

26.385

216.7856

461.4776

X6

240

Y6

45.5

37.995

262.6366

750.5277

X7

280

Y7

62

51.715

306.5811

1028.496

X8

320

Y8

78.5

67.546

344.9725

1095.383

X9

360

Y9

100

85.488

389.3584

1451.187

X10

400

Y10

122

105.541

430.0605

1645.91

Analysis and Calculations

-

-

The theoretical velocity 2 gH Vth= = 2.72 m /s The actual velocity

0.360

X

Vact=Vx = -

√

2Y g

Coefficient of velocity Cv Cv=

=

√

V act V th

2(0.1) 9.81

= 2.52 m/s

= 0.926

The actual volume flow rate �� �� =

= 0.30414 * 10-3 (m3/s)

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The theoretical volume flow rate �th π 2 π 2 gH 2 d (0.013) �th = VA = 4 = 4

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Coefficient of discharge

-

5

0.05 16.44

2 * 9.81 * 0.379 = 0.3619* 10-3 (m3/s)

Cd =

Q act  Q th

−3

0.30414∗10 −3 0.3619∗10

= 0.84

The coefficient of contraction Cc Cd Cv

Cc =

= 0.907

X versus 2√�� 500 400 300

2√��

200 100 0 0

50

100 150 200 250 300 350 400 450 500 X

•

•

Frome the graph

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dX CV= d (2 ( YH ) .5)

Figure 1 : X (m) vs �√(��)

=

282−240 308−260

= 0.875

0

50 100 150 200 250 300 350 400 450

0 20 40 60

Teoretical curves of the jet trajectory

80

experimental curves of the jet trajectory

100 120 140

Figure 2 : Theoretical and Experimental Curves of the Jet Trajectory Path

Figure 3 : The values of Y(exp) from the lab

Discussion

 Discussion that the actual flow rate QA is different from the theoretical one, Q, which is corresponding to that the velocity of jet is less than the velocity calculated because there is losses of energy 7

 The coefficient of contraction indicates the losses of flow energy due to the change of the orifice shape. Mathematically expressed as The ratio of the area of the jet, at venacontracta, to the area of the orifice

 Typical values of coefficient of velocity, coefficient of discharge and coefficient of contraction include 0.96, 0.62 and 0.64 respectively. As it can be observed errors have been introduced within the experiment most of them systematic as the values although precise are not accurate. The experimental procedure has been observed to be flawed in the following respect  There was a differences between the calculated ( theoretical) and measured (experimental) due to the human error during experiment for many factors : such that the apparatuses does not stand with level, the accuracy for determining the flow bath has not done well.  What is the effect of the water height H on the jet trajectory path. The effect of the water head on the orifice is the increasing of the flow energy such that the more height of the water head the more velocity value will experiences the water flow ejected by the orifice. Conclusions

Experimental errors have significantly affected the values of the coefficients. The precision of the results show that the errors are mostly systematic as well as human errors during the insertion of gauge pins and hence procedure wise it is deemed to be successful. The experimental values for the coefficients are therefore not a good approximation of the true value. References:

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[1] http://www.academia.edu/8952330/Flow_through_an_orifice [2] http://uh.edu/engines/VelocityCoefficients.pdf [3]Fluid Mechanics Report 3ed edition, (Nov.2015), King Faisal University department of mechanical engineering, (Eng. Omar Osta).