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Orifice

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EXPERIMENT 7 : ORIFICE COEFFICIENT MEASUREMENT
INTRODUCTION
From application of Bernoulli’s equation (conservation of mechanical energy for a steady, incompressible, frictionless flow) : ideal orifice outflow velocity at the jet vena contracta (narrowest diameter) is: vi= 2gh
Where h is the height of fluid above the orifice. The actual flow rate of the jet is defined as:
Qt= Acv
Where Ac is the cross-sectional area of the vena contracta, given by:
Ac= CcAo
Where Ao is the area of orifice and Cc is the coefficient of area contraction and, therefore, Cc<1, hence:
Qt = CcAoCv2gh
The product CcCv is called the discharge coefficient, Cd, so finally:
Qt = CdAo2gh
If Cd is assumed to be constant, then graph of Qt plotted against h will be linear and the slope, S= CdAo2g
Under varying head, the coefficient discharge can be calculated from:
Cd= -ARAo2gslope
Where slope is obtained from time h vs t plot.

APPARATUS
Orifice apparatus, measuring cylinder, ruler, stopwatch
OBJECTIVE
To determine the coefficient of discharge for a small orifice based on flow under constant head and flow under varying head.
PROCEDURE
1. The orifice diameter is measured. The orifice plate is removed if necessary and the internal dimension of the header tank is measured. 2. The apparatus is connected to the bench, leveling by adjusting the feet, ensuring the overflow pipe runs into the sump tank. 3. Overflow pipe is raised to a suitable level, release water into the head tank. 4. The flow is control until the water is just spilling into the overflow. 5. The head, h is recorded on the scale and the flowrate, Q is measured using the volumetric tank and stopwatch. 6. The reading is confirmed by intercepting the jet with a measuring cylinder. 7. The three different water levels, h are repeated. 8. For flow under varying head, the overflow pipe is raised to obtain maximum head. The tank is filled to overflow level and the flow control valve is closed. 9. Start a stop watch when the level reaches the first convenient scale mark (noted as h1). Take a reading of the head (h2) at 20 seconds intervals.

Orifice apparatus

RESULT (Constant Head) No. | Orifice diameter, d,(m) | Head, h(m) | Volume, V(m3) | Time, t(s) | Flow Rate, Qt(m3s) | h0.5(m0.5) | DischargeCoefficient,Cd(m3s) | 1 | 0.003 | 0.400 | 9.20 x 10-4 | 60 | 1.533 x 10-5 | 0.632 | 0.742 | 2 | 0.003 | 0.380 | 9.00 x 10-4 | 60 | 1.500 x 10-5 | 0.616 | 0.742 | 3 | 0.003 | 0.360 | 8.85 x 10-4 | 60 | 1.475 x 10-5 | 0.600 | 0.742 | 4 | 0.003 | 0.340 | 8.50 x 10-4 | 60 | 1.417 x 10-5 | 0.583 | 0.742 | 5 | 0.003 | 0.320 | 8.25 x 10-4 | 60 | 1.375 x 10-5 | 0.566 | 0.742 | 6 | 0.003 | 0.29 | 7.90 x 10-4 | 60 | 1.317 x 10-5 | 0.539 | 0.742 | CALCULATION (constant head) vi = 2gh Cc = AcAo vi = 29.810.40 Cc = 5.473 ×10-67.07 ×10-6 vi = 2.801 Cc = 0.774 , Cc < 1
Qt = vt From the graph:
Qt = 9.2 ×10-460 S = 2.323 x 10-5
Qt = 1.533 × 10-5 m3s Cd = sAo2g
Qt = Acvi Cd = 2.323 × 10-5(7.07 ×10-6)(2(9.81)
Ac = 1.533 x 10-52.801 Cd = 0. 742
Ac = 5.473×10-6 m2
Ao = πd24
Ao = π(0.003)24
Ao = 7.07 × 10-6 m2

RESULT ( varying head) No. | Bearing head, h(m) | Time, t(s) | h(m) | Cd | 1 | 0.400 | 0 | 0.632 | 0.119 | 2 | 0.384 | 5 | 0.620 | | 3 | 0.378 | 10 | 0.615 | | 4 | 0.365 | 15 | 0.604 | | 5 | 0.352 | 20 | 0.593 | | 6 | 0.340 | 25 | 0.583 | | 7 | 0.327 | 30 | 0.572 | | 8 | 0.314 | 35 | 0.560 | | 9 | 0.301 | 40 | 0.549 | | 10 | 0.289 | 45 | 0.538 | | 11 | 0.279 | 50 | 0.528 | | 12 | 0.266 | 55 | 0.516 | | 13 | 0.255 | 60 | 0.505 | | 14 | 0.243 | 65 | 0.493 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

Calculation (Varying head)
Qt avg = 1.413×10-5 Ao = πd24 havg = 0.321 Ao = π(0.003)24 vi = 2gh Ao = 7.07 × 10-6 m2 vi = 29.810.321 Cd = - 5.63 ×10-67.07×10-6 29.81 (-465.04) vi = 2.51 Cd = 0.119
Qt = Acvi
Ac = 1.413 ×10-52.51 = 5.63×10-6

CONCLUSION
The value of the coefficient of discharge, Cd can be obtained by using two different methods which is flow under constant head where the time taken is constant and under varying head where the time interval is taken at 5 seconds each. This two method bring two different way but have a same objective but between these two methods, the most accurate reading is by using variable head. This is because, we will take many bearing head in the time interval then we can get the average from the result we can get.
DISCUSSION
From the result we calculated, the value of Cd on varying head which is 0.119 which is smaller in value than the value of Cd in constant head which is 0.742. Both of the method is using the linear slope in the graph to calculate Cd by using the formula given. The value of Cd in both methods are different from each other. This is maybe because of us while conducting the experiment such as the eye are not perpendicular to the scale while reading the result. To prevent this from happening, we can use the average reading to get the accurate result and the eye must be perpendicular to the scale reading. And it also can be effect by time taken that not perfect and it will affect the result Cd.
REFERENCES
1. Hydraulics and water quality laboratory manual. 2. Manual laboratory report CEW531

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