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IIT Hyderabad, ME 08, fluid lab report, determination of discharge coefficient for a venturimeter
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M V HARISH BABU (ME08B013)
MANOJ K TRIPATHI (ME08B014)
M KRISHNAKALYAN (ME08B015)
M SALIMUDDIN (ME08B016)
GROUP IV (BATCH 1)
EXPERIMENT 5:VENTURI METER
AIM
To determine the discharge coefficient Cd
To show that the relation between flow rate (Q)
and pressure difference (∆P) is quadratic
Components required
Long and short nipples (GI pipe)
Joints
Flow control valves
Outlet pipe
Measuring jar
Manometer (made using wooden plank, plastic tube and graph sheet)
Venturimeter
Meter scale
theory
Venturimeter, essentially a short pipe consisting of
two conical parts with a short portion (throat) of
uniform cross-section in between
Contd.
It is always used in such a way that the upstream part
of the flow goes through short conical portion while the
downstream part flows through the long one
This ensures a rapid converging passage and a gradual
diverging passage in the direction of flow to avoid the
loss of energy due to separation
In course of flow through the converging part, the
velocity increases in the direction of flow according to
“the principle of continuity”, while the pressure
decreases according to “Bernoulli’s principle”
Formula used
From Bernoulli’s equation
Here, since the height is same for two points of
venturimeter where the pressure is measured, h1= h2
Contd.
From equation of continuity,
A1V1 = A2V2
Combining these two,
To compensate for the loss due to viscosity and other factors, the discharge coefficient (Cd ) is introduced in the above relation, which gives
Experimental set-up
Observations
S.N
o
H (cm) H (m) ln H Q
l /s
Q x10-4
m3/s
ln Q
1 4 .040 -3.218 .1089 1.089 -9.125
2 6.4 .064 -2.7488 .1378 1.378 -8.889
3 7.8 .078 -2.5510 .1531 1.531 -8.784
4 11.6 .116 -2.1541 .1855 1.855 -8.592
5 15 .150 -1.8971 .2122 2.112 -8.458
6 18.2 .182 -1.7037 .2324 2.324 -8.367
Calculations
The intercept from the plot(ln Q vs. ln H) is found to be -7.059
Therefore, we have , -7.059 = ln Cd A1A2 (2g/A12 – A2
2)
Using the data,
A1 = 5.064 x 10-4 m2
A2 = 1.267 x 10-4 m2
g = 9.81 ms-2
Cd = 0.9457
Plot(ln Q vs. ln H)
y = 0.501x - 7.509
-9.2
-9.1
-9
-8.9
-8.8
-8.7
-8.6
-8.5
-8.4
-8.3
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0
ln Q
ln H
lnQ
Linear (lnQ)
Observations
S.No Flow rate, Q , x10-4 m3 /s ∆P , Pa
1 1.089 392.4
2 1.378 627.8
3 1.531 756.2
4 1.855 1137.9
5 2.112 1471.5
6 2.324 1785.4
Q vs. ∆P
0
0.5
1
1.5
2
2.5
0 500 1000 1500 2000
Q
∆P
Q
Poly. (Q)
Conclusions
The value of discharge coefficient is found to be
0.9457 ≈ 0.95
This is close to the expected value of Cd for a
venturimeter which usually lies between 0.95 to
0.98
The graph of Q vs. ∆P is parabolic, which clearly
shows that the relation between Q and ∆P is
parabolic
Practical Values of Cd
S.No Q , x10-4 , m3 /s Qt , x10-4 , m3 /s Cd = Q/ Qt
1 1.089 1.1591 0.9395
2 1.378 1.4662 0.9398
3 1.531 1.6186 0.9458
4 1.855 1.9739 0.9397
5 2.112 2.2446 0.9409
6 2.324 2.4725 0.9399