Venturimeter (discharge coefficient)

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