### Coefficient of Discharge of Venturi Meter

The rate of flow of water in a 150 mm diameter pipe is measured with a venturi meter of 50 mm diameter throat. When the pressure drop over the converging section is 100 mm of water, the flow rate is 2.7 kg/sec. What is the coefficient of the meter?

Data:

Dia of pipe (Da) = 150 mm = 0.15 m

Dia of throat (Db) = 50 mm = 0.05 m

Pressure drop (Pa - Pb) = 100 mm of water = (0.1/10.33) x 101325 N/m2 = 980.9 N/m2

Mass flow rate = 2.7 kg/sec

Formulae:

Velocity at the throat

$$\displaystyle v_b = \frac{C_v}{\sqrt{1-\beta^4}}\sqrt{\frac{2(P_a-P_b)}{\rho}}$$

Where β = Db/Da

Calculations:

Volumetric flow rate = mass flow rate / density = 2.7 / 1000 = 0.0027 m3/sec

Velocity at the throat = Volumetric flow rate / cross sectional area of throat

= 0.0027 / (πDb2/4) = 0.0027 / (π x 0.052/4) = 1.375 m/sec

Therefore,

Cv = 1.375 x ( 1 - (0.05/0.15)4 )0.5 / (2 x 980.9/1000)0.5 = 0.976