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 (D_{a}) = 150 mm = 0.15 m

Dia of throat (D_{b}) = 50 mm = 0.05 m

Pressure drop (P_{a} - P_{b}) = 100 mm of water = (0.1/10.33) x 101325 N/m^{2} = 980.9 N/m^{2}

Mass flow rate = 2.7 kg/sec

Formulae:

Velocity at the throat

Where b = D_{b}/D_{a}

Calculations:

Volumetric flow rate = mass flow rate / density = 2.7 / 1000 = 0.0027 m^{3}/sec

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

= 0.0027 / (pD_{b}^{2}/4) = 0.0027 / (p x 0.05^{2}/4) = 1.375 m/sec

Therefore,

C_{v} = 1.375 x ( 1 - (0.05/0.15)^{4 })^{0.5} / (2 x 980.9/1000)^{0.5} = **0.976**