### Fluid Mechanics

# Power Required for Venturi Meter

A horizontal venturi meter having a throat diameter of 4 cm is set in a 10 cm I.D. pipeline. Water flows through the system and the pressure differential across the venturi meter is measured by means of a simple U-tube manometer filled with mercury. Estimate the flow rate when the manometer reading is 30 cm. Assume C_{v }= 0.98. If 10% of the pressure differential is permanently lost, calculate the power consumption of the meter.

Data:

Dia of pipe (D_{a}) = 10 cm = 0.1 m

Dia of throat (D_{b}) = 4 cm = 0.04 m

Manometer reading (h_{m}) = 30 cm of Hg

Venturi coefficient (C_{v}) = 0.98

Permanent pressure loss = 10 % of the pressure differential measured by the manometer.

r_{m} = 13.6 g/cc = 13.6 x 10^{-3} kg/m^{3}

r = 1 g/cc = 1000 kg/m^{3}

Formulae:

Flow rate = Velocity at the throat x cross sectional area of throat

Velocity at the throat

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

The pressure difference measured by the manometer

P_{a} - P_{b} = (r_{m} - r)gh_{m}

Power consumption of the meter = volumetric flow rate x permanent pressure loss

Calculations:

P_{a} - P_{b} = (13600 - 1000) x 9.812 x 0.3 = 37089.4 N/m^{2}

b = 0.04/0.1 = 0.4

V_{b} = (0.98/(1-0.4^{4})^{0.5}) x (2 x 37089.4 / 1000)^{0.5} = 0.993 x 8.613 = 8.553 m/sec

Cross sectional area of throat = pD_{b}^{2}/4 = p x 0.04^{2} / 4 = 0.00126 m^{2}

Volumetric flow rate = 8.553 x 0.00126 = 0.01078 m^{3}/sec = **10.78 lit/sec**

Permanent pressure loss = 0.1 x 37089.4 = 3708.94 N/m^{2}

Power consumption of the meter = 0.01078 x 3708.94 = **40 watt**