### 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 Cv = 0.98. If 10% of the pressure differential is permanently lost, calculate the power consumption of the meter.

Data:

Dia of pipe (Da) = 10 cm = 0.1 m

Dia of throat (Db) = 4 cm = 0.04 m

Manometer reading (hm) = 30 cm of Hg

Venturi coefficient (Cv) = 0.98

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

ρm = 13.6 g/cc = 13.6 x 10-3 kg/m3

ρ = 1 g/cc = 1000 kg/m3

Formulae:

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

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

The pressure difference measured by the manometer

Pa - Pb = (ρm - ρ)ghm

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

Calculations:

Pa - Pb = (13600 - 1000) x 9.812 x 0.3 = 37089.4 N/m2

β = 0.04/0.1 = 0.4

vb = (0.98/(1-0.44)0.5) x (2 x 37089.4 / 1000)0.5 = 0.993 x 8.613 = 8.553 m/sec

Cross sectional area of throat = πDb2/4 = p x 0.042 / 4 = 0.00126 m2

Volumetric flow rate = 8.553 x 0.00126 = 0.01078 m3/sec = 10.78 lit/sec

Permanent pressure loss = 0.1 x 37089.4 = 3708.94 N/m2

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