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 wattLast Modified on: 04-Feb-2022
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