Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Ideal and real fluids, properties of fluids
Question Statement:
A venturimeter of 75 mm diameter is fitted to a horizontal pipe of 150 mm diameter. Gauge pressure in the venturimeter in case of no flow is 2 m of water. Taking atmospheric pressure as 10 m of water, the theoretical flow through the pipeline in litres per second, when the throat point pressure is 2.60 m of water (absolute), is
Options:
(A) 15
(B) 30
(C) 60
(D) 75
Official Answer Key:
C
Step-by-Step Solution & Explanation
With no flow, pressure is uniform throughout, so the pipe (upstream) absolute pressure head = atm + gauge = 10 + 2 = 12 m of water. Available head at the throat during flow: h = 12 − 2.60 = 9.40 m of water. A1 = (π/4)(0.150)² = 0.01767 m², A2 = (π/4)(0.075)² = 0.004418 m². Q = A2·√[2gh / (1 − (A2/A1)²)] = 0.004418 × √[2×9.81×9.40/(1−0.0625)] = 0.004418×√(196.7) = 0.004418×14.02 = 0.06196 m³/s = 61.96 L/s ≈ 60 L/s, matching option (C).
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