Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Laminar and turbulent flow in pipes, Darcy–Weisbach and Hazen–Williams equations
Question Statement:
A pipeline carrying 500 litres/min branches into two parallel pipes X (L=500 m, D=0.2 m) and Y (L=500 m, D=0.3 m) reconnecting downstream. Friction factor f=0.030 for all pipes. The ratio of flow in pipes X and Y is
Figure (reconstruction): pipeline M splitting into parallel pipes X and Y, rejoining at N
Options:
(A) 0.36
(B) 0.44
(C) 0.67
(D) 1.00
Official Answer Key:
A
Step-by-Step Solution & Explanation
For parallel pipes the head loss is common: h_f = fLQ²/(12.1D⁵) (Darcy–Weisbach in discharge form), so f·L_X·Q_X²/D_X⁵ = f·L_Y·Q_Y²/D_Y⁵. With L_X = L_Y = 500 m and f common, this reduces to Q_X/Q_Y = (D_X/D_Y)^2.5 = (0.2/0.3)^2.5 = 0.363 ≈ 0.36.
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