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Fluid Mechanics
Flow Through Pipes
GATE 2011
Medium

A liquid flows through a piping network where pipe sections P, Q, R and S have equal lengths. The diameters of sections P and R are equal, and the diameter of section Q is twice that of S. The flow (P into a parallel split of Q and S, rejoining into R) is steady and laminar. Neglecting curvature and entrance effects, the ratio of the volumetric flow rate in section Q to that in S is

  • 16
  • B8
  • C2
  • D1

Explanation

Q and S are in parallel (same ΔP, same length). By Hagen-Poiseuille, laminar flow rate ∝ D⁴ for fixed ΔP and L. With DQ=2DS: QQ/QS=(DQ/DS)⁴=2⁴=16.

Source: GATE CH 2011 (2011)

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