GATE AG 2019 • Q48 MCQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow through orifices, weirs and notches

Question Statement:

Fluid Mechanics: Ideal and real fluids, properties of fluids; hydrostatic pressure and its measurement; continuity equation, kinematics and dynamics of flow; Bernoulli's theorem; laminar and turbulent flow in pipes, Darcy- Weisbach and Hazen-Williams equations; flow through orifices, weirs and notches; flow in open channels, dimensional analysis – concepts of geometric dimensionless numbers. Water flows at velocity 1.6 m/s in a pipe of diameter 8 cm and length 100 m. With coefficient of friction f = 0.005 and g = 9.81 m/s², the head loss (m) due to friction in the pipe is

Options:

  • (A) 1.28
  • (B) 2.28
  • (C) 2.78
  • (D) 3.26

Official Answer Key:

D

Step-by-Step Solution & Explanation

Darcy-Weisbach equation (British convention, with friction coefficient f used as h_f = 4fLV²/2gD): h_f = 4 × 0.005 × 100 × (1.6)² / (2 × 9.81 × 0.08) = 4 × 0.005 × 100 × 2.56 / 1.5696 = 5.12/1.5696 = 3.262 ≈ 3.26 m. Answer: (D) 3.26.

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