GATE AG 2022 • Q43 MCQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Continuity equation, kinematics and dynamics of flow

Question Statement:

The pressure drop through a well-designed constriction is to be used for measuring the velocity of flow through a circular pipe. If the pressure drop from a 0.1 m diameter section to a 0.05 m diameter section of the pipe is 7.5 kPa, the velocity in m s⁻¹ in the 0.1 m diameter section of the pipe is ____________. (Take density of liquid = 1000 kg m⁻³)

Options:

  • (A) 0.5
  • (B) 1.0
  • (C) 1.5
  • (D) 2.0

Official Answer Key:

B

Step-by-Step Solution & Explanation

• By continuity, V2 = V1(D1/D2)² = 4V1. • Bernoulli: ΔP = (ρ/2)(V2²−V1²) = (ρ/2)(15V1²) • 7500 = 500×15×V1² = 7500V1² ⟹ V1² = 1 ⟹ V1 = 1.0 m/s

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