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⚛️ Physics  ·  Mechanical Properties of Fluids  ·  NEET & JEE

The rate of flow through a capillary tube is measured by Poiseuille: Q = πr⁴ΔP/8ηL. If the tube radius is halved, the flow rate:

Answer: Decreases by factor 16.

  • A Decreases by factor 16
  • B Decreases by factor 2
  • C Increases by factor 16
  • D Decreases by factor 4

Correct answer: A. Decreases by factor 16

Explanation: Q ∝ r⁴. If r halves (r/2), Q = (r/2)⁴ × (original Q/r⁴) = Q/16. The flow rate decreases by factor 16.

Continuity Equation: Narrow Pipe → Faster FlowA₁, v₁ (wide, slow)A₂, v₂ (narrow, fast)A₁v₁ = A₂v₂ (continuity)Smaller area → higher speed → (by Bernoulli) LOWER pressure

Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.

Concept context

Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.

Read the full Mechanical Properties of Fluids notes →