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⚛️ Physics  ·  Mechanical Properties of Fluids  ·  NEET & JEE

A capillary tube of radius r shows a liquid rise h. If a tube of radius r/2 is used, the rise becomes:

Answer: 2h.

  • A h/2
  • B h
  • C 2h
  • D 4h

Correct answer: C. 2h

Explanation: Capillary rise h = 2T cosθ/(ρgr), so h ∝ 1/r; halving r doubles the rise to 2h.

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 →