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⚛️ Physics  ·  Mechanical Properties of Fluids  ·  NEET & JEE

A capillary tube of radius 0.1 mm is dipped in water (T = 0.07 N/m, contact angle = 0, ρ = 1000 kg/m³). Height of capillary rise is:

Answer: 14.3 cm.

  • A 14.3 cm
  • B 1.43 cm
  • C 143 cm
  • D 0.143 cm

Correct answer: A. 14.3 cm

Explanation: h = 2T cosθ/(ρgr) = 2 × 0.07 × 1/(1000 × 10 × 0.1×10⁻³) = 0.14/(1) = 0.14 m = 14 cm ≈ 14.3 cm.

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 →