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⚛️ Physics  ·  Mechanical Properties of Fluids  ·  NEET & JEE

In a U-tube, oil of density 800 kg m<sup>-3</sup> in one arm balances a water column in the other. If the oil column is 10 cm, the balancing water column is:

Answer: 8 cm.

  • A 12.5 cm
  • B 8 cm
  • C 6.4 cm
  • D 10 cm

Correct answer: B. 8 cm

Explanation: Equal pressures give &rho;<sub>oil</sub>h<sub>oil</sub> = &rho;<sub>w</sub>h<sub>w</sub>, so h<sub>w</sub> = 800 &times; 10 / 1000 = 8 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 →