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GATE 2024 CH – Question 15

Fluid Mechanics and Mechanical Operations · Fluid properties, fluid statics and fluid kinematics · 1 mark · Multiple choice

An infinitely long cylindrical water filament of radius $R$ is surrounded by air. Assume water and air to be static. The pressure outside the filament is $P_{out}$ and the pressure inside is $P_{in}$. If $\gamma$ is the surface tension of the water-air interface, then $P_{in} - P_{out}$ is

  1. $\frac{2\gamma}{R}$
  2. 0
  3. $\frac{\gamma}{R}$
  4. $\frac{4\gamma}{R}$

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Correct answer: (C) $\frac{\gamma}{R}$

Explanation

For a cylindrical interface only one principal curvature is non-zero, $\frac{1}{R}$ (a sphere has two). The Young-Laplace equation gives $\Delta P = \frac{\gamma}{R}$.