Chemegate

GATE 2024 Chemical Engineering, Q15 · Fluid Mechanics

The correct answer is C, γ/r.

Question

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 PoutP_{out} and the pressure inside is Pin.P_{in}. If γγ is the surface tension of the water-air interface, then PinPoutP_{in} − P_{out} is

  • A. 2γ/r2γ/r
  • B. 0
  • C. γ/rγ/r
  • D. 4γ/r4γ/r

Official answer: γ/rγ/r

Why

GATE 2024 official key: (C). Young-Laplace: ΔP=γ(1/R1+1/R2).\Delta P = γ(1/R₁ + 1/R₂). For a cylinder, R1=R₁ = r and R2=,R₂ = \infty , giving ΔP=γ/r.\Delta P = γ/r. (For a sphere it would be 2γ/r;2γ/r; for a soap bubble, 4γ/r.)4γ/r.)

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.