Chemegate

GATE 2026 Chemical Engineering, Q59 · Fluid Mechanics

The correct answer is 400.

Question

A cylindrical capillary glass tube, open at both ends, is vertically inserted in a pool of water; the water level in the tube rises 7 cm relative to the level outside. Surface tension of water is 0.07 N m1,m⁻¹, contact angle 0°,0°, density 1000 kg m3,m⁻³, g = 10 m s2.s⁻². The diameter of the capillary tube (in μm)μm) is __________ (rounded off to the nearest integer).

Official answer: 400

Why

GATE 2026 official key: 400. Capillary rise: h =4γcosθ/(ρgd);= 4γcosθ/(ρgd); with θ=0°(cosθ=1),θ=0° (cosθ=1), solve for d =4γ/(ρgh)=4×0.07/(1000×10×0.07)=0.0004= 4γ/(ρgh) = 4 \times 0.07/(1000 \times 10 \times 0.07) = 0.0004 m =400μm.= 400 μm.

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