GATE 2026 MN – Question 33

Surface Environment, Mine Ventilation and Underground Hazards · Mine Ventilation · 1 mark · Numerical answer

A500 m long circular airway of diameter5 m carries30 m³/s. With unchanged surface roughness and length, find diameter needed to double flow at the same pressure loss, to two decimals.

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Correct answer: 6.40 to 6.80

Explanation

For turbulent mine-airway flow, Δp∝(perimeter/area³)Q². A circular section gives perimeter/area³∝D⁻⁵. At fixed pressure, Q²/D⁵ is constant, so D₂=5(2²)^(1/5)=6.598 m, or6.60 m.

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