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GATE 2023 MN – Question 33

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

Increase roadway resistance by 1.5 N s²/m⁸ using a regulator. Find its opening area in m² to two decimals, using the conventional equivalent-orifice relation.

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Correct answer: 0.95 to 1.07

Explanation

The conventional mine equivalent-orifice formula is A = 1.2Q/√p, with Q in m³/s and p in Pa. Since p = RQ², it becomes A = 1.2/√R. For R = 1.5, A = 0.979796 m², or 0.98 m². The coefficient 1.2 is outside the square root.

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