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GATE 2026 MN – Question 40

Surface Environment, Mine Ventilation and Underground Hazards · Mine Ventilation · 2 marks · Multiple choice

Two parallel ventilation districts A and B initially have common pressure drop ΔP and flows QA,QB. A booster increases B flow to Q′B while A flow stays unchanged. What booster pressure PB is needed?

Diagram for GATE 2026 MN question 40
  1. $\Delta P(Q_B/Q_B\prime)^2-\Delta P$
  2. $\Delta P(Q_B\prime/Q_B)^2-\Delta P$
  3. $\Delta P-\Delta P(Q_B\prime/Q_B)^2$
  4. $\Delta P+\Delta P(Q_B\prime/Q_B)^2$

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Show answer and explanation

Correct answer: (B) $\Delta P(Q_B\prime/Q_B)^2-\Delta P$

Explanation

District resistance is unchanged, so RB=ΔP/QB². Unchanged A flow keeps the common pressure difference atΔP. B now requires RB(Q′B)²=ΔP+PB. Subtracting gives PB=ΔP(Q′B/QB)²−ΔP, B.

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