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GATE 2025 Chemical Engineering, Q49 · Mechanical Operations

The correct answer is 1.61 to 1.68.

Question

A leaf filter is operated at 1 atm (gauge). The volume of filtrate collected (V in m3)m³) is related with the volumetric flow rate of the filtrate (q in m3/s)m³/s) as: 1/q=1/(dV/dt) = 50V + 100. The volumetric flow rate of the filtrate at 1 hour is ____ ×10−3m3/s \times 10⁻³ m³/s (rounded off to 2 decimal places).

Official answer: 1.61 to 1.68

Why

GATE 2025 official key: 1.61 to 1.68(×10−3).1.68 ( \times 10⁻³). Integrating dt = (50V+100)dV from V=0 gives t =25V2+100V.= 25V²+100V. At t=3600 s, solving 25V2+100V−3600=025V²+100V−3600=0 gives V≈10.17m3,V\approx 10.17 m³, so dV/dt =1/(50×10.17+100)≈1.64×10−3m3/s.= 1/(50 \times 10.17+100) \approx 1.64 \times 10⁻³ m³/s.

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

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