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GATE 2026 Chemical Engineering, Q49 · Mechanical Operations

The correct answer is D, 3 × 10¹¹.

Question

Laboratory filtration is conducted at constant pressure drop of 200 kPa on a slurry of CaCO3 in water at room temperature: 1×10−3m31 \times 10⁻³ m³ filtrate collected in 40 s, 2×10−3m32 \times 10⁻³ m³ in 100 s. The filter area is 0.05m20.05 m² and viscosity of filtrate is 10−310⁻³ Pa·s. Which one of the following is the filter medium resistance (in m−1)?m⁻¹)?

  • A. 3×10−113 \times 10⁻¹¹
  • B. 3×10−83 \times 10⁻⁸
  • C. 3×1083 \times 10⁸
  • D. 3×10113 \times 10¹¹

Official answer: 3×10113 \times 10¹¹

Why

GATE 2026 official key: (D). From the t/V vs V data, the intercept μRm/(AΔP)≈30000s/m3;μR_{m}/(A\Delta P) \approx 30000 s/m³; solving for RmR_{m} with A=0.05 m2,ΔP=200m², \Delta P=200 kPa, μ=10−3μ=10⁻³ Pa·s gives Rm≈3×1011m−1.R_{m} \approx 3 \times 10¹¹ m⁻¹.

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

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