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Fluid Mechanics
Mechanical Operations
GATE 2020
Medium

In a constant-pressure cake filtration with an incompressible cake layer, the plot of t/V versus V results in a straight line with an intercept of 10⁴ s/m³. Filter area is 0.05 m², filtrate viscosity is 10⁻³ Pa·s, and overall pressure drop is 200 kPa. The filter-medium resistance (in m⁻¹) is

  • A1×10⁹
  • B1×10¹⁰
  • 1×10¹¹
  • D1×10¹²

Explanation

The standard cake filtration equation t/V=(μαc/2A²ΔP)V+μRm/(AΔP) has intercept=μRm/(AΔP). So Rm=intercept×A×ΔP/μ=10⁴×0.05×200,000/0.001=1×10¹¹ m⁻¹.

Source: GATE CH 2020 (2020)

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