GATE 2025 AG – Question 64

Dairy and Food Engineering · Unit Operations in Dairy and Food Engineering · 2 marks · Numerical answer

Apple juice of viscosity 1.6 cP is filtered at constant pressure through 2 m². Solids concentration per filtrate volume is .04 g/mL, pressure drop 325.33 kPa, specific cake resistance 1.85×10¹¹ m/kg and medium resistance 3.50×10¹¹ m⁻¹. Find time to filter 800 L, in integer hours.

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Correct answer: 1 to 1

Explanation

Integrated constant-pressure filtration gives $$t=\frac{\mu\alpha cV^2}{2A^2\Delta P}+\frac{\mu R_mV}{A\Delta P}.$$ In SI units,$\mu=.0016$ Pa·s,$c=40$ kg/m³,$V=.8$ m³,$A=2$ m²,$\Delta P=325330$ Pa. Substitution gives approximately 3600.04 s, or 1.00001 h. The integer answer is **1 hour**. Both cake and medium resistances contribute.

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