GATE 2023 AG – Question 44

Dairy and Food Engineering · Unit Operations in Dairy and Food Engineering · 2 marks · Multiple choice

Juice solids concentration is .2 kg per m³ filtrate. Filtration of 12.49 m³ juice deposits.02 m cake of porosity.32. Solids collected are2.5 kg in 180 s. Viscosity is 2.12×10⁻³ Pa·s and specific cake resistance1.2×10⁸ m/kg. Find cake pressure drop in kPa.

0.18
1.81
18.06
180.60

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Show answer and explanation

Correct answer: (C) 18.06

Explanation

The official answer is **18.06 kPa, C**. Its apparent intended construction estimates filtrate volume as $V_f=m_s/c=2.5/.2=12.5$ m³ and takes the.01 m³ difference from 12.49 as cake pore liquid. Then filter area $A=.01/(.32\cdot.02)=1.5625$ m² and cake Darcy loss is $\Delta p=\mu\alpha m_s(V_f/t)/A^2\approx18.09$ kPa, close to C. However, the printed feed volume 12.49 is smaller than inferred filtrate12.5,so that pore-volume difference has the wrong physical sign. A consistent feed/filtrate or area datum is needed; the key is retained with this source inconsistency explicit.

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