GATE 2022 CH – Question 53
In a constant-rate cake filtration operation, the collected filtrate volumes are 120 m$^3$ and 240 m$^3$ at 1 min and 2 min, respectively. Assume the cake resistance to be constant and the filter medium resistance to be negligible. If the pressure-drop across the cake is 10 kPa at 1 min, its value at 2 min is _________ kPa (rounded off to the nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 20
Explanation
At a constant rate of filtration, the pressure drop across the cake is $\Delta P = \mu\alpha\frac{V}{A^2}\cdot\frac{dV}{dt}$ (with $R_m \approx 0$), which is proportional to the volume collected $V$, since $\frac{dV}{dt}$ is constant. The volume doubles from 1 to 2 min, so the pressure drop doubles to 20 kPa.