Project ForgeFluid Mechanics
Mechanical Operations
GATE 2015
Hard
A batch filtration cycle collects 5L filtrate in 100s (constant-pressure), then washes for tW seconds using 1L wash water, with ΔP/L=k1(dV/dt), L=k2V (during filtration). The wash time tW (s), rounded to 1 decimal place, is
40 s(± 0.5 accepted)
Explanation
During filtration: V·dV=C·dt (C constant), integrating gives V²=2Ct, so C=V²/(2t)=25/200=0.125. During washing, cake is now fixed at its final L, so the constant washing rate = final filtration rate = C/V_final=0.125/5=0.025 L/s. tW=1/0.025=40s.
Source: GATE CH 2015 (2015)
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