Question

Laboratory filtration is conducted at a constant pressure drop of 200 kPa on a slurry of \(\mathrm{CaCO_3}\) in water at room temperature. The time taken to collect filtrate is shown in the table.

Filtrate volume collected (in \(\mathrm{m^3}\))	Time (in s)
\(1 \times 10^{-3}\)	40
\(2 \times 10^{-3}\)	100

The filter area is \(0.05\ \mathrm{m^2}\) and the viscosity of the filtrate is \(10^{-3}\ \mathrm{Pa\,s}\). Which one of the following is the filter medium resistance (in \(\mathrm{m^{-1}}\))?

• A. \(3 \times 10^{-11}\)
• B. \(3 \times 10^{-8}\)
• C. \(3 \times 10^{8}\)
• D. \(3 \times 10^{11}\)

Hint:

Plot \(t/V\) versus \(V\); the intercept of this straight line equals \(\mu R_m/(A\Delta P)\), from which \(R_m\) can be isolated.

Answer 1

The Correct Option is D

Solve two simultaneous equations directly from the two data points: $K=1\times10^7$, $L=30000$, giving $R_m = LA\Delta P/\mu = 3\times10^{11}\ \mathrm{m^{-1}}$, matching option (D).