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 \(\mathrm{m^{-1}}\))?
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 \(\mathrm{m^{-1}}\))?
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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.
Updated On: Jul 17, 2026
- \(3 \times 10^{-11}\)
- \(3 \times 10^{-8}\)
- \(3 \times 10^{8}\)
- \(3 \times 10^{11}\)
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The Correct Option is D
Solution and Explanation
Step 1: Constant pressure filtration equation.
\[ \frac{t}{V} = \frac{\mu \alpha c}{2 A^2 \Delta P} V + \frac{\mu R_m}{A \Delta P} \]
Step 2: Compute t/V for the two data points.
\((t/V)_1 = 40000\), \((t/V)_2 = 50000\) s/m3
Step 3: Slope and intercept.
\[ a = 1 \times 10^{7}\ \text{s/m}^6,\quad b = 30000\ \text{s/m}^3 \]Step 4: Extract Rm from the intercept.
\[ R_m = \frac{b\, A\, \Delta P}{\mu} = \frac{(30000)(0.05)(2\times 10^{5})}{1\times 10^{-3}} = 3\times 10^{11}\ \mathrm{m^{-1}} \]Was this answer helpful?
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