Question

In S.I. system, the unit of filter medium resistance is ..............

• A. $\dfrac{\text{kg}}{\text{m}^2 \cdot \text{s}}$
• B. $\dfrac{\text{m}^2}{\text{s}}$
• C. $\dfrac{\text{kg}}{\text{m}^3 \cdot \text{s}}$
• D. $\text{m}^{-1}$

Hint:

Filter resistance represents opposition per unit length, which is why its SI unit is $\text{m}^{-1}$. Remember this for filtration calculations.

Answer 1

The Correct Option is D

In filtration theory, filter medium resistance is a parameter that quantifies the opposition offered by a filter medium to the flow of fluid through it. According to Darcy’s law, the flow through a porous medium is inversely proportional to the resistance.
The basic relation is: \[ \Delta P = \mu \cdot R_m \cdot v \] where:
- $\Delta P$ is the pressure drop across the filter medium,
- $\mu$ is the fluid viscosity,
- $R_m$ is the medium resistance,
- $v$ is the superficial velocity.
Rearranging for $R_m$: \[ R_m = \frac{\Delta P}{\mu \cdot v} \] In SI units:
- $\Delta P$: $\text{N/m}^2$ or $\text{kg}/(\text{m} \cdot \text{s}^2)$
- $\mu$: $\text{kg}/(\text{m} \cdot \text{s})$
- $v$: $\text{m/s}$
So, \[ R_m = \frac{\text{kg}/(\text{m} \cdot \text{s}^2)}{[\text{kg}/(\text{m} \cdot \text{s})] \cdot [\text{m/s}]} = \frac{1}{\text{m}} \] Hence, the SI unit of filter medium resistance is $\text{m}^{-1}$.