Question:
Theory of filtration is related to
Theory of filtration is related to
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Darcy’s Law is essential in filter design and predicting flow rates during filtration. It helps optimize filtration efficiency and filter media selection.
Updated On: Jul 14, 2026
- Dalton's method
- Darcy equation
- BET equation
- Stokes' equation
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The Correct Option is B
Approach Solution - 1
Filtration is a unit operation widely used in pharmaceutical and chemical industries to separate solids from liquids. The theory of filtration is fundamentally described by Darcy's Law, which explains the relationship between the rate of fluid flow through a porous medium and the applied pressure.
Darcy's Law equation:
\[
Q = \frac{k \cdot A \cdot \Delta P}{\mu \cdot L}
\]
Where:
- \( Q \) = volumetric flow rate (m³/s)
- \( k \) = permeability of the medium (m²)
- \( A \) = cross-sectional area (m²)
- \( \Delta P \) = pressure difference (Pa)
- \( \mu \) = viscosity of the fluid (Pa·s)
- \( L \) = thickness of the filter medium (m)
Explanation of options: - (a) Dalton's method deals with partial pressures of gases. Not relevant to filtration.
- (b) Darcy equation is directly related to filtration theory, especially constant pressure filtration.
- (c) BET equation relates to surface area determination through gas adsorption, not filtration.
- (d) Stokes' equation is used for sedimentation and particle settling, not for filtration mechanisms.
- \( k \) = permeability of the medium (m²)
- \( A \) = cross-sectional area (m²)
- \( \Delta P \) = pressure difference (Pa)
- \( \mu \) = viscosity of the fluid (Pa·s)
- \( L \) = thickness of the filter medium (m)
Explanation of options: - (a) Dalton's method deals with partial pressures of gases. Not relevant to filtration.
- (b) Darcy equation is directly related to filtration theory, especially constant pressure filtration.
- (c) BET equation relates to surface area determination through gas adsorption, not filtration.
- (d) Stokes' equation is used for sedimentation and particle settling, not for filtration mechanisms.
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Approach Solution -2
This question asks which named equation forms the basis of filtration theory. Checking what each equation is actually used for shows which one describes fluid flow through a filter medium.
- Dalton's method: Dalton's law deals with the total pressure of a mixture of gases being the sum of each gas's partial pressure. It has no connection to liquid flow through a porous filter medium.
- Darcy equation: Darcy's law relates the rate at which a fluid flows through a porous medium to the pressure difference driving that flow, the permeability of the medium, and the fluid's viscosity. Filtration is exactly this situation, a liquid being pushed through a porous filter cake or membrane under pressure, so Darcy's law is the equation filtration theory is built on.
- BET equation: The BET equation is used to calculate a solid's surface area from how much gas adsorbs onto it in multiple layers. It describes a surface phenomenon, not fluid flow through a bed, so it does not apply to filtration.
- Stokes' equation: Stokes' law describes how fast a single particle settles through a fluid under gravity, which is relevant to sedimentation, not to the pressure-driven flow of liquid through a filter medium.
Since filtration is fundamentally about a fluid being driven through a porous medium under a pressure difference, the equation that governs this process is the Darcy equation.
So the correct answer is Darcy equation.
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