Question

Which filtration law describes the relationship between filtration rate and pressure drop for incompressible filter cakes?

• A. Stokes' Law
• B. Darcy's Law
• C. Fick's Law
• D. Henry's Law

Hint:

In filtration questions, Darcy's law is the foundational flow equation through porous beds, matching pressure drop and flow rate.

Answer 1

The Correct Option is B

Step 1: Understanding the Problem:
The question asks to identify the classical equation/law of fluid dynamics that describes the flow of filtrate through a porous, incompressible cake under an applied pressure drop.

Step 2: Key Formula or Approach: Darcy's Law describes fluid flow through porous media:
\[ \frac{dV}{dt} = \frac{A \cdot \Delta P}{\mu \cdot R} \]
where $\frac{dV}{dt}$ is the volumetric filtration rate, $A$ is the filtration area, $\Delta P$ is the pressure drop across the bed, $\mu$ is the viscosity of the filtrate, and $R$ is the total resistance of the cake.

Step 3: Detailed Explanation:

• Darcy's Law: Formulates that the velocity of fluid passing through a porous bed is directly proportional to the pressure gradient and inversely proportional to the viscosity of the fluid and the flow resistance of the bed. It forms the foundation for analyzing filtration rate in incompressible cakes.

• Stokes' Law: Relates to the terminal velocity of a solid particle falling through a viscous fluid under gravity.

• Fick's Law: Governs molecular mass transfer by diffusion.

• Henry's Law: Relates the concentration of a dissolved gas to its partial pressure above the liquid.

Step 4: Final Answer:
Consequently, Darcy's Law is the correct governing law.