ANS:A - Kozney-Karman

The flow of filtrate through the cake in a plate and frame filter press is best described by the Darcy's law equation.

Explanation:

• Darcy's Law: This law describes the flow of fluid through a porous medium, such as a filter cake formed in a plate and frame filter press. It states that the volumetric flow rate QQQ of fluid through the porous medium is directly proportional to the pressure gradient ΔP\Delta PΔP across the medium and inversely proportional to the viscosity μ\muμ of the fluid: Q=k⋅A⋅ΔPμ⋅LQ = \frac{k \cdot A \cdot \Delta P}{\mu \cdot L}Q=μ⋅Lk⋅A⋅ΔP​ Where:
  • QQQ is the volumetric flow rate of filtrate,
  • kkk is the permeability of the filter cake,
  • AAA is the area of the filter medium,
  • ΔP\Delta PΔP is the pressure drop across the filter cake,
  • μ\muμ is the viscosity of the filtrate,
  • LLL is the thickness of the filter cake.
• Application to Plate and Frame Filter Press:
  • In a plate and frame filter press, the filter cake forms between the plates, allowing the filtrate to pass through while retaining solids.
  • Darcy's law is used to model the flow of filtrate through the filter cake, where the pressure drop across the cake and its permeability determine the rate of filtration.
• Other Laws:
  • Kozney-Karman equation: Describes the permeability of porous media and is used in various engineering applications, including filtration studies.
  • Hagen-Poiseuille's law: Describes laminar flow of fluids through pipes and is not directly applicable to the filtration through a porous cake.
  • Fanning's equation: Relates to pressure drop in pipes and is also not directly applicable to filtration through a filter cake.
  • Kremser equation: Not a widely recognized equation in the context of fluid flow through porous media or filter cakes.