ANS:C -

The Kozney-Karman equation, which is valid for low Reynolds numbers (ReReRe), describes fluid flow through a packed bed of solids. It relates the permeability of the porous medium (packed bed) to the porosity and specific surface area of the particles. The Kozney-Karman equation is given by: ΔPL=150μ(1−ϵ)2ϵ3dp2⋅vρ\frac{\Delta P}{L} = \frac{150 \mu (1 - \epsilon)^2}{\epsilon^3 d_p^2} \cdot \frac{v}{\rho}LΔP​=ϵ3dp2​150μ(1−ϵ)2​⋅ρv​ where:

• ΔP\Delta PΔP is the pressure drop across the packed bed,
• LLL is the length of the bed,
• μ\muμ is the dynamic viscosity of the fluid,
• ϵ\epsilonϵ is the porosity of the bed (fraction of void space),
• dpd_pdp​ is the diameter of the particles,
• vvv is the superficial velocity of the fluid,
• ρ\rhoρ is the density of the fluid.

Explanation:

• Permeability: The term 150μ(1−ϵ)2ϵ3dp2\frac{150 \mu (1 - \epsilon)^2}{\epsilon^3 d_p^2}ϵ3dp2​150μ(1−ϵ)2​ represents the permeability KKK of the porous medium (packed bed).
• Superficial Velocity: vρ\frac{v}{\rho}ρv​ is the superficial velocity of the fluid.

Application:

The Kozney-Karman equation is useful in predicting pressure drop across packed beds used in various industrial processes, such as fluidized beds, packed columns in chemical engineering, and filtration systems. It assumes laminar flow conditions (low Reynolds numbers), where viscous forces dominate and inertial forces are negligible.

Conclusion:

Therefore, the Kozney-Karman equation, which is valid for low Reynolds numbers and describes fluid flow through a packed bed of solids, is: ΔPL=150μ(1−ϵ)2ϵ3dp2⋅vρ\frac{\Delta P}{L} = \frac{150 \mu (1 - \epsilon)^2}{\epsilon^3 d_p^2} \cdot \frac{v}{\rho}LΔP​=ϵ3dp2​150μ(1−ϵ)2​⋅ρv​