Q.29 In dead-end filtration, rate of filtration is
(A) directly proportional to the square root of pressure drop across the filter medium
(B) inversely proportional to the pressure drop across the filter medium
(C) inversely proportional to the viscosity of the solution
(D) inversely proportional to the square of viscosity of the solution
In dead-end filtration, all fluid passes perpendicularly through the filter medium,
building a cake that impacts flow dynamics. The correct answer to the MCQ is
(C) inversely proportional to the viscosity of the solution,
as established by filtration equations like Darcy’s law.
Filtration Rate Fundamentals
Filtration rate, or flux, follows Darcy’s law:
dV⁄dt =
A ΔP⁄μR
where:
- dV⁄dt = rate of filtration
- A = filter area
- ΔP = pressure drop
- μ = viscosity of the fluid
- R = resistance of filter medium and cake
Higher viscosity increases flow resistance, slowing the filtration rate inversely.
This relationship holds for dead-end setups where cake buildup causes resistance
to increase with time.
Correct Answer: Option (C)
Option (C) states that the rate of filtration is inversely proportional to the
viscosity of the solution. This directly follows from the Kozeny–Carman and Darcy
equations used in dead-end filtration.
A more viscous (thicker) fluid resists flow through pores, reducing filtration rate.
Increasing temperature lowers viscosity and is often used to improve filtration
efficiency in practice.
