# Bioseparation Engineering Questions and Answers – Constant Rate Cake Filtration

This set of Bioseparation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Constant Rate Cake Filtration”.

1. Constant rate filtration refers to _____________
a) constant filtration rate
b) variable filtration rate
c) change in Pressure drop
d) change in the membrane size

Explanation: Constant rate filtration in the process of filtration in bioseparation engineering refers to a process in which during the process of filtration, the rate of filtration is constant by adjusting the pressure drop.

2. What is the expression given for the constant rate of filtration?
a) Q = $$\frac{A\Delta P(t)}{\mu(\frac{\alpha C_\delta Qt}{A})}$$
b) Q = $$\frac{A\Delta P(t)}{(R_M+\frac{\alpha C_\delta Qt}{A})}$$
c) Q = $$\frac{A\Delta P(t)}{\mu(R_M+\frac{C_\delta Qt}{A})}$$
d) Q = $$\frac{A\Delta P(t)}{\mu(R_M+\frac{\alpha C_\delta Qt}{A})}$$

Explanation: The expression for constant rate of filtration is Q = $$\frac{A\Delta P(t)}{\mu(R_M+\frac{\alpha C_\delta Qt}{A})}$$ where, ΔP(t) is the instantaneous pressure drop.

3. When this equation is used ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t }{A^2}$$?
a) Medium resistance maximum
b) Medium resistance negligible
c) Medium resistance minimum
d) Spontaneous pressure drop

Explanation: The equation ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t }{A^2}$$ is used when the medium resistance is negligible than the resistance developed by the cake.

4. How can you rearrange the equation of constant filtration rate in terms of ΔP(t)?
a) ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t}{A^2} – \frac{\mu QR_M}{A}$$
b) ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t}{A^2} . \frac{\mu QR_M}{A}$$
c) ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t}{A^2} + \frac{\mu QR_M}{A}$$
d) ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t}{A^2}$$ μQRM

Explanation: The equation ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t}{A^2} + \frac{\mu QR_M}{A}$$ refers to the rearrangement of the spontaneous pressure drop in the process of constant filtration rate.

5. If the time taken for filtration is twice the rate of filtration what will be the pressure drop after 60 minutes?
a) 100 kPa
b) 200 kPa
c) 130kPa
d) 120kPa

Explanation: ΔP(t) = 2t and t is 60 mins therefore, ΔP(t) = 2 × 60 = 120 kPa.

6. When the filtration rate is doubled what will be the fate of slope in the ∆P(t)vs t plot?
a) Twice
b) Four times
c) No change
d) Thrice

Explanation: The graph can be plotted using the equation ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t}{A^2} + \frac{\mu QR_M}{A}$$ and hence when the filtration rate is doubled then the slope w.r.t the pressure drop and time will be four times.

7. What will be the fate of the intercept when the filtration rate is doubled?
a) Twice
b) Thrice
c) Four times
d) No change

Explanation: The intercept is proportional to the filtration rate when plotted in the graph for ΔP(t) vs t. Therefore, the intercept becomes twice when the filtration rate is doubled.

8. When the pressure drop is 5kPa at time t min then what will be equation for pressure drop?
a) ΔP(t) = t + 5
b) ΔP(t) = 5t
c) ΔP(t) = t – 5
d) ΔP(t) = t

Explanation: When the graph is plotted for ΔP(t)vs.t, then the best fitting line which can be obtained from the plot depending on the given pressure drop and time will be ΔP(t) = t + 5.

9. What will be the fate of variables in the equation ΔP(t) = $$\frac{\mu \alpha C_\delta Q^2 t}{A^2} + \frac{\mu QR_M}{A}$$ when the graph is plotted for ΔP(t)vs.t?
a) Changes twice the pressure drop
b) Changes depending on time
c) Remains same
d) Changes thrice

Explanation: The variables μ, α, Cδ, A, RM remains constant when ΔP(t)vs.t is plotted only the filtration rate varies depending on the pressure drop and the time.

10. What will be the fate of the pressure drop when the filtration rate is constant?
a) Directly proportional
b) Indirect proportional
c) No change
d) Remains constant

Explanation: The pressure drop is directly proportional to the filtration rate, it can be seen from the equation $$\frac{A\Delta P(t)}{\mu(R_M+\frac{\alpha C_\delta Qt}{A})}$$.

Sanfoundry Global Education & Learning Series – Bioseparation Engineering.

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