In industrial filtration operations, the flowing filtrate must overcome multiple resistances. Which of the following resistances are encountered during normal cake filtration on a porous medium?

Introduction / Context:
Industrial liquid–solid separation by cake filtration is governed by the hydraulic resistances that oppose flow. Understanding where these pressure losses occur helps engineers diagnose slow filtration, choose filter aids or precoats, and size equipment correctly.

Given Data / Assumptions:

• A porous septum (cloth, screen, leaf) supports the cake.
• A cake builds on the medium as filtration proceeds.
• Piping/porting delivers slurry to the filter and removes filtrate.

Concept / Approach:
The total pressure drop (ΔP_total) equals the sum of the pressure drops across the cake (ΔP_cake), the clean or partially blinded medium (ΔP_medium), and ancillary hydraulic losses in manifolds, channels, and nozzles (ΔP_channel). Engineers often model cake and medium using Darcy’s law, then add estimated minor losses.

Step-by-Step Solution:
Recognize contributions: cake resistance, medium resistance, and channel losses.State relation: ΔP_total = ΔP_cake + ΔP_medium + ΔP_channel.Therefore, all three listed resistances are encountered.

Verification / Alternative check:
Plotting reciprocal filtration rate versus filtrate volume usually shows an intercept (medium + channel resistance at zero cake) and a slope term (cake resistance growth), confirming multiple contributions.

Why Other Options Are Wrong:
Filter medium only: ignores the dominant growing cake layer.Cake only: neglects initial resistance and hydraulic losses.Channels only: these are typically smaller but non-zero contributors.

Common Pitfalls:
Underestimating channel losses in small lab filters, and overfocusing on cake while a blinded cloth or plugged outlet governs flow.

Final Answer:
all (a), (b) and (c)