Filtration rate dependencies: which statement correctly reflects the variables that filtration rate depends upon in pressure or vacuum filtration?

Introduction / Context:
Designing filtration cycles requires recognizing the variables that control volumetric flow through porous media. Darcy’s law describes the dependence on pressure drop, viscosity, resistance of medium and cake, and area. The question asks which items filtration rate depends upon—and the trick is that it depends on all of them, so “None of these” (meaning “not only one” of them) is the correct choice.

Given Data / Assumptions:

• Darcy model: ΔP = μ * (Rm + α * w/A) * (V̇/A).
• μ depends on filtrate properties; α and w characterize cake.
• A is filter area; ΔP is pressure drop.

Concept / Approach:
From the model, filtration rate V̇/A is proportional to ΔP/μ and inversely proportional to the sum of resistances (Rm + α·w/A). Thus, pressure drop, area, cake resistance, medium resistance, and filtrate properties (viscosity) all matter. No single listed subset alone is sufficient to describe the rate fully.

Step-by-Step Solution:
Recognize each factor: ΔP, A, Rm, α, w, μ.Map to options: (a) covers ΔP and A; (b) covers resistances; (c) covers cake and filtrate properties.Conclusion: filtration rate depends on all; therefore “None of these” is correct in this single-choice framing.

Verification / Alternative check:
Pilot filtration tests that vary only ΔP show diminishing returns when cake compressibility rises, confirming multi-factor dependence.

Why Other Options Are Wrong:
(a), (b), (c): each is partially true but incomplete; selecting any one excludes other essential variables.

Common Pitfalls:
Overemphasizing pressure drop while ignoring viscosity or cake compressibility.

Final Answer:
None of these.