In a rotary drum vacuum filter operating at steady conditions, which resistance term most often controls the overall filtration rate once cake formation has begun?

Introduction / Context:
Filtration rate is governed by Darcy’s law-like relations, with resistances in series. In rotary drum vacuum filters, after a precoat or initial medium resistance, the growing cake dominates pressure drop and thus the rate.

Given Data / Assumptions:

• Steady operation with continuous cake formation.
• Vacuum level and submergence set.
• Filter medium is clean or periodically washed.

Concept / Approach:
Overall resistance R_total ≈ R_medium + R_cake. As cake thickness increases, R_cake rapidly exceeds R_medium and any minor line losses. Therefore, the cake resistance controls throughput and dictates cycle times and knife settings in precoat operations.

Step-by-Step Solution:
Express rate: Q ∝ ΔP / (μ * (R_medium + R_cake)).Recognise growth of R_cake with time/rotation.Conclude cake resistance is controlling.

Verification / Alternative check:
Empirical filtration curves show declining rate with cake build-up, consistent with dominating R_cake.

Why Other Options Are Wrong:
Piping/receiver line: usually minor compared with porous cake.Medium: initially important but overwhelmed by cake resistance during operation.None of these: incorrect because cake resistance is the standard controlling term.

Common Pitfalls:
Ignoring cake compressibility, which further increases resistance under vacuum.

Final Answer:
Cake resistance