Baghouse resistance scaling:\nIn a bag filter, the additional resistance offered by the dust cake varies with dust concentration c and particle size s approximately as:

Introduction / Context:
Pressure drop across a baghouse increases due to both the fabric and the growing dust cake. Qualitatively, finer particles pack more densely and build higher resistance per unit mass deposited; greater dust concentration causes the cake to build faster. This question probes the common proportionality used for quick reasoning in troubleshooting filtration systems.

Given Data / Assumptions:

• c denotes dust concentration in the gas phase.
• s denotes a characteristic particle size.
• Other factors (air-to-cloth ratio, pulse cleaning) are held nominally constant.

Concept / Approach:
Smaller particles (lower s) produce more compact cakes with lower permeability, increasing resistance. Higher dust concentration (higher c) accelerates cake growth, also increasing resistance. A simple proportionality that captures both tendencies is resistance ∝ c/s: directly with concentration and inversely with particle size. While detailed models use Kozeny–Carman-type relations and porosity, the c/s scaling is a widely taught qualitative rule-of-thumb.

Step-by-Step Solution:

Verification / Alternative check:
Filtration handbooks present cake resistance proportional to mass deposited and inversely to a permeability term that increases with particle size, supporting the c/s logic qualitatively.

Why Other Options Are Wrong:

• s/c or 1/(s·c): contradict observed trends for finer particles and higher concentrations.
• s·c: predicts larger particles increase resistance, contrary to practice.
• Independence: unrealistic for cake-dominated pressure drop.

Common Pitfalls:
Overinterpreting this proportionality as a rigorous design equation; it is a heuristic for quick troubleshooting.

Final Answer:
Proportional to c/s