Gas filtration through fabric (bag filter): how does clean-side pressure drop scale with gas properties in first-cut sizing?

Introduction / Context:
Bag filters remove particulates by forcing gas through a porous fabric. The pressure drop (ΔP) across the medium is a key design parameter because it drives fan power and operating cost. Understanding which gas properties influence ΔP helps avoid incorrect scaling during preliminary selection.

Given Data / Assumptions:

• Clean or lightly dust-loaded fabric (cake resistance negligible for the moment).
• Low to moderate face velocity; laminar flow through pores (Darcy regime).
• Ideal gas behavior; steady operation at a given temperature.

Concept / Approach:
In laminar flow through porous media, Darcy’s law gives ΔP = (μ * v * L) / k, where μ is dynamic viscosity, v is superficial velocity, L is thickness, and k is permeability. In this regime, ΔP is directly proportional to viscosity and velocity; gas density does not directly appear in the linear term (density mainly affects fan power through volumetric flow and can appear in non-Darcy/inertial terms at higher velocities). Hence, simple statements that assert a direct or inverse proportionality to density are not generally correct for the Darcy regime.

Step-by-Step Solution:
Start from Darcy’s law: ΔP ∝ μ * v for a given medium.Note that none of the options (a), (b), or (c) matches this clean dependence because each imposes a specific density proportionality.Therefore, the only accurate choice within the given list is “None of these.”

Verification / Alternative check:
At higher velocities, Forchheimer (inertial) effects add a term ∝ ρ * v^2. That would make ΔP partly depend on density, but not “directly only” as in options given; it becomes a mixed μ and ρ dependence, still inconsistent with (a)–(c).

Why Other Options Are Wrong:
(a) ignores viscosity dependence; (b) and (c) assign density dependencies that are not inherent in Darcy’s linear regime; (e) compressibility factor is not a primary parameter here.

Common Pitfalls:
Confusing fan power (which depends on ρ via volumetric flow) with filter ΔP scaling; neglecting cake growth, which later dominates ΔP and may change scaling.

Final Answer:
None of these.