For a fabric (baghouse) filter, how does gas temperature (through its effect on density and viscosity) influence pressure drop across the bags and dust cake?

Introduction / Context:
Bag filters capture particulates on a fabric medium. The pressure drop (ΔP) is a critical operating parameter influenced by filtration velocity, fabric and dust-cake resistance, and gas properties (notably viscosity and density), both of which vary with temperature.

Given Data / Assumptions:

• Laminar/transition flow through porous media dominates pressure drop.
• Superficial gas velocity and dust-cake thickness are comparable across cases.
• Ideal-gas effects: density decreases as temperature rises at fixed pressure.

Concept / Approach:
For flow through porous media, ΔP often scales with gas viscosity and filtration velocity (Darcy-type behavior). Gas density influences dynamic terms and fan power; at a given mass flow, higher temperature lowers density, increasing volumetric flow and velocity, which in turn raises ΔP. Absolute static pressure itself does not linearly set ΔP across the filter—velocity/viscosity and cake resistance dominate.

Step-by-Step Solution:
Relate ΔP to gas properties: ΔP ∝ μ * v through fabric/cake resistance.Consider density indirectly via v: at constant mass flow, lower density → higher volumetric flow → higher v → higher ΔP.Therefore, ΔP increases with viscosity and (through velocity) density effects; option (b) captures this dependence best.

Verification / Alternative check:
Baghouse models and manufacturer curves show ΔP rising with temperature when viscosity increases and when volumetric flow rises due to density drop at constant mass flow.

Why Other Options Are Wrong:
(a) Inverse with viscosity is incorrect for porous-media flow.
(c) Direct proportionality to absolute pressure is not the governing relationship for ΔP across the medium.

Common Pitfalls:
Ignoring the coupling between density, volumetric flow, and face velocity; neglecting cake conditioning and pulsing effects on resistance.

Final Answer:
Pressure drop is proportional to the viscosity and density of the gas.