State the unit of specific cake resistance (alpha) used in filtration calculations when expressed in centimetre–gram units.

Introduction / Context:Specific cake resistance alpha links filtration pressure drop to flow through a porous cake. Using proper units ensures consistent scale-up and design. Alpha is widely reported either in SI (m/kg) or in cgs equivalents.

Given Data / Assumptions:

• We work in cgs-style units for clarity.
• Darcy-type filtration equations relate deltaP to mu, alpha, cake mass per area, and superficial velocity.

Concept / Approach:In constant pressure filtration, the cake contribution to resistance can be written as R_cake = alpha * (M/A), where M/A is mass of solids deposited per unit area. Since R has dimensions of length (in cgs, cm) and M/A has dimensions of g/cm^2, the dimensions of alpha must be (length) / (mass per area) = cm / (g/cm^2) = cm^3/g·cm = cm/g.

Step-by-Step Solution:Start with R_cake = alpha * (M/A).[R_cake] = length; [M/A] = g/cm^2.Thus [alpha] = length / (g/cm^2) = cm * (cm^2/g) = cm^3/g per cm of area basis → simplifies to cm/g.

Verification / Alternative check:In SI, alpha is often reported as m/kg. Converting m/kg to cm/g yields the same dimensional form.

Why Other Options Are Wrong:g/cm^2 and g/g: mass ratios, not resistance factors.cm/g^2: incorrect mass exponent.

Common Pitfalls:Confusing alpha with medium resistance R_m; the latter has dimension of length, while alpha couples length with mass loading.

Final Answer:cm/g