Deriving the Porous Coefficients Based on Experimental Pressure and Velocity Data

Experimental data, that is available in the form of pressure drop against velocity through the porous component, can be extrapolated to determine the coefficients for the porous media. To effect a pressure drop across a porous medium, the coefficients of the porous media are determined in the manner described below.

Then a curve can be plotted through these points, in the form ΔP/Δx = Av² + Bv, in this case yielding ΔP/Δx = 0.27394v² + 4.68819v.

Viscous Resistance Coefficient, C₁

From this curve the viscous resistance factor, C₁, can be determined by C₁ = B/µ, where B is from the fitted curve, and μ is the fluid viscosity. In this example, B = 4.68816 kg/(m³ s) and if μ = 1.7894 x 10^-5, then C₁ = 261996 1/m²

Inertial Resistance Coefficient, C₂

From this curve the inertial resistance factor, C₂, can be determined by C₂ = 2A/ρ, where A is from the fitted curve, and ρ is the density of the fluid. In this example, A = 0.27394 kg/m⁴ and if ρ = 1.225 kg/m³, this leads to C₂ = 0.4472 1/m.