Ergun equation

The Ergun equation, derived by the Turkish chemical engineer Sabri Ergun in 1952, expresses the friction factor in a packed column as a function of the modified Reynolds number. The Ergun equation, derived by the Turkish chemical engineer Sabri Ergun in 1952, expresses the friction factor in a packed column as a function of the modified Reynolds number. f p = 150 G r p + 1.75 {displaystyle f_{p}={frac {150}{Gr_{p}}}+1.75} where f p {displaystyle f_{p}} and G r p {displaystyle Gr_{p}} are defined as f p = Δ p L D p ρ v s 2 ( ϵ 3 1 − ϵ ) {displaystyle f_{p}={frac {Delta p}{L}}{frac {D_{p}}{ ho v_{s}^{2}}}left({frac {epsilon ^{3}}{1-epsilon }} ight)} and G r p = ρ v s D p ( 1 − ϵ ) μ {displaystyle Gr_{p}={frac { ho v_{s}D_{p}}{(1-epsilon )mu }}} where: G r p {displaystyle Gr_{p}} is the modified Reynolds number, fp is the packed bed friction factor Δ p {displaystyle Delta p} is the pressure drop across the bed, L {displaystyle L} is the length of the bed (not the column), D p {displaystyle D_{p}} is the equivalent spherical diameter of the packing, ρ {displaystyle ho } is the density of fluid, μ {displaystyle mu } is the dynamic viscosity of the fluid, v s {displaystyle v_{s}} is the superficial velocity (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate), and ϵ {displaystyle epsilon } is the void fraction of the bed (bed porosity at any time).