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.
Equation.
formula_1 
where formula_2 and formula_3 are defined as
formula_4 and formula_5
where:
formula_3 is the modified Reynolds number,<br>
formula_2 is the packed bed friction factor<br>
formula_8 is the pressure drop across the bed,<br>
formula_9 is the length of the bed (not the column),<br>
formula_10 is the equivalent spherical diameter of the packing,<br>
formula_11 is the density of fluid,<br>
formula_12 is the dynamic viscosity of the fluid,<br>
formula_13 is the superficial velocity (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate)<br>
formula_14 is the void fraction (porosity) of the bed.<br>
formula_15 is the particle Reynolds Number.<br>
Extension.
To calculate the pressure drop in a given reactor, the following equation may be deduced
formula_16
This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation which describes laminar flow of fluids across packed beds via the first term on the right hand side. On the continuum level, the second order velocity term demonstrates that the Ergun equation also includes the pressure drop due to inertia, as described by the Darcy–Forchheimer equation.
The extension of the Ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by Akgiray and Saatçı (2001). 