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.
where: To calculate the pressure drop in a given reactor, the following equation may be deduced:
( 1 − ϵ
ϵ
( 1 − ϵ )
ϵ
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.
Specifically, the Ergun equation gives the following permeability
and inertial permeability
from the Darcy-Forchheimer law:
ϵ
The extension of the Ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by Akgiray and Saatçı (2001).