Philipp Forchheimer

Forchheimer proposed a modification to Darcy's Law, describing fluid flow through packed beds in 1901. This also had a significant influence on the development of the Ergun equation.[1]

${\displaystyle -{dP \over dx}={\mu \over K}u+b\rho |u|u}$

where:

${\displaystyle dP}$ is the pressure drop across the bed,
${\displaystyle \mu }$ is the viscosity of the fluid,
${\displaystyle K}$ permeability (const.),
${\displaystyle u}$ is the (area-averaged) velocity of the fluid,
${\displaystyle b}$ is an empirical constant,
${\displaystyle \rho }$ is the density of the fluid.

A more general expression of the friction factor follows from Forchheimers modification:[1]

${\displaystyle f={1 \over Re}+C}$

where ${\displaystyle Re}$ is the Reynold's number and C is a constant.

• Darcy's Law
• Ergun Equation
• Reynold's Number

• Forchheimer, Philipp: Teaching and the hydraulic manual, 5 volumes, 1914-16.
• JR: Philipp Forchheimer (1852–1933). Water Management 73 (1983), No. 10, p. 350 - 351st