Forchheimer's equation

The Forchheimer equation (after Philipp Forchheimer ) describes the pressure loss in a flow (mostly in porous media). The equation extends Darcy's law , which only takes pressure losses from dynamic viscosity into account, by a term for pressure losses from turbulence :

${\displaystyle -{\frac {dp}{dx}}={\frac {\eta }{K}}u+{\frac {\rho }{k_{2}}}u^{2}}$

With

• the pressure loss over the route ${\displaystyle dp}$ ${\displaystyle dx}$
• the dynamic viscosity of the flowing fluid ${\displaystyle \eta }$
• the permeability (unit m²) of the porous medium ${\displaystyle K}$
• the flow rate of the fluid ${\displaystyle u}$
• the density of the flowing fluid ${\displaystyle \rho }$
• the non-Darcy's permeability coefficient (unit m) of the porous medium. ${\displaystyle k_{2}}$

The two coefficients and are mostly determined experimentally and are only dependent on the geometry of the porous medium, but not on the flowing fluid. ${\displaystyle K}$ ${\displaystyle k_{2}}$

For the Forchheimer equation changes into Darcy's law. ${\displaystyle k_{2}\to \infty }$

See also

• Keulegan-Carpenter number

Web links

• HD Baehr, K. Stephan: Heat and mass transfer, see formula 3.275 on p. 417