Carman-Kozeny equation

The Kozeny-Carman equation , or Carman-Kozeny equation , describes a relation in the field of flow dynamics in order to calculate the pressure loss of a fluid caused by a fine-grained bed of solids . It is named after Josef Kozeny and Philip C. Carman . The equation only applies to laminar flows . It says that the volume flow can be calculated using the pressure difference and the properties of the bed and the fluid: ${\displaystyle {\frac {\mathrm {d} V}{\mathrm {d} t}}}$

${\displaystyle {\frac {\mathrm {d} V}{\mathrm {d} t}}={\varepsilon ^{3}\cdot \Delta p\cdot A\cdot d_{\mathrm {p} }^{2} \over {(1-\varepsilon )^{2}\cdot \eta _{L}\cdot H\cdot K}}}$

• ${\displaystyle \varepsilon }$= Porosity
• ${\displaystyle \Delta p}$ = Pressure difference above and below the substance column
• ${\displaystyle A}$ = Inflow area or cross-section of the substance column through which the substance flows
• ${\displaystyle \eta _{L}}$= Viscosity of the flowing fluid
• ${\displaystyle H}$ = Height of the bed
• ${\displaystyle d_{\mathrm {p} }}$ = Particle diameter

The constant is to be determined by measurement. If you combine the material-specific factors into a hydraulic resistance , you get with ${\displaystyle K}$ ${\displaystyle R}$

${\displaystyle {\frac {\mathrm {d} V}{\mathrm {d} t}}={\Delta p\cdot A \over {\eta _{L}\cdot R}}}$

the Darcy equation .

Individual evidence

1. ↑ ^{a b c} Walter Müller: Basic mechanical operations and their laws . Oldenbourg Verlag, 2008, ISBN 3-486-57842-1 , p. 117 ( limited preview in Google Book search).