Synaptotagmin

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 Reynolds number:

$f_p=\frac{150}{G{r}_p}+1.75$

where $f_p$ and $G{r}_p$ are defined as

$f_p=\frac{\mathrm{\Delta }p}{L}\frac{D_p}{\rho V_s^2}\left(\frac{{ϵ}^3}{1-ϵ}\right)$ and $G{r}_p=\frac{D_p{V}_s\rho }{(1-ϵ)\mu }$

where: $\mathrm{\Delta }p$ is the pressure drop across the bed,
$L$ is the length of the bed (not the column),
$D_p$ is the equivalent spherical diameter of the packing,
$\rho$ is the density of fluid,
$\mu$ is the dynamic viscosity of the fluid,
$V_s$ is the superficial velocity (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate), and
$ϵ$ is the void fraction of the bed (bed porosity at any time).

Extension of the Ergun equation to fluidized beds is discussed by Akgiray and Saatçı (2001).

To calculate the pressure drop in a given reactor, the following equation may be deduced $\mathrm{\Delta }p=\frac{150\mu (1-ϵ{)}^2{V}_{s}L}{{ϵ}^3{D}_p^2}+\frac{1.75(1-ϵ)\rho V_s^{2}L}{{ϵ}^3{D}_p}$

See also

Kozeny–Carman equation

References

• S. Ergun, Chem. Process Eng. London 48, 89 1952. legacy.library.ucsf.edu/documentStore/e/f/k/.../Sefk76a99.pdf‎
• Ö. Akgiray and A. M. Saatçı, Water Science and Technology: Water Supply, Vol:1, Issue:2, pp. 65–72, 2001.