HOME

TheInfoList



OR:

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.


Equation

f_p = \frac +1.75 where f_p and Gr_p are defined as f_p = \frac \frac \left(\frac\right) and Gr_p = \frac = \frac; where: Gr_p is the modified Reynolds number,
f_p is the packed bed friction factor
\Delta p is the
pressure drop Pressure drop is defined as the difference in total pressure between two points of a fluid carrying network. A pressure drop occurs when frictional forces, caused by the resistance to flow, act on a fluid as it flows through the tube. The main de ...
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 Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
of fluid,
\mu is the dynamic viscosity of the fluid,
v_s is the
superficial velocity Superficial velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity calculated as if the given phase or fluid were the only one flowing or present in a give ...
(i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate)
\epsilon is the void fraction (
porosity Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measur ...
) of the bed.
Re is the particle Reynolds Number (based on
superficial velocity Superficial velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity calculated as if the given phase or fluid were the only one flowing or present in a give ...
Ergun equation
on archive.org, originally from washington.edu site.
) .


Extension

To calculate the pressure drop in a given reactor, the following equation may be deduced \Delta p = \frac ~\fracv_s + \frac~ \fracv_s, v_s, . 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. The extension of the Ergun equation to
fluidized bed A fluidized bed is a physical phenomenon that occurs when a solid particulate substance (usually present in a holding vessel) is under the right conditions so that it behaves like a fluid. The usual way to achieve a fluidize bed is to pump pressur ...
s, where the solid particles flow with the fluid, is discussed by Akgiray and Saatçı (2001).


See also

*
Hagen–Poiseuille equation In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar fl ...
* Kozeny–Carman equation


References

{{Reflist * Ergun, Sabri. "Fluid flow through packed columns." Chem. Eng. Prog. 48 (1952). * Ö. Akgiray and A. M. Saatçı, Water Science and Technology: Water Supply, Vol:1, Issue:2, pp. 65–72, 2001. Equations Chemical process engineering Fluid dynamics