Equação de Ergun
Ergun equation

Input data

Volumetric flow

Specific mass

Porosity

Diameter of the particles

Viscosity

Sphericity

Bed length

Output data

Pressure loss

Description

The Ergun equation is used to calculate pressure loss in porous media. This method takes into account the characteristics of the flow and particles to determine the resistance the fluid encounters as it moves through the medium.

The Ergun equation is expressed as follows:

ΔPL=150μ(1ϵ)2dp2ϵ3qA+1.75ρ(1ϵ)dpϵ3(qA)2\frac{\Delta P}{L} = \frac{150 \mu (1 - \epsilon)^2}{d_p^2 \epsilon^3} \cdot \frac{q}{A} + \frac{1.75 \rho (1 - \epsilon)}{d_p \epsilon^3} \cdot \left(\frac{q}{A}\right)^2

Where:

  • ΔP\Delta P is the pressure drop
  • LL is the length of the porous bed
  • μ\mu is the fluid viscosity
  • ϵ\epsilon is the porosity of the medium
  • dpd_p is the average particle diameter
  • qq is the volumetric flow rate
  • AA is the cross-sectional area
  • ρ\rho is the fluid density

Ergun Equation

Input and Output Parameters

ParameterDefault UnitsDescription
Volumetric flow (qq)-Flow rate through the medium
Specific mass (ρ\rho)kg/m³Fluid density
Porosity (ϵ\epsilon)-Fraction of volume that is pore space
Diameter of the particles (dpd_p)mAverage size of the particles
Viscosity (μ\mu)Pa.sFluid's resistance to flow
Sphericity-Measure of the shape of the particles
Bed length (LL)mLength of the porous medium

Output

ParameterDefault UnitsDescription
Pressure loss (ΔP\Delta P)PaPressure drop across the porous medium

References

  • Fonte: AZEVEDO NETTO, J. M. de; FERNANDEZ Y FERNANDEZ, Miguel. Manual de hidráulica, 9.ed. São Paulo: Blucher, 2015.