Packed Bed Pressure Drop Calculator (Ergun Equation)

Estimate the packed bed pressure drop by providing the superficial velocity, particle diameter, viscosity, and voidage.

Inputs

How to use

Enter the superficial velocity, particle diameter, viscosity, and voidage. Click Calculate or rely on the debounced inputs to recompute the pressure drop instantly.

Methodology

The calculator applies the Ergun equation to quantify the combined viscous and inertial resistance in packed beds assuming steady, incompressible flow with water density fixed at 1000 kg/m³.

Full original guide (expanded)

This version preserves the classic Ergun derivation and tracks each term so the pressure drop contributions remain transparent for chemical engineering scenarios.

Illustrative example

Using v = 0.1 m/s, d = 0.01 m, μ = 0.001 Pa·s, and ε = 0.4 yields a pressure drop near 200 Pa. Smaller particles or higher velocities increase the inertia term dramatically.

FAQ

  • What dominates the pressure drop? Low Reynolds numbers make the viscous term dominant, while higher velocities favor the inertial term.
  • Why does voidage matter? Voidage appears cubed in the denominator, so small changes have a large effect on the loss.
Formulas

Ergun equation:

\[\Delta P = \frac{150(1-\varepsilon)}{\varepsilon^3}\frac{\mu v}{d^2} + \frac{1.75(1-\varepsilon)}{\varepsilon^3}\frac{\rho v^2}{d}\]
  • $\Delta P$: Pressure drop (Pa)
  • $v$: Superficial velocity (m/s)
  • $d$: Particle diameter (m)
  • $\mu$: Fluid viscosity (Pa·s)
  • $\varepsilon$: Bed voidage (–)
  • $\rho$: Fluid density (kg/m³), fixed at 1000 for this calculator
Citations

Wikipedia — Ergun equation

Changelog
  • 0.1.0-draft — 2026-01-19: Initial audit draft covering original metadata.
Verified by Ugo Candido
Last Updated: 2026-01-19
Version 0.1.0-draft