Calculator Inputs
Use direct superficial velocity or derive it from flow rate and column diameter.
Example Data Table
Illustrative operating points showing how pressure losses rise with superficial velocity.
| Superficial Velocity (m/s) | Viscous Term (kPa/m) | Inertial Term (kPa/m) | Total Gradient (kPa/m) | Total ΔP (kPa) |
|---|---|---|---|---|
| 0.0600 | 6.9444 | 21.8750 | 28.8194 | 34.5833 |
| 0.0900 | 10.4167 | 49.2188 | 59.6354 | 71.5625 |
| 0.1200 | 13.8889 | 87.5000 | 101.3889 | 121.6667 |
| 0.1500 | 17.3611 | 136.7188 | 154.0799 | 184.8958 |
| 0.1800 | 20.8333 | 196.8750 | 217.7083 | 261.2500 |
Formula Used
Ergun equation for packed beds:
ΔP / L = [150 μ U (1 − ε)²] / [dp² φ² ε³] + [1.75 ρ U² (1 − ε)] / [dp φ ε³]
Total pressure drop: ΔP = (ΔP / L) × L
Packed-bed Reynolds number: Rep = ρ U dp / [μ (1 − ε)]
Packed-bed friction factor: fp = 150 / Rep + 1.75
Where μ is dynamic viscosity, ρ is fluid density, U is superficial velocity, ε is bed void fraction, dp is particle diameter, φ is particle sphericity, and L is bed length.
The first term represents viscous resistance and dominates slower flows. The second term represents inertial resistance and grows faster as velocity increases.
How to Use This Calculator
- Enter fluid density and viscosity using the unit selectors.
- Provide bed porosity, particle diameter, sphericity, and bed length.
- Choose direct superficial velocity or derive velocity from flow rate and column diameter.
- Submit the form to calculate the pressure gradient and total packed-bed pressure drop.
- Review the viscous and inertial split, Reynolds number, regime indicator, and chart.
- Use the CSV or PDF buttons to export results and the example table.
Frequently Asked Questions
1) What does this calculator estimate?
It estimates pressure gradient and total pressure drop across a packed bed using the Ergun equation. It also separates viscous and inertial contributions for easier interpretation.
2) When should the Ergun equation be used?
Use it for flow through packed particles, pellets, catalyst beds, or granular media when you know porosity, particle size, fluid properties, and superficial velocity.
3) Why is void fraction important?
Void fraction strongly affects channel space and resistance. Lower porosity shrinks open flow area, increasing both viscous and inertial losses significantly.
4) Why does particle sphericity matter?
Less spherical particles create more drag and tortuous flow paths. Including sphericity adjusts the Ergun prediction for nonideal particle shape effects.
5) Can this be used for gases and liquids?
Yes. The method works for both, provided the chosen density and viscosity reflect actual operating conditions and the bed remains reasonably uniform.
6) What does a high inertial share indicate?
It means velocity-driven losses are becoming dominant. This often happens at higher flow rates, where pressure drop rises faster than linearly.
7) Does the calculator use superficial or interstitial velocity?
It uses superficial velocity in the Ergun equation. If you enter flow rate and column diameter, the tool first converts them into superficial velocity.
8) How can I improve prediction accuracy?
Use realistic viscosity and density at process temperature, accurate porosity, representative particle size, and measured sphericity. Nonuniform beds or channeling can cause deviation from ideal predictions.