The Ergun Equation Calculator estimates the pressure drop that occurs when a fluid flows through a packed bed of solid particles. This is essential in industries such as chemical processing, filtration, petroleum refining, and wastewater treatment. The calculator applies the Ergun equation, a well-known model that combines both viscous and inertial losses in porous media to compute the total pressure drop per unit length of the bed.
Engineers use this tool to design and optimize packed bed reactors and filtration systems, ensuring that energy costs remain efficient while maintaining effective flow through the system. Instead of manually solving the complex equation every time, users can enter values into the calculator and receive accurate, fast results.
formula of Ergun Equation Calculator
ΔP / L = (150 × (1 − ε)² × μ × v) / (dₚ² × ε³) + (1.75 × (1 − ε) × ρ × v²) / (dₚ × ε³)
Where:
ΔP / L = pressure drop per unit length (Pa/m)
ε = bed void fraction (dimensionless)
μ = dynamic viscosity of the fluid (Pa·s)
v = superficial fluid velocity (m/s)
dₚ = particle diameter (m)
ρ = fluid density (kg/m³)
This formula includes two parts:
- The first term accounts for viscous (laminar) flow losses.
- The second term accounts for kinetic (turbulent) losses.
It works well across different flow regimes, making it a reliable model for industrial fluid systems.
Helpful Reference Table
The table below shows typical values and ranges that engineers often use when calculating pressure drops in packed beds.
| Parameter | Typical Range | Description |
|---|---|---|
| Void fraction (ε) | 0.35 – 0.45 | Space between particles in the bed |
| Viscosity (μ) | 0.001 – 0.01 Pa·s | Water ≈ 0.001 Pa·s, oils ≈ higher values |
| Velocity (v) | 0.01 – 1.0 m/s | Flow speed of fluid across the bed |
| Particle diameter (dₚ) | 0.001 – 0.01 m | Size of packing particles |
| Fluid density (ρ) | 1000 kg/m³ (water) | Changes with fluid type |
These typical values help users check if their inputs fall within expected ranges, which is useful for verifying results or setting up experiments.
Example of Ergun Equation Calculator
Assume the following values:
- ε = 0.4
- μ = 0.001 Pa·s (water)
- v = 0.1 m/s
- dₚ = 0.005 m
- ρ = 1000 kg/m³
Apply the formula:
First term (viscous):
(150 × (1 − 0.4)² × 0.001 × 0.1) / (0.005² × 0.4³)
= (150 × 0.36 × 0.001 × 0.1) / (0.000025 × 0.064)
= 0.0054 / 0.0000016 = 3375 Pa/m
Second term (inertial):
(1.75 × (1 − 0.4) × 1000 × 0.1²) / (0.005 × 0.064)
= (1.75 × 0.6 × 1000 × 0.01) / (0.00032)
= 10.5 / 0.00032 = 32812.5 Pa/m
Total pressure drop:
ΔP / L = 3375 + 32812.5 = 36187.5 Pa/m
So, the pressure drop per meter of the packed bed is about 36,188 pascals.
Most Common FAQs
It calculates pressure drop in packed beds, such as filters or reactors. It combines both laminar and turbulent flow effects to give accurate predictions in mixed-flow conditions.
Void fraction represents the empty space in the packed bed. It greatly affects fluid flow. A higher void fraction means less resistance, and a lower one means tighter packing and more pressure drop.
Yes. As long as you input the correct viscosity and density for your fluid, the Ergun equation works for both gases and liquids.