Formula & Calculator
Ergun Equation (Packed Bed Pressure Drop)
Predicts frictional pressure drop per unit length of fluid flowing through a packed bed of particles, combining laminar and turbulent contributions.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| dP/L | Pressure drop per unit bed length | Pa/m |
| mu | Fluid viscosity | Pa.s |
| e | Bed void fraction | |
| v | Superficial velocity | m/s |
| dp | Particle diameter | m |
| rho | Fluid density | kg/m3 |
What it means
The Ergun equation is used to calculate the pressure drop per unit length in a packed bed of particles. It is a combination of the Kozeny‑Carman equation for laminar flow (viscous term) and the Burke‑Plummer equation for turbulent flow (inertial term). The equation is: dP/L = 150 μ (1−ε)² v / (ε³ d_p²) + 1.75 ρ (1−ε) v² / (ε³ d_p), where μ is fluid viscosity, ρ is fluid density, v is superficial velocity, d_p is particle diameter, and ε is void fraction. The first term dominates at low Reynolds numbers (creeping flow), while the second dominates at high Re. This equation is essential for designing fixed‑bed reactors, catalytic converters, and packed columns in absorption and distillation. It is also used in filtration and in the design of sand filters. Accurate prediction of pressure drop is critical for sizing pumps or compressors and for ensuring proper fluid distribution. The Ergun equation is widely used in chemical engineering and is a standard reference for packed bed hydrodynamics.
Worked example
Ergun Equation – Two Examples
Real‑World| Parameter | Value |
|---|---|
| μ | 0.001 Pa·s |
| ε | 0.4 |
| v | 0.02 m/s |
| dp | 0.005 m |
| ρ | 1000 kg/m³ |
| Parameter | Value |
|---|---|
| μ | 2×10⁻⁵ |
| ε | 0.4 |
| v | 0.5 |
| dp | 0.01 |
| ρ | 1.2 |
Common mistakes
- Void fraction ε: The fraction of bed volume that is voids (porosity); typical values 0.35‑0.45 for random packing.
- Particle diameter d_p: For non‑spherical particles, use the equivalent sphere diameter.
- Viscosity μ and density ρ: Fluid properties at the bed temperature.
- Superficial velocity v: Flow velocity based on the empty tube cross‑section (not the interstitial velocity).
- Units: Ensure consistent SI units – the pressure drop will be in Pa/m.
Applications
The Ergun equation predicts the pressure drop through a packed bed of particles, combining viscous (Darcy) and inertial (Forchheimer) contributions. It is used extensively in the design of fixed‑bed catalytic reactors, adsorption columns, and packed distillation towers. The equation accounts for void fraction, particle diameter, fluid properties, and velocity. Engineers use it to calculate the required pump or compressor power, to assess the likelihood of fluidisation, and to design distributors. Accurate pressure drop estimation prevents over‑sizing of equipment and ensures uniform flow distribution. The Ergun equation is also applied in filtration, soil mechanics, and other porous media flow problems, making it a versatile tool in chemical and environmental engineering.
- Design of fixed‑bed catalytic reactors (e.g., steam methane reforming)
- Sizing of adsorption and ion‑exchange columns
- Design of packed distillation and absorption columns
- Assessment of fluidisation and entrainment risks
- Porous media flow in filtration and soil mechanics