Packed Bed Pressure Loss Calculation (Ergun Equation)

Estimate pressure loss through a packed bed from velocity, particle diameter, porosity, viscosity, density, and bed length.

The Ergun equation combines viscous and inertial pressure-loss terms for flow through a packed particle bed.

STEP 1

Enter Packed Bed Conditions

Enter superficial velocity, particle diameter, porosity, fluid properties, bed length, and the desired pressure loss unit.

Flow velocity

Velocity unit

Particle diameter

Particle diameter unit

Porosity

Use a value between 0 and 1.

Viscosity

Viscosity unit

Fluid density

Density unit

Packed bed length

Length unit

Pressure loss unit

Calculation Result

Enter packed bed conditions and press Calculate to see pressure loss.

Ergun Equation

The Ergun equation predicts pressure loss for fluid flow through a fixed packed bed. It combines a viscous term that dominates at low velocity and an inertial term that grows at higher velocity.

Delta P / L = 150 mu (1 - epsilon)^2 v / (d_p^2 epsilon^3) + 1.75 rho (1 - epsilon) v^2 / (d_p epsilon^3)

Delta P: pressure loss
L: bed length
v: superficial velocity
d_p: particle diameter
epsilon: bed porosity
mu: fluid viscosity
rho: fluid density

The equation is most accurate for reasonably uniform particles. Very high velocities, elongated particles, wall effects, and real packed-bed geometry may require empirical adjustment.

How to Use the Result

Use the pressure loss as an estimate for pump, blower, or compressor margin. Compare alternative particle sizes, porosity values, and bed lengths to understand which parameter is driving pressure loss.