Ergun equation for packed-bed pressure drop

It is volumetric flow divided by the full empty-column cross-sectional area. Fluid actually passes only through voids, so mean pore velocity is higher. Ergun is written in terms of superficial velocity; substituting pore velocity directly can count porosity twice and distort the pressure drop. The correlation uses superficial velocity and empirical coefficients for packed beds. Application: Estimate pressure loss in catalyst beds, filters and packed columns. The numerical example For ε=0.40, μ=0.001 Pa·s, ρ=1000 kg/m³, us=0.010 m/s and dp=0.005 m, the viscous term is 337.5 Pa/m and the inertial term 328.1 Pa/m. Total gradient is about 665.6 Pa/m. Both terms have units Pa/m; one scales with us and the other with us² anchors the idea in a concrete measurement case.

At low velocity, the first term scales with us while the second scales with us². The linear viscous contribution therefore often matters more at slow flow; the inertial part grows faster as velocity rises. These are additive contributions, not regimes with a sharp boundary. Calculate both before simplifying. The correlation uses superficial velocity and empirical coefficients for packed beds. The corresponding units are Δp/L in Pa/m; μ in Pa·s; superficial velocity in m/s; dp in m; density in kg/m³; ε dimensionless. For ε=0.40, μ=0.001 Pa·s, ρ=1000 kg/m³, us=0.010 m/s and dp=0.005 m, the viscous term is 337.5 Pa/m and the inertial term 328.1 Pa/m. Total gradient is about 665.6 Pa/m. Both terms have units Pa/m; one scales with us and the other with us². This checks that the reference quantities are compatible.

Both terms contain strong factors with ε³ in the denominator, so a denser bed has a much larger pressure drop at the same particles and flow rate. Small porosity changes can therefore matter. Use measured or defensibly estimated porosity and check wall and channel effects; a uniform ideal bed may miss real packing structure. The correlation uses superficial velocity and empirical coefficients for packed beds. Scope: This empirical correlation describes flow through a packed bed; superficial velocity is based on the empty vessel cross-section, not pore velocity. It assumes a suitable particle-size representation, porosity and fluid properties. Wall channeling, irregular particles, compressibility, very short beds and fluidization may require corrections. The two terms represent viscous and inertial losses; the range and coefficients are empirical. A practical application is Estimate pressure loss in catalyst beds, filters and packed columns.

The example gives 337.5 Pa/m from the viscous term and 328.1 Pa/m from the inertial term. Their sum is about 665.6 Pa/m. Multiplying by bed length gives total pressure drop only if properties remain constant along it. Use dp in metres and μ in Pa·s; convert millimetre inputs first. The correlation uses superficial velocity and empirical coefficients for packed beds. Check the calculation with this case: For ε=0.40, μ=0.001 Pa·s, ρ=1000 kg/m³, us=0.010 m/s and dp=0.005 m, the viscous term is 337.5 Pa/m and the inertial term 328.1 Pa/m. Total gradient is about 665.6 Pa/m. Both terms have units Pa/m; one scales with us and the other with us². Keep the model limits and units in view.

A packed bed is a tortuous pore network with changing passages, unlike a smooth pipe with wall friction. Ergun uses particle diameter and porosity, whereas pipe models use Reynolds number, roughness and pipe diameter. Use Ergun or a validated packing correlation for beds, and a suitable pipe-loss equation for conduits. The correlation uses superficial velocity and empirical coefficients for packed beds. The relation describes The Ergun equation combines viscous and inertial contributions to the pressure gradient through a packed particle bed. This helps distinguish its target quantity from neighbouring quantities.