Utilities

This page gathers small interactive tools for quick calculations.

Terminal velocity calculator

This utility calculates the terminal velocity, Reynolds number and drag coefficient of a spherical particle. The forces accounted for are drag, buoyancy and gravity. Various drag models are available.

Diameter d_p [m]

Particle density ρ_p [kg/m³]

Fluid density ρ_f [kg/m³]

Dynamic viscosity μ [Pa·s]

Compute

Drag model

Stokes Schiller–Naumann (1933) Clift–Gauvin (1970) Clift–Grace–Weber (2005)

C_D = 24 / Re_p (Stokes)

Terminal Velocity – m/s

Particle Reynolds Number –

Drag Coefficient –

Minimum fluidization & bed expansion

Estimate the minimum fluidization velocity from hindered-drag correlations. Visualize how the bed expands with superficial gas/liquid velocity (top graph) or what is the equilibrium superficial velocity as a function of the bed voidage (bottom graph).

Particle diameter d_p [m]

Particle density ρ_p [kg/m³]

Fluid density ρ_f [kg/m³]

Dynamic viscosity μ [Pa·s]

Packed voidage ε₀ [–]

Compute

Hindered drag model

Beetstra et al. (2007) Di Felice (1994) Tenneti et al. (2011) Rong et al. (2015) Wen–Yu (1966)

Beetstra et al. (2007)

Minimum fluidization velocity U_mf – m/s

Slip velocity at U_mf – m/s

Particle Re at U_mf –