Schmidt Number Calculator

Sc = ν/D_AB — ratio of momentum diffusivity to mass diffusivity. The mass-transfer analogue of the Prandtl number; governs the relative thickness of velocity and concentration boundary layers.

Mass Transfer · Dimensionless Number

Inputs

Solve for:

Fluid pair preset (fills ν, D_AB, ρ):

Kinematic viscosity ν (m²/s)

Air ≈ 1.5×10⁻⁵ · Water ≈ 1×10⁻⁶ · Oil ≈ 10⁻⁴–10⁻³ m²/s

Mass diffusivity D (m²/s)

Gas pairs ≈ 10⁻⁵ · Solute in water ≈ 10⁻⁹ m²/s

Also compute dynamic viscosity μ = ρν — enter density ρ

Theory

Definition:

Sc = ν / D_AB [dimensionless]

Sc = μ / (ρ × D_AB) [equivalent form using μ and ρ]

ν = μ / ρ [kinematic viscosity, m²/s]

D_AB = binary mass diffusivity [m²/s]

Physical meaning — boundary layer thickness ratio:

δ_c / δ_v ≈ Sc^(−1/3) (for Sc >> 1)

δ_c ≈ δ_v (for Sc ≈ 1, gases)

For water (Sc ≈ 500), the concentration boundary layer is about 8× thinner than the velocity boundary layer.

Sc vs Pr — heat/mass transfer analogy:

Pr = ν / α (thermal: momentum vs heat diffusion)

Sc = ν / D_AB (mass: momentum vs species diffusion)

Le = α / D_AB = Sc / Pr (Lewis number: heat vs mass diffusion)

The heat-mass transfer analogy lets you replace Pr with Sc (and Nu with Sh) in most forced-convection correlations.

Typical Sc values:

System	Sc	Regime
H₂ in air	0.21	fast diffusion
O₂ in air	0.84	Sc ≈ 1 (gas)
CO₂ in air	0.95	Sc ≈ 1 (gas)
O₂ in water at 25 °C	≈ 425	liquid
NaCl in water at 25 °C	≈ 555	liquid
Sucrose in water 25 °C	≈ 1 700	heavy solute