Which dimensionless number is defined as the ratio of kinematic viscosity to diffusivity?

Which dimensionless number is defined as the ratio of kinematic viscosity to diffusivity?

• A. Froude number
• B. Prandtl number
• C. Nusselt number
• D. Schmidt number

Answer: (D)

The key idea is comparing how quickly momentum spreads versus how quickly a species diffuses. The Schmidt number is defined as the ratio of kinematic viscosity to mass diffusivity, Sc = ν/D. Since ν and D share the same units (area per time), this ratio is dimensionless and tells you which transport process dominates: a large Sc means momentum diffusion is much faster than mass diffusion, so mass transfer is the limiting factor; a small Sc means mass diffuses readily relative to momentum. The other numbers involve different physics—Froude with gravity versus inertia, Nusselt for convective versus conductive heat transfer, and Prandtl for momentum versus thermal diffusivity—so their definitions don’t match the ratio of ν to a diffusivity of a species.

The key idea is comparing how quickly momentum spreads versus how quickly a species diffuses. The Schmidt number is defined as the ratio of kinematic viscosity to mass diffusivity, Sc = ν/D. Since ν and D share the same units (area per time), this ratio is dimensionless and tells you which transport process dominates: a large Sc means momentum diffusion is much faster than mass diffusion, so mass transfer is the limiting factor; a small Sc means mass diffuses readily relative to momentum. The other numbers involve different physics—Froude with gravity versus inertia, Nusselt for convective versus conductive heat transfer, and Prandtl for momentum versus thermal diffusivity—so their definitions don’t match the ratio of ν to a diffusivity of a species.