The Schmidt Number is defined as the ratio of what to what?

The Schmidt Number is defined as the ratio of what to what?

• A. Dimensionless number defined as the ratio of mass diffusivity to momentum diffusivity
• B. Dimensionless number defined as the ratio of momentum diffusivity to viscous diffusivity
• C. Dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity
• D. Dimensionless number defined as the ratio of momentum diffusivity to mass diffusivity

Answer: (D)

It compares how fast momentum diffuses versus how fast mass diffuses. Momentum diffusion is described by the kinematic viscosity ν = μ/ρ, and mass diffusion is described by the mass diffusivity D. The Schmidt number is the ratio Sc = ν / D = (μ/ρ) / D = μ / (ρ D). So a larger Sc means momentum diffuses much faster than mass, while a smaller Sc means mass diffusion is relatively faster. The other options mix up these ideas: the reciprocal D/ν is not the Schmidt number, the ratio of thermal to mass diffusivity is the Lewis number, and the ratio of momentum to viscous diffusivity is not the standard definition and would not generally yield the correct concept.

It compares how fast momentum diffuses versus how fast mass diffuses. Momentum diffusion is described by the kinematic viscosity ν = μ/ρ, and mass diffusion is described by the mass diffusivity D. The Schmidt number is the ratio Sc = ν / D = (μ/ρ) / D = μ / (ρ D).

So a larger Sc means momentum diffuses much faster than mass, while a smaller Sc means mass diffusion is relatively faster. The other options mix up these ideas: the reciprocal D/ν is not the Schmidt number, the ratio of thermal to mass diffusivity is the Lewis number, and the ratio of momentum to viscous diffusivity is not the standard definition and would not generally yield the correct concept.