# Schmidt Number

on . Posted in Dimensionless Numbers

Schmidt number, abbreviated as Sc, a dimensionless number, is used in fluid mechanics and heat transfer to characterize the relative importance of mass transfer (diffusion) to momentum transfer (viscous forces).  The Schmidt number is particularly important in problems involving mass transfer, such as the diffusion of solute in a solvent or the transfer of heat in a fluid through convection and conduction.

### Schmidt number categorizes fluids into different regimes

• Low Sc < 1  -  Momentum transfer dominates over mass transfer.  The fluid is often characterized as having a rapid diffusion of mass relative to momentum.
• High Sc > 1  -  Mass transfer is more significant than momentum transfer.  The fluid is characterized by slower diffusion of mass compared to momentum.

In many cases, for common fluids and solutes, the Schmidt number can be approximated as a constant, simplifying calculations involving mass transfer.  For example, in the case of heat transfer in a fluid, the Prandtl number is used to characterize the ratio of momentum diffusivity to thermal diffusivity, and the Schmidt number plays a similar role but for mass transfer.

## Schmidt Number formula

$$\large{ Sc = \frac{ \nu }{ D_m } }$$     (Schmidt Number)

$$\large{ \nu = Sc \; D_m }$$

$$\large{ D_m = \frac{ \nu }{ Sc } }$$

Symbol English Metric
$$\large{ Sc }$$ = Schmidt number $$\large{dimensionless}$$
$$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$
$$\large{ D_m }$$ = mass diffusivity $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$

## Schmidt Number formula

$$\large{ Sc = \frac{ \mu }{ \rho \; D_m } }$$     (Schmidt Number)

$$\large{ \mu = Sc \; \rho \; D_m }$$

$$\large{ \rho = \frac{ \mu }{ Sc \; D_m } }$$

$$\large{ D_m = \frac{ \mu }{ Sc \; \rho } }$$

Symbol English Metric
$$\large{ Sc }$$ = Schmidt number $$\large{dimensionless}$$
$$\large{ \mu }$$  (Greek symbol mu) = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ D_m }$$ = mass diffusivity $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$

Tags: Flow