Sutherland's Law for Gas Dynamic Viscosity vs Temperature

Use a consistent reference parameter set

The approximation is mu(T)=mu0×(T/T0)^1.5×(T0+S)/(T+S). For this air example, the COMSOL table supplies mu0=1.716×10^-5 Pa·s, T0=273 K and S=111 K. B2 stores the equivalent 17.16 micro-Pa·s. Keep these reference values together rather than mixing constants from different fits.

Sutherland’s correlation describes gas viscosity approximately, primarily at low pressure. It is not a universal model for liquids, arbitrary gas mixtures, dense gases or reacting flows. Its numeric guards are not a validation of the temperature and pressure range for a particular application.

Calculate the dimensionless temperature factor

E2 evaluates the temperature factor from B3:B5. Both reference and target temperatures must be positive Kelvin values; S is restricted to nonnegative values in this exercise. Convert a Celsius input with T(K)=T(°C)+273.15 before using it.

The factor equals one when T=T0. It does not depend on mu0, so it remains available if the reference viscosity is missing. A numeric-looking text value is rejected instead of silently treated as a temperature.

=IF(COUNT(B3:B5)<>3,"Enter numeric T0,S,T",IF(OR(B3<=0,B4<0,B5<=0),"Require T0,T>0 and S>=0",(B5/B3)^1.5*(B3+B4)/(B5+B4)))

Return dynamic viscosity in two units

E3 multiplies the factor by the positive reference viscosity in micro-Pa·s. E4 converts the unrounded result to Pa·s by dividing by one million. At 600 K the model gives about 30.197 micro-Pa·s; at 220 K it gives about 14.402 micro-Pa·s.

These are dynamic viscosity values, not kinematic viscosity. To calculate kinematic viscosity in m²/s, a compatible density in kg/m³ is also required and nu=mu/rho must use mu in Pa·s.

=IF(NOT(ISNUMBER(E2)),E2,IF(NOT(ISNUMBER(B2)),"Enter numeric reference viscosity",IF(B2<=0,"Require reference viscosity>0",B2*E2)))

Experiment without changing the physical meaning

Return T to 273 K: E3 must recover 17.16 micro-Pa·s. Doubling only mu0 doubles E3 but leaves E2 unchanged. Setting S=0 gives the mathematical square-root temperature scaling; that is a limiting test, not a new calibrated air model.

The predicted viscosity increases with temperature for these positive parameters. Display rounding can make small changes look equal, so keep the underlying values unrounded. No pressure, altitude or compressor-performance calculation is performed here.

=IF(ISNUMBER(E3),E3/1000000,E3)

Further reading

• COMSOL — Sutherland’s Law and air parameters