William Sutherland was an Australian scientist who studied the temperature-dependence of ideal gases. In 1893, he developed an empirical-theoretical relationship between the temperature and viscosity of an ideal gas.
Essentially, the method uses a known reference viscosity and temperature to find another viscosity at a specified temperature.
Sutherland's formula is
- μ is the dynamic viscosity (Pa s or kg m-1 s-1)
- T is the temperature (K)
- μref is a reference viscosity (Pa s or kg m-1 s-1)
- Tref is a reference temperature (K)
- S is the Sutherland Constant for the gas (K)
The Sutherland Constant is characteristic for the gas. For example,
- air at 323 K has a viscosity of 1.716 x 10-5 Pa s, with a Sutherland Constant of 110 K
- helium at 273K has a viscosity of 1.9 x 10-5 Pa s, with a Sutherland Constant of 79.4 K
The spreadsheet also
- finds the density of the gas with the Ideal Gas Law
- calculates the kinematic viscosity by dividing the dynamic viscosity by the gas density
The Ideal Gas Law is given by this formula
where
- R is the Universal Gas Constant (8314.4 J kmol-1 K-1)
- M is the molecular weight of the gas (kg kmol-1)
- P is the pressure (Pa)
- ρ is the density (kg m-3)
Sutherland's Law is accurate for moderate temperatures and pressures, and also describes the viscosity-temperature relationship of gasses at hypersonic speeds.
Download Excel Spreadsheet to Calculate Gas Viscosity with Sutherland's Law
