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

where

- μ is the dynamic viscosity (Pa s or kg m
^{-1}s^{-1}) - T is the temperature (K)
- μ
_{ref}is a reference viscosity (Pa s or kg m^{-1}s^{-1}) - T
_{ref}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})

^{-1}.

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**

## 0 comments:

## Post a Comment