### Calculate Gas Viscosity with Sutherland's Law

This Excel spreadsheet calculates the viscosity of gasses with Sutherland's Law. The spreadsheet contains constants suitable for air, but can be used for other gases.

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)
• 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

• 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)
The molecular weight of air, for example, is 28.96 kg kmol-1.

Sutherland's Law is accurate for moderate temperatures and pressures, and also describes the viscosity-temperature relationship of gasses at hypersonic speeds.

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