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Sutherland's law

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In 1893 William Sutherland, an Australian physicist, published a relationship between the absolute temperature, T, of an ideal gas and its dynamic visocity, \mu, based on kinetic theory of ideal gases and an idealized intermolecular-force potential. This formula, often called Sutherland's law, is still commonly used and most often gives fairly accurate results with an error less than a few percent over a wide range of temperatures. Sutherland's law can be expressed as:

\mu = \mu_r \left( \frac{T}{T_r} \right)^{3/2}\frac{T_r + S}{T + S}
T_r is a reference temperature.
\mu_r is the viscosity at the T_r reference temperature
S is the Sutherland temperature

Some authors instead express Sutherland's law in the following form:

\mu = \frac{C_1 T^{3/2}}{T + S}

Comparing the formulas above the C_1 constant can be written as:

C_1 = \frac{\mu_r}{T_r^{3/2}}(T_r + S)


  • Sutherland, W. (1893), "The viscosity of gases and molecular force", Philosophical Magazine, S. 5, 36, pp. 507-531 (1893).
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