# Sutherland's law

(Difference between revisions)
 Revision as of 13:38, 17 May 2007 (view source)Jola (Talk | contribs)← Older edit Revision as of 13:46, 17 May 2007 (view source)Jola (Talk | contribs) Newer edit → Line 1: Line 1: - In 1893 [http://en.wikipedia.org/wiki/William_Sutherland_(physicist) William Sutherland], an Australian physicist, published a relationship between the absolute temperature, $T$, of an ideal gas and its dynamic visocity, $\mu$, based on the 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 (up to several thousand degrees depending on the gas). Sutherland's law can be expressed as: + In 1893 [http://en.wikipedia.org/wiki/William_Sutherland_(physicist) 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: - :$\mu = \mu_0 \left( \frac{T}{T_0} \right)^{3/2}\frac{T_0 + S}{T + S}$ + :$\mu = \mu_r \left( \frac{T}{T_r} \right)^{3/2}\frac{T_r + S}{T + S}$ + + :$T_r$ 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: Some authors instead express Sutherland's law in the following form: Line 9: Line 13: Comparing the formulas above the $C_1$ constant can be written as: Comparing the formulas above the $C_1$ constant can be written as: - :$C_1 = \frac{\mu_0}{T_0^{3/2}}(T_0 + S)$ + :$C_1 = \frac{\mu_r}{T_r^{3/2}}(T_r + S)$ == References == == References == * {{reference-paper|author=Sutherland, W.|year=1893|title=The viscosity of gases and molecular force|rest=Philosophical Magazine, S. 5, 36, pp. 507-531 (1893)}} * {{reference-paper|author=Sutherland, W.|year=1893|title=The viscosity of gases and molecular force|rest=Philosophical Magazine, S. 5, 36, pp. 507-531 (1893)}}

## Revision as of 13:46, 17 May 2007

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:

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

## References

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