# Sutherland's law

(Difference between revisions)
 Revision as of 14:16, 17 May 2007 (view source)Jola (Talk | contribs)← Older edit Revision as of 17:14, 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 dynamic visocity, $\mu$, and the absolute temperature, $T$, of an ideal gas. This formula, often called Sutherland's law, is based on kinetic theory of ideal gases and an idealized intermolecular-force potential. 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: In 1893 [http://en.wikipedia.org/wiki/William_Sutherland_(physicist) William Sutherland], an Australian physicist, published a relationship between the dynamic visocity, $\mu$, and the absolute temperature, $T$, of an ideal gas. This formula, often called Sutherland's law, is based on kinetic theory of ideal gases and an idealized intermolecular-force potential. 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: - :$\mu = \mu_r \left( \frac{T}{T_r} \right)^{3/2}\frac{T_r + S}{T + S}$ + :$\mu = \mu_ref \left( \frac{T}{T_ref} \right)^{3/2}\frac{T_ref + S}{T + S}$ - :$T_r$ is a reference temperature. + :$T_ref$ is a reference temperature. - :$\mu_r$ is the viscosity at the $T_r$ reference temperature + :$\mu_ref$ is the viscosity at the $T_ref$ reference temperature :S is the Sutherland temperature :S is the Sutherland temperature Line 13: 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: - :$C_1 = \frac{\mu_r}{T_r^{3/2}}(T_r + S)$ + :$C_1 = \frac{\mu_ref}{T_ref^{3/2}}(T_ref + S)$ {| align=center border=1 {| align=center border=1 |+ Sutherland's law coefficients |+ Sutherland's law coefficients - ! Gas !! $\mu_0 [\frac{kg}{m s}]$ !! $T_0 [K]$ !! $S [K]$ !! $C_1 [\frac{kg}{m s k ^ {0.5}}]$ + ! Gas !! $\mu_0 [\frac{kg}{m s}]$ !! $T_0 [K]$ !! $S [K]$ !! $C_1 [\frac{kg}{m s K ^ {0.5}}]$ |- |- | Air | Air - | $17.16*10^{-6}$ + | $1.716 \times 10^{-5}$ - | 0 + | $273.15$ - | 0 + | $110.4$ - | 0 + | |} |}

## Revision as of 17:14, 17 May 2007

In 1893 William Sutherland, an Australian physicist, published a relationship between the dynamic visocity, $\mu$, and the absolute temperature, $T$, of an ideal gas. This formula, often called Sutherland's law, is based on kinetic theory of ideal gases and an idealized intermolecular-force potential. 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:

$\mu = \mu_ref \left( \frac{T}{T_ref} \right)^{3/2}\frac{T_ref + S}{T + S}$
$T_ref$ is a reference temperature.
$\mu_ref$ is the viscosity at the $T_ref$ 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:

$C_1 = \frac{\mu_ref}{T_ref^{3/2}}(T_ref + S)$
Sutherland's law coefficients
Gas $\mu_0 [\frac{kg}{m s}]$ $T_0 [K]$ $S [K]$ $C_1 [\frac{kg}{m s K ^ {0.5}}]$
Air $1.716 \times 10^{-5}$ $273.15$ $110.4$

## References

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