Sutherland's law

From CFD-Wiki

(Difference between revisions)

Revision as of 14:16, 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:

$\mu = \mu_r \left( \frac{T}{T_r} \right)^{3/2}\frac{T_r + S}{T + S}$

$T_r$ 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'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	$17.16*10^{-6}$	0	0	0

References

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

@@ 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, <math>T</math>, of an ideal gas and its dynamic visocity, <math>\mu</math>, 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:
+In 1893 [http://en.wikipedia.org/wiki/William_Sutherland_(physicist) William Sutherland], an Australian physicist, published a relationship between the dynamic visocity, <math>\mu</math>, and the absolute temperature, <math>T</math>, 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:
 :<math>\mu = \mu_r \left( \frac{T}{T_r} \right)^{3/2}\frac{T_r + S}{T + S}</math>
@@ Line 14: / Line 14: @@
 :<math>C_1 = \frac{\mu_r}{T_r^{3/2}}(T_r + S)</math>
+{| align=center border=1
+|+ Sutherland's law coefficients
+! Gas !! <math>\mu_0 [\frac{kg}{m s}]</math> !! <math>T_0 [K]</math> !! <math>S [K]</math> !! <math>C_1 [\frac{kg}{m s k ^ {0.5}}]</math>
+|-
+| Air
+| <math>17.16*10^{-6}</math>
+| 0
+| 0
+| 0
+|}
 == 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)}}

Sutherland's law

From CFD-Wiki

Revision as of 14:16, 17 May 2007

References

Views

My wiki

wiki navigation

wiki search

wiki toolbox