Sutherland's law

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(Difference between revisions)

Latest revision as of 04:13, 25 October 2008

In 1893 William Sutherland, an Australian physicist, published a relationship between the dynamic viscosity, $\mu$ , 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	$\mu_0 [\frac{kg}{m s}]$	$T_0 [K]$	$S [K]$	$C_1 [\frac{kg}{m s \sqrt{K}}]$
Air	$1.716 \times 10^{-5}$	$273.15$	$110.4$	$1.458 \times 10^{-6}$

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 viscosity, <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>
+:<math>\mu = \mu_{ref} \left( \frac{T}{T_{ref}} \right)^{3/2}\frac{T_{ref} + S}{T + S}</math>
-:<math>T_r</math> is a reference temperature.
+:<math>T_{ref}</math> is a reference temperature.
-:<math>\mu_r</math> is the viscosity at the <math>T_r</math> reference temperature
+:<math>\mu_{ref}</math> is the viscosity at the <math>T_{ref}</math> reference temperature
 :S is the Sutherland temperature
@@ Line 13: / Line 13: @@
 Comparing the formulas above the <math>C_1</math> constant can be written as:
-:<math>C_1 = \frac{\mu_r}{T_r^{3/2}}(T_r + S)</math>
+:<math>C_1 = \frac{\mu_{ref}}{T_{ref}^{3/2}}(T_{ref} + S)</math>
+{| border=2
+|+ 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 \sqrt{K}}]</math>
+|-
+| Air
+| <math>1.716 \times 10^{-5}</math>
+| <math>273.15</math>
+| <math>110.4</math>
+| <math>1.458 \times 10^{-6}</math>
+|}
 == 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

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Latest revision as of 04:13, 25 October 2008

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