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Sutherland's law

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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:
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>
+
:<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
:S is the Sutherland temperature
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Comparing the formulas above the <math>C_1</math> constant can be written as:
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>
{| align=center border=1
{| align=center border=1
|+ Sutherland's law coefficients
|+ 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>  
+
! 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  
| Air  
-
| <math>17.16*10^{-6}</math>  
+
| <math>1.716 \times 10^{-5}</math>  
-
| 0
+
| <math>273.15</math>
-
| 0
+
| <math>110.4</math>
-
| 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).
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