# Dynamic viscosity of gas

Dynamic viscosity (also known as absolute viscosity) is the measurement of the fluid's internal resistance to flow.

The sources are:

• Values for 0, 15, and 25°C are taken from encyclopedia.airliquide.com
• Values for 50, 75, and 100°C are taken from nist.gov
• Values for 50, 75, and 100°C for SF6 have been interpolated from values published in J. Wilhelm et.al: 'Viscosity Measurements on Gaseous Sulfur Hexafluoride. Journal of Chemical & Engineering Data', 2005
• Values for 50, 75, and 100°C for SO2 have been interpolated from values published in C.Y. Ho: 'Properties of Inorganic and Organic Fluids, CINDAS, Data Series on Materials Properties, Vol. V-1, 1988.
• Values for 50, 75, and 100°C for dry air have been calculated using the equation from Irvine & Liley, 1984.
• Equation for humid air is taken from paper by P.T. Tsilingiris: 'Thermophysical and transport properties of humid air at temperature range between 0 and 100°C', 2007
• Equation for dry air is taken from paper by T.F. Irvine and P. Liley: 'Steam and gas tables with computer equations', 1984
• Equations for N2 and SF6 are taken from paper by J. Vermeer: 'A simple formula for the calculation of the convective heat transfer between conductor and sheath in compressed gas insulated (CGI) cables', 1983 as published in Elektra 87
• Equation for CO2 is a linear interpolation of the values calculated acc. Sutherland's model between 0 and 90°C.

Sutherland's formula can be used to derive the dynamic viscosity of an ideal gas as a function of the temperature. According to Sutherland's formula, if the absolute temperature is less than $S_{gas}$, the relative change in viscosity for a small change in temperature is greater than the relative change in the absolute temperature, but it is smaller when $T_{gas}$ is above $S_{gas}$. The kinematic viscosity though always increases faster than the temperature.

Note: Often called $\mu$ instead of $\eta$

Note: 1 Pa = 1 kg/(m.s$^2$)

Symbol
$\eta_{gas}$
Unit
Pa.s
Formulae
 $1.715747771{\cdot}{10}^{-5}+4.722402075{\cdot}{10}^{-8} \theta_{gas}-3.663027156{\cdot}{10}^{-10} {\theta_{gas}}^2+1.873236686{\cdot}{10}^{-12} {\theta_{gas}}^3-8.050218737{\cdot}{10}^{-14} {\theta_{gas}}^4$ humid air @ 1 atm (Tsilingiris2007) ${10}^{-6}\frac{1.4592{T_{gas}}^{\frac{3}{2}}}{109.1+T_{gas}}$ air @ 1 bar (UW/MHTL 8406, 1984) ${10}^{-6}\left(-9.8601{\cdot}{10}^{-1}+9.080125{\cdot}{10}^{-2} T_{gas}-1.17635575{\cdot}{10}^{-4} {T_{gas}}^2+1.2349703{\cdot}{10}^{-7} {T_{gas}}^3-5.7971299{\cdot}{10}^{-11} {T_{gas}}^4\right)$ dry air @ at 1 atm (Irvine&Liley1984) $1.66{\cdot}{10}^{-5}+4.14{\cdot}{10}^{-8} \theta_{gas}$ N2 (Vermeer1983) $1.47{\cdot}{10}^{-5}+4.11{\cdot}{10}^{-8} \theta_{gas}$ SF6 (Vermeer1983) $1.11{\cdot}{10}^{-6}+4.669{\cdot}{10}^{-8} \left(\theta_{gas}+\theta_{abs}\right)$ CO2 (linear interpolation) $\nu_{gas} \rho_{gas}$ general formula for gases $\eta 0_{gas} \frac{T0_{gas}+S_{gas}}{T_{gas}+S_{gas}} \left(\frac{T_{gas}}{T0_{gas}}\right)^{1.5}$ Sutherland's model
Related
$\eta 0_{gas}$
$\nu_{gas}$
$\rho_{gas}$
Gas density [kg/m$^3$]
$S_{gas}$
$T0_{gas}$
$T_{gas}$
$\theta_{abs}$
$\theta_{gas}$
Used in
$\nu_{gas}$
$\mathrm{Pr}_{gas}$
$T_{conv,ce}$
Choices
GasFormula0°C15°C25°C50°C75°C100°C
Air78%N2+21%O2+minor1.7218e-051.7962e-051.8447e-051.9601e-052.0721e-052.018e-05
N2N21.6629e-051.7339e-051.7805e-051.8947e-052.0044e-052.1108e-05
SF6SF61.3771e-051.4589e-051.5123e-051.6675e-051.7786e-050.001888
CO2CO21.3711e-051.4446e-051.4932e-051.6134e-051.7315e-051.8475e-05
COCO1.6515e-051.7201e-051.7649e-051.8741e-051.9794e-052.0813e-05
O2O21.9143e-051.9993e-052.055e-051.8741e-051.9794e-052.0813e-05
H2H28.3969e-068.7098e-068.9154e-069.4193e-069.9103e-061.0389e-05
NH3NH39.1931e-069.7289e-061.0093e-051.102e-051.1968e-051.2929e-05
SO2SO21.1796e-051.2475e-051.2924e-059.589e-051.0664e-051.1739e-05
HeHe1.8695e-051.9388e-051.9846e-052.0971e-052.2073e-052.3154e-05
ArAr2.1017e-052.1987e-052.2624e-052.4114e-052.5624e-052.7093e-05
KrKr2.3219e-052.4375e-052.5132e-052.6984e-052.8774e-053.0509e-05
XeXe2.1216e-052.2278e-052.2985e-052.4745e-052.6493e-052.8224e-05
NeNe2.9382e-053.0427e-053.1113e-053.2791e-053.4419e-053.6005e-05