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)
${10}^{-6}\frac{1.4592{T_{gas}}^{\frac{3}{2}}}{109.1+T_{gas}}$	dry 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

$\eta 0_{gas}$

Reference dynamic viscosity of gas [Pa.s]

$\nu_{gas}$

Kinematic viscosity for gas [m$^2$/s]

$\rho_{gas}$

Gas density [kg/m$^3$]

$S_{gas}$

Sutherland's constant [K]

$T0_{gas}$

Gas reference temperature [K]

$T_{gas}$

Absolute gas temperature [K]

$\theta_{abs}$

Absolute temperature [K]

$\theta_{gas}$

Gas temperature [°C]

Used in

$\nu_{gas}$

Kinematic viscosity for gas [m$^2$/s]

$\mathrm{Pr}_{gas}$

Prandtl number for gas

$T_{conv,ce}$

Thermal resistance by convection, conductor to enclosure [K.m/W]

Choices

Gas	Formula	0°C	15°C	25°C	50°C	75°C	100°C
Air	78%N₂+21%O₂+minor	1.7218e-05	1.7962e-05	1.8447e-05	1.9601e-05	2.0721e-05	2.018e-05
N2	N₂	1.6629e-05	1.7339e-05	1.7805e-05	1.8947e-05	2.0044e-05	2.1108e-05
SF6	SF₆	1.3771e-05	1.4589e-05	1.5123e-05	1.6675e-05	1.7786e-05	0.001888
CO2	CO₂	1.3711e-05	1.4446e-05	1.4932e-05	1.6134e-05	1.7315e-05	1.8475e-05
CO	CO	1.6515e-05	1.7201e-05	1.7649e-05	1.8741e-05	1.9794e-05	2.0813e-05
O2	O₂	1.9143e-05	1.9993e-05	2.055e-05	1.8741e-05	1.9794e-05	2.0813e-05
H2	H₂	8.3969e-06	8.7098e-06	8.9154e-06	9.4193e-06	9.9103e-06	1.0389e-05
NH3	NH₃	9.1931e-06	9.7289e-06	1.0093e-05	1.102e-05	1.1968e-05	1.2929e-05
SO2	SO₂	1.1796e-05	1.2475e-05	1.2924e-05	9.589e-05	1.0664e-05	1.1739e-05
He	He	1.8695e-05	1.9388e-05	1.9846e-05	2.0971e-05	2.2073e-05	2.3154e-05
Ar	Ar	2.1017e-05	2.1987e-05	2.2624e-05	2.4114e-05	2.5624e-05	2.7093e-05
Kr	Kr	2.3219e-05	2.4375e-05	2.5132e-05	2.6984e-05	2.8774e-05	3.0509e-05
Xe	Xe	2.1216e-05	2.2278e-05	2.2985e-05	2.4745e-05	2.6493e-05	2.8224e-05
Ne	Ne	2.9382e-05	3.0427e-05	3.1113e-05	3.2791e-05	3.4419e-05	3.6005e-05