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44 2 Basic Properties of Gases

Table 2.2 Sutherland’s constants and reference temperatures
Gas Formula T s (K) T 0 (K) l 0 (10 −6 Pa s)
Hydrogen H 2 72 293.85 8.76
Nitrogen N 2 111 300.55 17.81
Oxygen O 2 127 292.25 20.18
Air – 120 291.15 18.27
Carbon dioxide CO 2 240 293.15 14.8
Carbon monoxide CO 118 288.15 17.2
Ammonia NH 3 370 293.15 9.82
Sulfur dioxide SO 2 416 293.65 12.54

where m is the mass of a single molecule. C N is the molecule number concentration.
1
The term C N m c stands for the average mass flow rate per unit area through plane
6
x. This leads to a net flux of momentum in the þx direction through the plane x as
1 ou
M x ¼ C N m c k ð2:66Þ
3 ox
Comparing with the definition of shear stress

ou
s ¼ l ð2:67Þ
ox
we can get the kinetic viscosity of the gas as

1 1
l ¼ C N m ck ¼ q ck ð2:68Þ
3 3
Combining this equation with Eqs. (2.7) and (2.51), we can get
p
r ffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffi
1 8kT RT 2 mkT
l ¼ q p ffiffiffi ¼ ð2:69Þ
1:5 2
2
3 pm 2pN a d P 3 p d
2
where l ¼ kinetic viscosity in Pa s or N s/m .
The effect of temperature on the dynamic viscosity of an ideal gas can also be
calculated using the Sutherland’s equation (Licht and Stechert 1944 cited by [12]).
l T 0 þ T s 3=2
T
¼ ð2:70Þ
l
0 T þ T s T 0
where l ¼ viscosity in Pa.s at input temperature T, l ¼ reference viscosity at
0
reference temperature T 0 , T ¼ input temperature, T 0 ¼ reference temperature, T s ¼
Sutherland’s constant. Values of Sutherland’s constant T s are taken from Crane [4].