雷诺数计算
其中D为物体的几何限度（如直径）
对于几何形状相似的管道，无论其ρ、v、D、η如何不同，只要比值 Re 相同，其流动情况就相同
泊肃叶公式
管的半径 R
管的长度 l
两端压强
流体的粘度
/
萨瑟兰公式
Viscosity in gas aris principally from the molecular diffusion
that transports momentum between layers of flow. The kinetic theory of
gas allows accurate prediction of the behavior of gaous viscosity.
Within the regime where the theory is applicable:
∙Viscosity is independent of pressure and
∙Viscosity increas as temperature increas.
James Clerk Maxwell
published a famous paper in 1866 using the kinetic theory of gas to
study gaous viscosity. (Reference: J.C. Maxwell, "On the viscosity or
internal friction of air and other gas", Philosophical Transactions
of the Royal Society of London, vol. 156 (1866), pp. 249-268.)
Effect of temperature on the viscosity of a gas
Sutherland's formula can be ud to derive the dynamic viscosity of an ideal gas as a function of the temperature:
where:
∙η = viscosity in (Pa·s) at input temperature T
∙η0 = reference viscosity in (Pa·s) at reference temperature T0
∙T = input temperature in kelvin
∙T0 = reference temperature in kelvin
∙C = Sutherland's constant for the gaous material in question
Valid for temperatures between 0 < T < 555 K with an error due to pressure less than 10% below 3.45 MPa
Sutherland's constant and reference temperature for some gas
Gas | C [K] | T0 [K] | η0 [10-6 Pa s] |
air | 120 | 291.15 | 18.27 |
nitrogen | 111 | 300.55 | 17.81 |
oxygen | 127 | 292.25 | 20.18 |
carbon dioxide | 240 | 293.15 | 14.8 |
carbon monoxide | 118 | 288.15 | 17.2 |
hydrogen | 72 | 293.85 | 8.76 |
ammonia | 370 | 293.15 | 9.82 |
sulfur dioxide | 416 | 293.65 | 12.54 |
helium | 79.4 | 273 | 19 |
| | | |
Viscosity of a dilute gas
The Chapman-Enskog equation
may be ud to estimate viscosity for a dilute gas. This equation is
bad on mi-theorethical assumption by Chapman and Enskoq. The
equation requires three empirically determined parameters: the
collision diameter (σ), the maximum energy of attraction divided by the
Boltzmann constant (є/к) and the collision integral (ω(T*)).
∙T*=κT/ε Reduced temperature (dimensionless)
∙η0 = viscosity for dilute gas (uP)
∙M = molecular mass (g/mol)
∙T = temperature (K)
∙σ = the collision diameter (Å)
∙ε / κ = the maximum energy of attraction divided by the Boltzmann constant (K)
∙ωη = the collision integral
