雷诺数计算公式(可编辑修改word版)

2

雷诺数计算

Re =

vD

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 p 1 , p 2 ( p 1 - p )r 2 +2rl dv = 0 dr

Viscosity in gases arises principally from the molecular diffusion

that transports momentum between layers of flow. The kinetic theory of

gases allows accurate prediction of the behavior of gaseous viscosity.

Within the regime where the theory is applicable:

•

Viscosity is independent of pressure and • Viscosity increases as temperature increases.

James Clerk Maxwell

published a famous paper in 1866 using the kinetic theory of gases to study gaseous viscosity. (Reference: J.C. Maxwell, "On the viscosity or

Q = V p 1 - p 2 R 4 8l

p - p 1 2 = Q V 8l R 4

Gas

C

[K]

T0

[K]

η0

[10-6Pa s]

internal friction of air and other gases", 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 used 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 gaseous 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 gases

air 120 291.1518.27

nitrogen 111 300.5517.81

oxygen 127 292.2520.18

carbon dioxide 240 293.1514.8

carbon monoxide118 288.1517.2

hydrogen 72 293.858.76

ammonia 370 293.159.82

sulfur dioxide 416 293.6512.54

helium 79.4 273 19

Viscosity of a dilute gas

The Chapman-Enskog equation

may be used to estimate viscosity for a dilute gas. This equation is

based on semi-theorethical assumption by Chapman and Enskoq. The

equation requires three empirically determined parameters: the

collision diameter (σ), the maximum energy of attraction di vided 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