雷諾方程 （英語：Reynolds equation ）是流體 潤滑理論 壓力 分佈，可由納維-斯托克斯方程 導出。該方程由英國物理學家奧斯鮑恩·雷諾 於1886年提出。[ 1]
流體動力軸承演示裝置 雷諾方程的導出建立在以下假設的基礎之上：
流體為牛頓流體
黏性力遠大於慣性力，即雷諾數 十分小
體積力可以忽略
壓力沿厚度方向基本不變（
∂
p
∂
z
=
0
{\displaystyle {\frac {\partial p}{\partial z}}=0}
流體膜厚度遠小於寬度與長度（
h
<<
l
{\displaystyle h<<l}
h
<<
w
{\displaystyle h<<w}
雷諾方程的表達式為：[ 2] [ 3]
∂
∂
x
(
ρ
h
3
12
μ
∂
p
∂
x
)
+
∂
∂
y
(
ρ
h
3
12
μ
∂
p
∂
y
)
=
∂
∂
x
(
ρ
h
(
u
a
+
u
b
)
2
)
+
∂
∂
y
(
ρ
h
(
v
a
+
v
b
)
2
)
+
ρ
(
w
a
−
w
b
)
−
ρ
u
a
∂
h
∂
x
−
ρ
v
a
∂
h
∂
y
+
h
∂
ρ
∂
t
{\displaystyle {\frac {\partial }{\partial x}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial x}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial y}}\right)={\frac {\partial }{\partial x}}\left({\frac {\rho h\left(u_{a}+u_{b}\right)}{2}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h\left(v_{a}+v_{b}\right)}{2}}\right)+\rho \left(w_{a}-w_{b}\right)-\rho u_{a}{\frac {\partial h}{\partial x}}-\rho v_{a}{\frac {\partial h}{\partial y}}+h{\frac {\partial \rho }{\partial t}}}
其中
p
{\displaystyle p}
x
{\displaystyle x}
y
{\displaystyle y}
z
{\displaystyle z}
h
{\displaystyle h}
μ
{\displaystyle \mu }
黏度 ，
ρ
{\displaystyle \rho }
密度 ，
u
,
v
,
w
{\displaystyle u,v,w}
x
,
y
,
z
{\displaystyle x,y,z}
a
,
b
{\displaystyle a,b}
^ Reynolds, O. 1886. On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil. Philosophical Transactions of the Royal Society of London .[1]
^ Fundamentals of Fluid Film Lubrication. Hamrock, B., Schmid, S., Jacobson. B. 2nd Edition. 2004. ISBN 0-8247-5371-2
^ Fluid Film Lubrication. Szeri, A. 2nd Edition. 2010. ISBN 0521898234 .
