# 雷诺方程

• 流体为牛顿流体
• 黏性力远大于惯性力，即雷诺数十分小
• 体积力可以忽略
• 压力沿厚度方向基本不变（${\displaystyle {\frac {\partial p}{\partial z}}=0}$
• 流体膜厚度远小于宽度与长度（${\displaystyle h<${\displaystyle h<

${\displaystyle {\frac {\partial }{\partial x}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial x}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h^{3}}{12\mu }}{\frac {\partial p}{\partial y}}\right)={\frac {\partial }{\partial x}}\left({\frac {\rho h\left(u_{a}+u_{b}\right)}{2}}\right)+{\frac {\partial }{\partial y}}\left({\frac {\rho h\left(v_{a}+v_{b}\right)}{2}}\right)+\rho \left(w_{a}-w_{b}\right)-\rho u_{a}{\frac {\partial h}{\partial x}}-\rho v_{a}{\frac {\partial h}{\partial y}}+h{\frac {\partial \rho }{\partial t}}}$

• ${\displaystyle p}$为流体膜压力，
• ${\displaystyle x}$${\displaystyle y}$为流体轴承宽度与长度方向坐标，
• ${\displaystyle z}$为流体膜厚度方向坐标，
• ${\displaystyle h}$为流体膜厚度，
• ${\displaystyle \mu }$为流体黏度
• ${\displaystyle \rho }$为流体密度
• ${\displaystyle u,v,w}$分别为${\displaystyle x,y,z}$方向的边界速度，
• ${\displaystyle a,b}$则分别表示上、下边界。

## 参考文献

1. ^ 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]
2. ^ Fundamentals of Fluid Film Lubrication. Hamrock, B., Schmid, S., Jacobson. B. 2nd Edition. 2004. ISBN 0-8247-5371-2
3. ^ Fluid Film Lubrication. Szeri, A. 2nd Edition. 2010. ISBN 0521898234.