流体连续性方程
$\color{Blue} {The\quad Equation \quad of \quad Continuity} $
流体连续性方程表达通式
物理意义： 物质进入系统的量等于 物质离开离开系统的量与物质在系统内累积量的加和。
1.直角坐标系($ x, y, z $)
| 直角坐标系Cartesian coordinates ($\textit { x,y,z }$): | NO. |
|---|---|
| $\dfrac {\partial \rho}{\partial t}+\dfrac {\partial}{\partial x}(\rho v_x)+\dfrac {\partial}{\partial y}(\rho v_y) +\dfrac {\partial}{\partial z}(\rho v_z)=0$ | 1-1 |
2.圆柱坐标系（$r,\theta, z$)
| 圆柱坐标系Cylindrical coordinates coordinates ($\textit {r, $\theta$, z }$): | NO. |
|---|---|
| $\dfrac {\partial \rho}{\partial t}+\dfrac {1}{r}\dfrac {\partial}{\partial r}(\rho r v_r)+\dfrac {1}{r} \dfrac {\partial}{\partial \theta}(\rho v_\theta) +\dfrac {\partial}{\partial z}(\rho v_z)=0$ | 2-1 |
3.球坐标系（$r, \theta, \phi $)
| 球坐标系Spherical coordinates（$\textit {r, $\theta$, $\phi$ }$): | NO. |
|---|---|
| $\dfrac {\partial \rho}{\partial t}+\dfrac {1}{r^2}\dfrac {\partial}{\partial r}(\rho r^2 v_r)+\dfrac {1}{r sin\theta} \dfrac {\partial}{\partial \theta}(\rho v_\theta sin\theta) +\dfrac {1}{r sin\theta}\dfrac {\partial}{\partial \phi}(\rho v_\phi)=0$ | 3-1 |
参考文献
- R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot. Transport phenomena:Revised second edition John Wiely &Sons, Inc.