流体动量控制方程【Motion Equation】

最新推荐文章于 2024-10-04 16:51:34 发布

Chem-To-Math

最新推荐文章于 2024-10-04 16:51:34 发布

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分类专栏：流体力学【Fluid Mechanics】

本文链接：https://blog.youkuaiyun.com/ChemToMath/article/details/80788199

这篇博客探讨了流体动量控制方程，详细介绍了在直角坐标系(x,y,z)、圆柱坐标系(r,θ,z)和球坐标系(r,θ,ϕ)下的方程形式。特别指出，当动量ττττ具有对称性时，τrθ−τθr=0τrθ−τθr=0。参考了R. Byron Bird等人的《Transport phenomena》一书。" 123676664,6695791,pyQt5安装配置与打包发布指南,"['pyQt5', '打包发布', 'Python图形界面', '软件工程', 'Windows开发']

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流体动量控制方程

The Equation of Motion in terms of $\tau$

控制方程通式：

ρ D v v D t = - \nabla p - \nabla \cdot τ τ + ρ g g

$\rho \dfrac {D \pmb v}{D t}=- \nabla p-\nabla \cdot \pmb \tau+\rho \pmb g$

1.直角坐标系( $x, y, z$ )

直角坐标系Cartesian coordinates ( $\textit { x,y,z }$ ):	NO.
$\rho \left (\dfrac{\partial v_x}{\partial t}+v_x \dfrac{\partial v_x}{\partial x}+v_y \dfrac{\partial v_x}{\partial y} + v_z \dfrac{\partial v_x}{\partial z}\right)=- \dfrac{\partial p}{\partial x}-\left [\dfrac {\partial}{\partial x}\tau_{xx}+\dfrac {\partial}{\partial y}\tau_{yx}+\dfrac {\partial}{\partial z}\tau_{zx}\right]+\rho g_x$	1-1
$\rho \left (\dfrac{\partial v_y}{\partial t}+v_x \dfrac{\partial v_y}{\partial x}+v_y \dfrac{\partial v_y}{\partial y} + v_z \dfrac{\partial v_y}{\partial z}\right)=- \dfrac{\partial p}{\partial y}-\left [\dfrac {\partial}{\partial x}\tau_{xy}+\dfrac {\partial}{\partial y}\tau_{yy}+\dfrac {\partial}{\partial z}\tau_{zy}\right]+\rho g_y$	1-2
ρ(∂vz∂t+vx∂vz∂x