流体连续性方程【The Equation of Continuity】

流体连续性方程

TheEquationofContinuity T h e E q u a t i o n o f C o n t i n u i t y

流体连续性方程表达通式

∂ρ∂t+∇⋅ρvv=0 ∂ ρ ∂ t + ∇ ⋅ ρ v v = 0

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。

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1.直角坐标系( x,y,z x , y , z )

直角坐标系Cartesian coordinates (  x,y,z   x,y,z  ):	NO.
∂ρ∂t+∂∂x(ρvx)+∂∂y(ρvy)+∂∂z(ρvz)=0 ∂ ρ ∂ t + ∂ ∂ x ( ρ v x ) + ∂ ∂ y ( ρ v y ) + ∂ ∂ z ( ρ v z ) = 0	1-1

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2.圆柱坐标系（ r,θ,z r , θ , z )

圆柱坐标系Cylindrical coordinates coordinates ( r, θ, z  r,  θ , z  ):	NO.
∂ρ∂t+1r∂∂r(ρrvr)+1r∂∂θ(ρvθ)+∂∂z(ρvz)=0 ∂ ρ ∂ t + 1 r ∂ ∂ r ( ρ r v r ) + 1 r ∂ ∂ θ ( ρ v θ ) + ∂ ∂ z ( ρ v z ) = 0	2-1

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3.球坐标系（ r,θ,ϕ r , θ , ϕ )

球坐标系Spherical coordinates（ r, θ, ϕ  r,  θ ,  ϕ   ):	NO.
∂ρ∂t+1r2∂∂r(ρr2vr)+1rsinθ∂∂θ(ρvθsinθ)+1rsinθ∂∂ϕ(ρvϕ)=0 ∂ ρ ∂ t + 1 r 2 ∂ ∂ r ( ρ r 2 v r ) + 1 r s i n θ ∂ ∂ θ ( ρ v θ s i n θ ) + 1 r s i n θ ∂ ∂ ϕ ( ρ v ϕ ) = 0	3-1

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参考文献

1. R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot.* Transport phenomena:Revised second edition* John Wiely &Sons, Inc.