A proposed conservation law for ξ, a new fluid property, takes the following form: (d)/(d t) ∫V(t) ρξd V ∫A(t) Θ·n d S=0, where V(t) is a material volume that moves with the fluid velocity 𝐮, A(t) is the surface of V(t), ρis the fluid density, and Θ=-ργ∇ξa) What partial differential equation is implied by the above conservation statement? b) Use the part a) result and the continuity equation to show: (∂ξ)/(∂t) 𝐮 ·∇ξ=(1)/(ρ) ∇·(ργ∇ξ) | Numerade
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