上游充通大睾 3.2雷诺输运定理 Shanghai Jiao Tong University 雷诺输运定理Reynolds Transport Theorem) Control volume at time t+At (CV remains fixed in time) 任何一个物理量G都满足下列物质体积与控 System(material volume) and control volume at time t 制体积的关系式： (shaded region) System at time t+△t (hatched region) GdV GdV GV.ndA + rate of change of the local rate of change of the net out-flux of the property within property within the fixed property across the the material volume control volume that happens entire control surface to coincide with the material volume at that instant p=density of fluid 2) G=an intensive property of fluid MV material volume that happens to coincide with CV at time t Inflow during△t CI=control volume (fixed in space) Outflow during△t CS control surface n unit outward normal to CS At time t:Sys =CV At time t+△t:Sys=CV-I+ⅡShanghai Jiao Tong University 3.2 雷诺输运定理 雷诺输运定理(Reynolds Transport Theorem) rate of change of the local rate of change of the property within property within the fixed the material volume control volume that happens to coincide with the material volume MV CV d dV dV dt t G G ∂ = ∂ ∫∫∫ ∫∫∫ 1442443 net out-flux of the property across the entire control surface at that instant CS + ⋅ G dA ∫∫ V n 1442443 1442443 materi dens al v ity of f olume th luid an intensi at happens to ve property o coincide f with at time fluid MV CV t G ρ = = = control volume (fixed in space) control surface unit outward normal to CV CS CS = = n = 任何一个物理量G都满足下列物质体积与控 制体积的关系式：