Lecture 13 Notes

Lecture 13 Notes - EGN 3353C Fluid Mechanics Lecture 13...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 13 Reynolds Transport Theorem Æ provides link between system and control volume approaches ± Recall that all laws of mechanics are written for systems (Lagrangian description). ± System Æ arbitrary quantity of mass of fixed identity ± In fluid dynamics, it is more convenient to study a region in space, called a control volume (CV) o Mass may cross the boundary of the CV o Boundary of control volume is the control surface (CS) o CV may deform and move, but many practical problems involve a fixed, non- deformable CV. (a) follow the fluid as it leaves Æ system approach (b) consider CV as can boundary & mass crosses boundary Æ CV approach

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Examples of System Laws 1. Conservation of Mass: 0 system dM dt = where system system syste M m d M md ρ = =∀ 2. Conservation of Linear Momentum: system dP F dt = G G where system system M Vdm Vd P = = ∫∫ G G G 3. Conservation of Angular Momentum: system dH T dt = G G where ( ) ( ) system system M rVd m Vd H r × = = ×∀ G G G G G 4. Conservation of Energy: First Law of Thermodynamics N N rate of work rate of heat done by system added to system system dE QW dt −= ± ± where N N N 2 internal potential energy/mass kinetic
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Lecture 13 Notes - EGN 3353C Fluid Mechanics Lecture 13...

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