Lecture 19.Notes

# Lecture 19.Notes - EGN 3353C Fluid Mechanics Chapter 6...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Chapter 6: MOMENTUM ANALYSIS OF FLOW SYSTEMS Lecture 19 ± We will now apply the Reynolds Transport Theorem (RTT) to the Conservation of Linear Momentum ± We will restrict our analysis to an inertial CV (CV in a non-accelerating reference frame) ± Recall we derived the RTT for the general case of a CV that can move and deform r system CV CS dB d bd bV ndA dt dt ρρ =∀ + ∫∫ G G ± For momentum, B Pm V = = GG so b V = G and Newton’s second law becomes NN rate of change of net flux of momentum in CV momentum out of CV = 0 for steady flow r r CV C VV CV CS system S dP d bd b V ndA dt dt d FV d V V n d A dt + + G G G ±²³²´ ±²²³ G G G ²²´ ± surface body F F F + = ∑∑ G G G o only body force we will consider in this course is gravitational grav CV F gd ρ = G G o surface forces Æ pressure and shear

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida ± pressure PA F d = − G G (already considered this in fluid statics) We only consider the net pressure forces on a CV Consider the CV shown at left o If only a uniform pressure (e.g., atm P ) acts on all sides (which acts in the – normal direction) ± pressure forces cancel o In general, only need to consider the gage pressure 1 atm gage PP P = o Note: Subsonic flows have exit atm = !
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Lecture 19.Notes - EGN 3353C Fluid Mechanics Chapter 6...

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