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Lecture 22 Notes

# Lecture 22 Notes - EGN 3353C Fluid Mechanics Lecture 22 We...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 22 We will now apply the Reynolds Transport Theorem (RTT) to the Conservation of Angular 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 ρ ρ = ∀ + G G For angular momentum, r B V H m = = × G G G so b r V = × G G and so N N N ( ) ( ) sum of all external moments acting on CV rate of change of net flux of a angular momentum in CV = 0 for steady flow r r V r V CV CS system r CV CS dH d b d b V ndA dt dt d M r V d r V V ndA dt ρ ρ ρ ρ × × = ∀ + = × ∀ + × G G G G G G G G G G G G G G ±²²³²²´ ngular momentum out of CV ±²²²³²²²´ o We need to worry about external moments due to body forces, pressure, shear forces, and any other external moments. Simplifications of ( ) ( ) r CV CS d M r V d r V V ndA dt ρ ρ = × ∀ + × G G G G G G G o For a fixed CV , the relative velocity CS r V V V = G G G V = G

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