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Lecture 14 Notes

# Lecture 14 Notes - EGN 3353C Fluid Mechanics Chapter 5 Mass...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Chapter 5: Mass, Bernoulli, and Energy Equations Lecture 14 ± We will now apply the Reynolds Transport Theorem (RTT) to the Conservation of Mass ± 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 ± Here, B m = so 1 b = and NN 1 ,, 1 0 CV out in CV out in CV avg r avg avg r avg r system CV C ut S oi n d mmm dt d dt d mV A V A dt dm d bd bV ndA dt dt =+− =+ + ∑∑ ±± G G

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida ± average velocity is obtained as follows 2 1 1 avg A h VV n A w d A =⋅ = G G () uyw 1 2 hh dy u y dy h −− = ∫∫ ± Special Cases 1. incompressible flow o recall incompressible flow means 1 0 d V dt =∇⋅ = G G but mm ρ =∀→∀ = so ² ( ) 11 1 dm dm dt d d dt t ρρ = = 2 1 00 md d d dt dt dt ρρρ ⎛⎞ =− = → = ⎜⎟ ⎝⎠ ² Recall ( ) ( ) V t d dt +∇ G
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Lecture 14 Notes - EGN 3353C Fluid Mechanics Chapter 5 Mass...

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