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ME521_Lecture_12

ME521_Lecture_12 - ME 521 Fall 2007 Professor John M...

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ME 521 Fall 2007 Professor John M. Cimbala Lecture 12 09/24/2007 Today, we will : Continue our discussion of the various forms of the energy equation Specifically, discuss deformation work, viscous dissipation, and the “real” energy equation From last lecture: Mechanical Energy Equation Non-conservative form: ( ) 1 2 ij i i i i i j D u u u g u Dt x τ ρ ρ = + Conservative form: ( ) ( ) 1 2 1 2 ij i i j i i i i i j j τ ρ u u u ρ u u ρ u g u t x x + = + or ( ) ij j i i i j j τ E u E ρ u g u t x x + = + where 2 1 2 mV is the kinetic energy (the conserved quantity), 1 2 i i E u u ρ is the kinetic energy per unit volume, and 1 2 i i u u is the kinetic energy per unit mass. The terms on the right are sources (or sinks) of kinetic energy per unit volume.
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