ME521_Lecture_14

ME521_Lecture_14 - ME 521 Fall 2007 Professor John M....

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ME 521 Fall 2007 Professor John M. Cimbala Lecture 14 09/28/2007 Today, we will : Continue our discussion of the various forms of the Bernoulli equation Discuss the Boussinesq approximation If time, begin a discussion about vorticity dynamics (Chapter 5) Do C a n d y Q u e s t i o n s f o r C a n d y F r i d a y From last lecture: 1. Incompressible Flow : Start with the incompressible N-S equation : 2 ii i ji j j uu u p ug tx x x x ρρ ρ μ ∂∂ += + + a. Incompressible, Unsteady, and Irrotational (can be viscous) : 2 1 2 () p qg z F t t φ ++ + = where 2 qu u = = magnitude of the velocity vector squared, is the velocity potential defined by u =∇ G G or , u = ( is definable only if the flow is irrotational ), and F is a function of time, but not of space.
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Various Forms of the Bernoulli Equation Author: John M. Cimbala, Penn State University Latest revision: 25 September 2007 Note : The fluid is assumed to be Newtonian, and gravity is assumed to act in the negative z direction [positive z is “up”] . All forms of the Bernoulli equation shown below are derived from the Navier-Stokes equation, along
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This note was uploaded on 07/23/2008 for the course ME 521 taught by Professor Cimbala during the Fall '07 term at Penn State.

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ME521_Lecture_14 - ME 521 Fall 2007 Professor John M....

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