04_inviscid_eq - 2.25 Fall 2004 G.H. McKinley Navier Stokes...

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Unformatted text preview: 2.25 Fall 2004 G.H. McKinley Navier Stokes Equation Dv v   =   + v  v = p + µ 2v + g Dt  t Euler Equation; inviscid flow  v   + v  v = p + g  t v  v =  Barotropic flow;  = f ( p ) only ( 1 vv 2 ) v    v    scalar potential for conservative body force (e.g.  =  gz )   v dp + 1 v  v + +  = v   2 t   steady flow v =0 t  =0 Steady Irrotational Inviscid Flow  dp B = 1 vv+  +  = constant everywhere 2   0 Integrate along a streamline Steady Rotational Inviscid Flow  dp  1 v v + +   = B = v   2    dp +  = constant along a Lamb surface where B = 1 v  v +  2  Unsteady Bernoulli equation along a streamline 2 2 v dr + t 1 ( 1 2 v 2 2 1 2 v+ 1 2 1 ) dp +( 2 1 )=0 Integrate along a streamline & assume Incompressible fluid Incompressible fluid steady flow Steady Bernoulli Equation along a streamline for an inviscid flow of an incompressible fluid 1 12 12 ( p2 p1 ) + g ( z2 z1 ) = 0 2 v2 2 v1 +  ( ) ...
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.25 taught by Professor Garethmckinley during the Fall '05 term at MIT.

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