3 - MoreBasics

# 3 - MoreBasics - MEM420 Aerodynamics Dr A Yousuff...

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MEM420 Aerodynamics Dr. A. Yousuff MEM/Drexel

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agenda substantial derivative streamlines vorticity circulation velocity potential Yousuff Aerodynamics 2 D Dt      ,     V   C d Vs  
Incompressible flow Yousuff Aerodynamics 3 The continuity eqn (2.52) for an incompressible flow becomes Expressions for the divergence 0:  V Cartesian: ; x y z V V V V i j k y x z V V V x y z V Cylindrical: ; r r z z V V V  V e e e   11 r z rV V V r r r z V Spherical: ; rr V V V   V e e e     2 2 1 1 1 r rV V VS r r rS rS  V

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example Yousuff Aerodynamics 4 ; r r z z V V V  V e e e cos , sin , rz b V a V a V const r   A velocity field V that satisfies is said to be physically possible . 0  V
Substantial derivative Yousuff Aerodynamics 5 Consider particles moving from a point 1 to point 2, and r (x,y,z,t). Then         2 1 2 1 2 1 2 1 2 1 x x y y z z t t x y z t rr 21 lim xy tt z t t x VV yt V z

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## This note was uploaded on 04/26/2011 for the course MEM 420 taught by Professor Ajamal during the Spring '11 term at Drexel.

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3 - MoreBasics - MEM420 Aerodynamics Dr A Yousuff...

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