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Unformatted text preview: LOW-SPEED AERODYNAMICS EQUATIONS OVERVIEW Continuity Equation t dV CV + ( r V r n ) dA CS = Cartesian coordinates: t + ( u ) x + ( v ) y + ( w ) z = cylindrical coordinates: t + 1 r rV r ( ) r + 1 r V ( ) + V z ( ) z = Momentum Equation r f dV + r F visc CV - P r n dA CS + r R = t r V dV CV + r V ( r V r n ) dA CS Cartesian coordinates: ( ) ( ) ( ) ( ) ( ) ( ) ~ ) ( ~ ) ( ~ ) ( =-- + + - =-- + + - =-- + + - z visc z y visc y x visc x F f z P V w t w direction z F f y P V v t v direction y F f x P V u t u direction x r r r r r r Wake-Rake: - = 2 2 1 2 2 ) ( dy u u u D Substantial Derivative D Dt = t + u x + v y + w z Streamlines d r s r V = Cartesian coordinates: w dy- vdz = u dz- w dx = v dx- udy = for 2-D flow: dy dx = v u Vorticity r 2 r = r r V = curl...
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This note was uploaded on 04/07/2008 for the course AE 2020 taught by Professor Ruffin during the Summer '07 term at Georgia Institute of Technology.
- Summer '07