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eqnsheetEXAM2 - AE311 Exam 2 Equation Sheet Uniform Flow...

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r π 2 Λ r ln 2 π Λ θ π 2 Λ r π 2 Γ r ln 2 π Γ θ π 2 Γ r K θ π sin 2 r K θ π cos 2 2 sin 2 r K θ π 2 cos 2 r K θ π ) ( 2 2 2 y x x + Λ π 2 / 1 2 2 ) ln( 2 y x + Λ π x y arctan 2 π Λ ) ( 2 2 2 y x x + Γ π 2 / 1 2 2 ) ln( 2 y x + Γ π x y arctan 2 π Γ ) ( 2 2 2 y x y K + π ) ( 2 2 2 y x x K + π 2 / 3 2 2 ) ( 2 y x y K + π 2 / 3 2 2 ) ( 2 y x x K + π ) ( 2 2 2 y x y + Λ π ) ( 2 2 2 y x y + Γ π AE311 Exam 2 Equation Sheet Ψ φ V r V θ Uniform Flow V rsin θ V rcos θ V cos θ - V sin θ from left to right Source Flow Vortex flow Doublet Ψ φ u v Uniform Flow V y V x V 0 from left to right Source Flow Vortex flow Doublet Cylinder K = 2 π V R 2
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( ) 0 . = + V t ρ ρ ( ) x vis x F f x p V u t u , . + + = + ρ ρ ρ ( ) ) cos 1 ( 2 1 cos 1 cos 2 1 sin 2 sin cos 1 2 ) ( ) 2 ( ) ( 2 1 0 0 0 0 0 1 1 0 ' 0 θ θ θ π α θ θ π θ π α θ θ θ θ γ π α ξ ξ ξ γ π π π π = = = = + + = + = =
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