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Problem 5.73 - Problem 5.73 Given Flow field...

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Problem 5.73 [Difficulty: 3] Given: Flow field Find: If the flow is incompressible and irrotational Solution: Basic equations: Incompressibility x u y v 0 Irrotationality x v y u 0 a) u x y ( ) x 7 21 x 5 y 2 35 x 3 y 4 7 x y 6 v x y ( ) 7 x 6 y 35 x 4 y 3 21 x 2 y 5 y 7 x u x y ( ) 7 x 6 105 x 4 y 2 105 x 2 y 4 7 y 6 y v x y ( ) 7 x 6 105 x 4 y 2 105 x 2 y 4 7 y 6 Hence x u y v 0 COMPRESSIBLE b) u x y ( ) x 7 21 x 5 y 2 35 x 3 y 4 7 x y 6 v x y ( ) 7 x 6 y 35 x 4 y 3 21 x 2 y 5 y 7
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