LectureExample_5-3

LectureExample_5-3 - Problem 5.67 Given: Flow field Find:...

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Problem 5.67 [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) uxy , () x 7 21 x 5 y 2 35 x 3 y 4 + 7x y 6 = vxy , () 7 x 6 y 35 x 4 y 3 21 x 2 y 5 + y 7 = x , () 6 105 x 4 y 2 105 x 2 y 4 + 7y 6 y , 6 105 x 4 y 2 105 x 2 y 4 + 6 Hence x u y v + 0 COMPRESSIBLE b) , 7 21 x 5 y 2 35 x 3 y 4 + y 6 = , x 6 y 35 x 4 y 3 21 x 2 y 5 + y 7 = x , 42 x 5 y 140 x 3 y 3 42 x
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