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Problem 5.45 - Problem 5.45[Difficulty 2 Given Velocity...

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Problem 5.45 [Difficulty: 2] Given: Velocity field Find: Whether flow is incompressible; expression for acceleration; evaluate acceleration along axes and along y = x Solution: The given data is A 10 m 2 s u x y ( ) A x x 2 y 2 v x y ( ) A y x 2 y 2 For incompressible flow x u y v 0 Hence, checking x u y v A x 2 y 2 x 2 y 2 2 A x 2 y 2 x 2 y 2 2 0 Incompressible flow The acceleration is given by For the present steady, 2D flow a x u du dx v du dy A x x 2 y 2 A x 2 y 2 x 2 y 2 2 A y x 2 y 2 2 A x y x 2 y 2 2 a x A 2 x x 2 y 2 2 a y u dv dx v dv dy A x x 2 y 2 2 A x y x 2 y 2 2 A y x 2 y 2 A x 2 y 2 x 2 y 2 2 a y A 2 y x 2 y 2 2 Along the
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