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 A1 0 m 2 s uxy () Ax x 2 y 2 vxy Ay 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 x 2 y 2 2 y 2 x 2 y 2 2 x 2 y 2 2A 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 x 2 y 2 x y x 2 y 2 2 x 2 y 2 2 y 2 x 2 y 2 2 a y A 2 y x 2 y 2 2 Along the x axis a x A 2 x 3 100 x 3 a y 0 Along the y axis a x 0 a y A 2 y 3 100 y 3
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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