Problem 2.23 - Problem 2.23 [Difficulty: 3] Given: Velocity...

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Problem 2.23 [Difficulty: 3] Given: Velocity field Find: Plot of pathline of particle for t = 0 to 1.5 s that was at point (1,1) at t = 0; compare to streamlines through same point at the instants t = 0, 1 and 1.5 s Solution: Governing equations: For pathlines u p dx dt = v p dy dt = For streamlines v u dy dx = Assumption: 2D flow Hence for pathlines u p dx dt = ax = a 1 5 = 1 s v p dy dt = by t = b 1 25 = 1 s 2 So, separating variables dx x ad t = dy b y t dt = dy y bt dt = Integrating ln x x 0 at = x 0 1 = m ln y y 0 b 1 2 t 2 = y 0 1 = m Hence xt () x 0 e = yt y 0 e 1 2 b t 2 = Using given data e t 5 = e t 2 50 = For streamlines v u dy dx = t = So, separating variables dy y dx = which we can integrate for any given t (t is treated as a constant)
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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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Problem 2.23 - Problem 2.23 [Difficulty: 3] Given: Velocity...

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