Problem 2.20 - Problem 2.20 [Difficulty: 3] Given: Velocity...

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Problem 2.20 [Difficulty: 3] Given: Velocity field Find: Plot of pathline traced out by particle that passes through point (1,1) at t = 0; compare to streamlines through same point at the instants t = 0, 1 and 2s 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 = Bx 1A t + () = A 0.5 1 s = B1 1 s = v p dy dt = Cy = C1 1 s = So, separating variables dx x B1 A t + dt = dy y Cd t = Integrating ln x () B t A t 2 2 + C 1 + = ln y () Ct C 2 + = ye Ct C 2 + = e C 2 e = c 2 e = xe BtA t 2 2 + C 1 + = e C 1 e t 2 2 + = c 1 e t 2 2 + = The pathlines are xc 1 e t 2 2 + = yc 2 e = Using given data t 2 2 + = = For streamlines v u dy dx
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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 2.20 - Problem 2.20 [Difficulty: 3] Given: Velocity...

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