Problem 2.19 - Problem 2.19 [Difficulty: 3] Given: Velocity...

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Problem 2.19 [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 = A1 B t + () = A1 m s = B1 1 s = v p dy dt = Ct y = C1 1 s 2 = So, separating variables dx A 1 B t + dt = dy y dt = Integrating xA tB t 2 2 + C 1 + = ln y 1 2 C t 2 C 2 + = ye 1 2 C t 2 C 2 + = e C 2 e 1 2 C t 2 = c 2 e 1 2 C t 2 = The pathlines are t 2 2 + C 1 + = yc 2 e 1 2 C t 2 = Using given data t 2 2 + 1 + = 1 2 C t 2 = For streamlines v u dy dx = Cy t t + = So, separating variables 1B t + dy y
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Problem 2.19 - Problem 2.19 [Difficulty: 3] Given: Velocity...

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