Problem 2.22

# Problem 2.22 - Problem 2.22[Difficulty 3 Given Velocity...

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Problem 2.22 [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 = a2 = 1 s v p dy dt = by 1c t + () = b2 = 1 s 2 c 0.4 = 1 s So, separating variables dx x ad t = dy b y t + dt = dy y b1 c t + dt = Integrating ln x x 0 at = x 0 1 = m ln y y 0 bt 1 2 c t 2 + = y 0 1 = m Hence xt x 0 e = yt e 1 2 c t 2 + = Using given data e 2t = e 0.4 t 2 + = For streamlines v u dy dx = t + ax = So, separating variables dy y t + dx = which we can integrate for any given t (t is treated as a constant)

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Problem 2.22 - Problem 2.22[Difficulty 3 Given Velocity...

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