Problem 2.33 - Problem 2.33 [Difficulty: 3] Given: Velocity...

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Problem 2.33 [Difficulty: 3] Given: Velocity field Find: Equation for streamline through point (1.1); coordinates of particle at t = 5 s and t = 10 s that was at (1,1) at t = 0; compare pathline, streamline, streakline Solution: Governing equations: For streamlines v u dy dx = For pathlines u p dx dt = v p dy dt = Assumption: 2D flow Given data a 1 5 = 1 s b1 = m s x 0 1 = y 0 1 = t 0 0 = For streamlines v u dy dx = b ax = So, separating variables a b dy dx x = Integrating a b yy 0 () ln x x 0 = The solution is then 0 b a ln x x 0 + 5lnx 1 + = = Hence for pathlines u p dx dt = = v p dy dt = b = Hence dx x ad t = dy b dt = Integrating ln x x 0 at t 0 = 0 bt t 0 = The pathlines are xx 0 e att 0 = 0 0 + = or 0 b a ln x x 0 + =
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For a particle that was at x 0 1 = m, y 0 1 = m at t 0 0 = s, at time t1 = s we find the position is xx 0 e att 0 () e 1 5 = = m yy 0 bt t 0 + 2 = = m For a particle that was at
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Problem 2.33 - Problem 2.33 [Difficulty: 3] Given: Velocity...

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