Problem 2.34 - Problem 2.34[Difficulty 3 Given Velocity field Find Equation for streamline through point(2.5 coordinates of particle at t = 2 s

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Problem 2.34 [Difficulty: 3] Given: Velocity field Find: Equation for streamline through point (2.5); coordinates of particle at t = 2 s that was at (0,4) at t = 0; coordinates of particle at t = 3 s that was at (1,4.25) at t = 1 s; 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 a2 = m s b1 = 1 s x 0 2 = y 0 5 = x1 = xx = For streamlines v u dy dx = bx a = So, separating variables a b dy xdx = Integrating a b yy 0 () 1 2 x 2 x 0 2 = The solution is then 0 b 2a x 2 x 0 2 + x 2 4 4 + = = Hence for pathlines u p dx dt = a = v p dy dt = = Hence dx a dt = dy b x dt = Integrating 0 at t 0 = dy b x 0 0 + dt = 0 0 tt 0 a 2 t 2 t 0 2 + at 0 0 = The pathlines are 0 0 + = 0 0 0 a 2 t 2 t 0 2 + 0 0 + =
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For a particle that was at x 0 0 = m, y 0 4 = m at t 0 0 = s, at time t2 = s we find the position is xx 0 at t 0 () + 4 = = m yy 0 bx 0 tt 0 a 2 t 2 t 0 2
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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 2.34 - Problem 2.34[Difficulty 3 Given Velocity field Find Equation for streamline through point(2.5 coordinates of particle at t = 2 s

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