Problem 2.36 - Problem 2.36 [Difficulty: 4] Given: Velocity...

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Problem 2.36 [Difficulty: 4] Given: Velocity field Find: Coordinates of particle at t = 2 s that was at (2,1) at t = 0; coordinates of particle at t = 3 s that was at (2,1) at t = 2 s; plot pathline and streakline through point (2,1) and compare with streamlines through same point at t = 0, 1 and 2 s Solution: Governing equations: For pathlines u p dx dt = v p dy dt = For streamlines v u dy dx = Following the discussion leading up to Eq. 2.10, we first find equations for the pathlines in form x p t () xtx 0 , y 0 , t 0 , = and y p t ytx 0 , y 0 , t 0 , = x st t 0 0 , y 0 , t 0 , = and y st t 0 0 , y 0 , t 0 , = which gives the streakline at t, where x 0 , y 0 is the point at which dye is released (t 0 is varied from 0 to t) Assumption: 2D flow Given data a 0.4 = m s 2 b2 = m s 2 Hence for pathlines u p dx dt = at = v p dy dt = b = Hence dx a t dt = dy b dt = Integrating xx 0 a 2 t 2 t 0 2 = yy 0 bt t 0 = The pathlines are xt x 0 a 2 t 2 t 0 2 + = yt y 0 0 + = These give the position (x,y) at any time t of a particle that was at (x 0 ,y 0 ) at time t 0
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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 2.36 - Problem 2.36 [Difficulty: 4] Given: Velocity...

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