Problem 2.30 - Problem 2.30 [Difficulty: 4] Given: Velocity...

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Problem 2.30 [Difficulty: 4] Given: Velocity field Find: Plot of pathline for t = 0 to 3 s for particle that started at point (1,2) at t = 0; compare to streakline through same point at the instant t = 3 Solution: Governing equations: For pathlines u p dx dt = v p dy dt = 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 For pathlines u p dx dt = ax t = a 1 4 = 1 s 2 b 1 3 = m s v p dy dt = b = So, separating variables dx x at dt = dy b dt = Integrating ln x x 0 a 2 t 2 t 0 2 = yy 0 bt t 0 = 0 0 + = xx 0 e 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 2.30 - Problem 2.30 [Difficulty: 4] Given: Velocity...

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