Problem 2.25 - Problem 2.25 [Difficulty: 3] Given: Flow...

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Problem 2.25 [Difficulty: 3] Given: Flow field Find: Pathline for particle starting at (3,1); Streamlines through same point at t = 1, 2, and 3 s Solution: For particle paths dx dt u = ax t = an d dy dt v = b = Separating variables and integrating dx x at dt = or ln x () 1 2 a t 2 c 1 + = dy b dt = or yb t c 2 + = Using initial condition (x,y) = (3,1) and the given values for a and b c 1 ln 3 m = an d c 2 1m = The pathline is then x3 e 0.05 t 2 = and y4 t 1 + = For streamlines (at any time t) v u dy dx = b t = So, separating variables dy b dx x = Integrating y b
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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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