Problem 2.14

# Problem 2.14 - Problem 2.14[Difficulty 2 Given Velocity...

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Problem 2.14 [Difficulty: 2] Given: Velocity field Find: Proof that the parametric equations for particle motion are x p c 1 e At = and y p c 2 e A t = ; pathline that was at (2,2) at t = 0; compare to streamline through same point, and explain why they are similar or not. Solution: Governing equations: For pathlines u p dx dt = v p dy dt = For streamlines v u dy dx = Assumption: 2D flow Hence for pathlines u p dx dt = Ax = v p dy dt = A y = So, separating variables dx x Adt = dy y A dt = Integrating ln x () A t C 1 + = ln y () A t C 2 + = xe C 1 + = e C 1 e = c 1 e = ye A t C 2 + = e C 2 e A t = c 2 e A t = The pathlines are xc 1 e = yc 2 e A t = Eliminating t t 1 A ln x c 1 = 1 A ln y c 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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