Problem 2.18 - Problem 2.18 [Difficulty: 2] Given:...

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Problem 2.18 [Difficulty: 2] Given: Time-varying velocity field Find: Streamlines at t = 0 s; Streamline through (3,3); velocity vector; will streamlines change with time Solution: For streamlines v u dy dx = ay 2 cos ω t () + ax 2 cos ω t + = y x = At t = 0 (actually all times!) dy dx y x = So, separating variables dy y dx x = Integrating ln y ( ) ln x c + = The solution is y C x = which is the equation of a hyperbola. For the streamline through point (3,3) C 3 3 = C1 = and y 1 x = The streamlines will not change with time since dy/dx does not change with time.
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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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