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Problem 2.11

# Problem 2.11 - Problem 2.11[Difficulty 3 Given Flow field...

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Problem 2.11 [Difficulty: 3] Given: Flow field Find: Plot of velocity magnitude along axes, and y = x; Equation for streamlines Solution: On the x axis, y = 0, so u My 2 π = 0 = v Mx 2 π = 0 0.2 0.4 0.6 0.8 1 50 100 150 200 x (km) v (m/s) Plotting The velocity is perpendicular to the axis and increases linearly with distance x. This can also be plotted in Excel. On the y axis, x = 0, so u 2 π = v 2 π = 0 = 0 0.2 0.4 0.6 0.8 1 200 150 100 50 y (km) u (m/s) Plotting The velocity is perpendicular to the axis and increases linearly with distance y. This can also be plotted in Excel.

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On the y = x axis u My 2 π = Mx 2 π = v 2 π = The flow is perpendicular to line y = x: Slope of line y = x: 1 Slope of trajectory of motion: u v 1 = If we define the radial position: rx 2 y 2 + = then along y = x 2 x 2 + = 2 x = Then the magnitude of the velocity along y = x is Vu 2 v 2 + = M 2 π x 2 x 2 + = M2 x 2 π = Mr 2 π = 0 0.2 0.4 0.6 0.8 1 50 100
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Problem 2.11 - Problem 2.11[Difficulty 3 Given Flow field...

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