HW4 - AE311 Fall 2008 Problem Set 4 Due Oct 22nd 2008...

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AE311 Fall 2008 Problem Set 4 Due: Oct 22nd 2008, before class 1. (15pts) Consider the incompressible, irrotational, two-dimensional flow, where the stream function is xy 2 = ψ a) What is the velocity at x = 1, y = 1? At x = 2, y =1/2? Are these points on the same streamline? Why or why not? b) Sketch the streamline pattern and discuss the significance of the spacing between the streamlines. c) What is the velocity potential for this flow? d) Sketch the lines of constant potential. How do the lines of equipotential relate to the streamlines? 2. (15pts) A source and a sink of equal strength 80 m 2 /s are located on the x-axis, separated by a distance of 8 m. (Let the midpoint be the origin of your coordinate system.) Sketch the streamlines. Calculate the velocity at the origin. Calculate the value of the streamfunction for the streamline passing through the point (0, 4) and calculate the velocity there. 3. (10pts) What is the strength required of a source at the origin will result in a velocity of 20 at the point (0, 5)?
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