HW5_313fall09

HW5_313fall09 - origin. 2. Consider a source of strength m...

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AERSP 313 Homework Assignment No. 5 - Complex Variables - Fluid Flows Assigned October 8, 2009, Due October 20, 2009 Sec. 18.4, p. 766, Nos. 9, 10, 11,15. (a) In the first two problems go through the following steps: 1. find the stagnation points, 2. find the value of the stagnation streamfunction 3. find the equation for the stagnation streamline 4. find a general equation for the streamlines and plot them (b) In the third problem, just find an equation for the streamlines. In the fourth problem, just find the streamlines, again. It is tricky so first invert the expression for the complex potential to get z in terms of φ and ψ . Then eliminate φ by using the expression that cos 2 φ + sin 2 φ = 1 AND. ...... 1. Consider a source of strength m and a vortex of strength κ both located at the origin.
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(a) What is the complex potential for this flow? (b) What is the equation for the streamlines? (c) Sketch a few streamlines (d) Determine whether the velocity is directed away from or towards the
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Unformatted text preview: origin. 2. Consider a source of strength m (m 2 /s) at the origin in a uniform stream given by u o = 10 m/s. (a) What is the complex potential for this ow? (b) Write down the equation for the stagnation streamline. (c) Find the stagnation point(s) (d) If the stagnation streamline is located at y = 1 m as x , what is the source strength in (m 2 /s)? 3. A double of strength is located at z = exp ( i 5 / 8), where = . 05 m. It is embedded in a uniform stream with velocity u o = 10 m/s. (a) What is the strength (the value of ) of a clockwise vortex that must be added to the source to make the stagnation point occur at z = 1 . 0 m? (b) What is the strength of the doublet in m 3 /s? (c) Draw the transform of the circle in the -plane under the Joukowski transformation. First write a short computer program to calculate and and then make the plot. Attach your computer code to the homework. 2...
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HW5_313fall09 - origin. 2. Consider a source of strength m...

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