HW5_313fall09

# HW5_313fall09 - origin 2 Consider a source of strength m(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 ﬂow? (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 μ is located at z = δ exp ( i 5 π/ 8), where δ = . 05 m. It is embedded in a uniform stream with velocity u o = 10 m/s. (a) What is the strength (the value of κ ) 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 ζ-plane under the Joukowski transformation. First write a short computer program to calculate ξ and η 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(m...

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