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308_mt2_sample - Mechanics of Fluids Aerospace 308/308H...

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Mechanics of Fluids: Aerospace 308/308H Sample Second Midterm Examination You have 75 minutes to complete the exam Answer 4 out of 5 questions only Question Points Check 1 25 2 25 3 25 4 25 5 25 1
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1. Two point sources of equal strength m are located at z = c and z = ic , with c > 1 and real. Find the complex potential for the flow repre- sented by these two sources outside a circle of radius a = 1 centered at the origin. Describe the resulting complex potential in terms of a distribution of point sources. Where are they located and what are their strengths? 2
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2. The curl of the velocity, or vorticity, is given by ω = ∇ × u = fl fl fl fl fl fl fl i j k ∂/∂x ∂/∂y ∂/∂z u v w fl fl fl fl fl fl fl Consider developed laminar flow in a channel of height 2 h where the axial velocity is given by u = U o ˆ 1 - y 2 h 2 ! where U o is the centerline velocity. (a) What is variation of the vorticity with y ? (b) If a streamfunction can be determined for this flow find ψ ( x, y ).
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