EGM6812_F10_HW10S - EGM 6812 Fluid Mechanics 1 - Fall 2010...

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Unformatted text preview: EGM 6812 Fluid Mechanics 1 - Fall 2010 12/8/10, 10 th Homework 1 HW8 Problem 1 Given: Consider a uniform, ideal flow over an ellipse with major and minor axes of A and B , respectively. The freestream velocity is U and the angle of attack is . Find: The complex potential for this z-plane flow field. The complex velocity for this z-plane flow field. Determine the circulation when the velocity at the trailing edge is zero. What is the lift on the ellipse? x iy U A iB Assumptions: 1) Ideal flow 2) Steady Solution: We need to use a Joukowski transform to map the ellipse into a circle in the -plane. The transform is 2 2 1, 0, z z a z x i y a a and the inverse transform is 1 1 , 2 z i a . We do not know the value of a and need to solve this as a function of what we are given, A and B We know that a circular cylinder of radius 1 is , i e and transforms into an ellipse in the z-plane....
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EGM6812_F10_HW10S - EGM 6812 Fluid Mechanics 1 - Fall 2010...

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