Fundamentals of Aerodynamics
Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.13P

Derive Equation ( 3 . 81 ) . Hint: Make use of the symmetry of the flow field shown in Figure 3.18; thai is, start with the knowledge that the stagnation points must lie on the axis aligned with the direction of V .

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5.17 The velocity field given by V =Axi-Ayj represents flow in a rectangular corner. Evaluate the circulation around the unit square with corners at (x.y)= (1,1), (1,2), (2,2) and (2,1) for the value of A =0 3s-!.
55. Derive the relation for angular velocity in terms of the velocity components for fluid rotation in a two-dimensional flow field. [Hint: Use the schematic for ro- tation in Figure IIa.3.5 and find the angular velocity for line oa as @a = doddt. Substitute for da= dl,/dx and for dl, from dl, = (JV,/dx)dxdt. Do the same for line ob to find @p. The z-component of rotation vector is the average of @a and @p. Do the same for x- and y- components].
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