Chapter 4, Problem 86P

The horizontal velocity in the wake behind an object in an air stream of velocity U is given by

$\begin{array}{l}u(r)=U\left[1-{\cos }^2\left(\frac{\pi r}{2}\right)\right]\left|r\right|\le 1\\ u(r)=U\left|r\right|\le 1\end{array}$

where r is the nondimensional radial coordinate, measured perpendicular to the flow. Find an expression for the drag on the object.