Chapter 10, Problem 70P

The stream function for steady, incompressible, two-dimensional flow over a circular cylinder of radius a and free-stream velocity $V_{\infty }\text{is}\psi =V_{\infty }\sin \theta \left(r-a^2/r\right)$ for the case in which the flow field is approximated as. irrotational (Fig. 10-70). Generate an expression for the velocity potential function $\varphi$ for this flow as a function of r and $\theta$. and parameters. $V_{\infty }$ and a.

FIGURE P10-70