Consider the nonlifting flow over a circular cylinder of a given radius, where \(V_{\infty} = 20 ft/s\). If \(V_{\infty}\) is doubled, that is, \(V_{\infty} = 40 ft/s\), does the shape of the streamlines change? Explain.
\[\frac{V_{r}}{V_{\infty}}=\left ( 1-\frac{R^{2}}{r^{2}} \right )cos\theta\]
\[\frac{V_{\theta}}{V_{\infty}}=-\left ( 1+\frac{R^{2}}{r^{2}} \right )sin\theta\]
At \(\left ( r,\theta \right ) \) ,\(V_{r}\) and \(V_{\infty}\) is proportional to \(V_{\infty}\). Therefore \(\overrightarrow{V}\) is same what \(V_{\infty} \) may be. The shape of the streamlines will remain same it will not change.
