Consider the lifting flow over a circular cylinder of a given radius and with a given circulation. If \(V_{\infty}\) is doubled, keeping the circulation the same, does the shape of the streamlines change? Explain.
Consider the lifting flow over a circular cylinder of a given radius and with a given circulation. If \(V_{\infty}\) is doubled, keeping the circulation the same, does the shape of the streamlines change? Explain.
\[\frac{V_{r}}{V_{\infty}}=\left ( 1-\frac{R^{2}}{r^{2}} \right )cos\theta \;\;\;\mathrm{and}\;\;\;\frac{V_{\theta}}{V_{\infty}}=-\left ( 1+\frac{R^{2}}{r^{2}} \right )sin\theta-\frac{\tau}{2\pi V_{\infty}}\]
\(\frac{V_{\theta}}{V_{\infty}}\) is itself a function of \(V_{\infty}\).This shows that as \(V_{\infty}\) changes ,the direction of the resultant velocity at a given point will also change.Therefore the shape of the streamlines changes when \(V_{\infty}\) change.
