Consider the lifting flow over a circular cylinder of a given radius and with a given circulation. If velocity is doubled does the shape of streamlines change.
If the velocity \({V_\infty }\) of a flow is doubled in the case of lifting flow over a circular cylinder of a given radius and with a given circulation, does the shape of the streamline change on keeping the circulation same.
Since for the case of lifting flow over a circular cylinder \[\left( {\frac{{{V_r}}}{{{V_\infty }}}} \right) = \left( {1 – \frac{{{R^2}}}{{{r^2}}}} \right)\cos \theta \]and\[\left( {\frac{{{V_\theta }}}{{{V_\infty }}}} \right) = – \left( {1 + \frac{{{R^2}}}{{{r^2}}}} \right)\sin \theta – \frac{\tau }{{2\pi r{V_\infty }}}\]Since\(\left( {\frac{{{V_\theta }}}{{{V_\infty }}}} \right)\) is a function of \({V_\infty }\), so as \({V_\infty }\) changes, the direction of the resultant velocity at a given point also changes.Therefore as \({V_\infty }\) is changing the shape of streamlines also changes.
