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.
