The velocity field for steady inviscid flow from left to right over a circular cylinder, of radius \(R\) is given by

\[\vec{V}=U \cos \theta\left[1-\left(\frac{R}{r}\right)^{2}\right] \hat{e}_{r}-U \sin \theta\left[1+\left(\frac{R}{r}\right)^{2}\right] \hat{e}_{\theta}\]

Obtain expressions for the acceleration of a fluid particle moving along the stagnation streamline \((\theta=\pi)\) and for the acceleration along the cylinder surface \((r=R)\). Plot \(a_{r}\) as a function of \(r / R\) for \(\theta=\pi\), and as a function of \(\theta\) for \(r=R\); plot \(a_{\theta}\) as a function of \(\theta\) for \(r=R\). Comment on the plots. Determine the locations at which these accelerations reach maximum and minimum values.