Chapter 5, Problem 46P

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

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

Obtain expressions for the acceleration of a fluid particle moving along the stagnation streamline (θ = π) and for the acceleration along the cylinder surface (r = R). Plot a_r as a function of r = R for θ = π, and as a function of θ for r = R; plot a_θ as a function of θ for r = R. Comment on the plots. Determine the locations at which these accelerations reach maximum and minimum values.