Calculate the kinetic energy correction factor for each of the following velocity profiles for a circular pipe:

(a) \(u=u_{\max }\left(1-\frac{r}{R}\right)\)

(b) \(u=u_{\max }\left(1-\frac{r^{2}}{R^{2}}\right)\);

(c) \(u=u_{\max }\left(1-\frac{r}{R}\right)^{1 / 9}\)

\(R\) is the pipe radius and \(r\) is the radial coordinate.