Which one of the following equations given the velocity distribution across a circular pipe having a viscous flow?
(a) $u=u_{max}\left [ 1-\left ( r/R \right )^{2} \right ]$
(b)$u=u_{max}\left [ 1-\left ( R^{2}-r^{2} \right ) \right ]$
(c)$u=u_{max}\left [ 1-\left ( r/R \right ) \right ]^{2}$
(d)$u=u_{max}\left [ 1+\left ( r/R \right ) \right ]^{2}$