A constant-density fluid flows between two flat parallel plates that are separated by a distance \(\delta\) (Figure P2.2). Sketch the velocity distribution and compute the mass average velocity based on the velocity \(u\) given by:

(a) \(u=k_{1} y\).

(b) \(u=k_{2} y^{2}\).

(c) \(u=k_{3}\left(\delta y-y^{2}\right)\).
In each case, express your answer in terms of the maximum velocity \(U_{m}\).

Figure P2.2