Question $2$:$(10$ Marks$)$

Fluid flow down a vertical wall can be described for a film of thickness $h$ in terms of a parabolic velocity

profile $u_x=(3u\frac{y}{2}h)[2-\frac{y}{h}]$ where $y=0$ at the wall, and the maximum and average fluid velocities are

related by $u=(\frac{2}{3})u_{\text{m}\text{a}\text{x}}.$ Show that the longitudinal dispersion coefficient is given by $E_L=2h^2\frac{u^{}{?}^2}{105D_c}.$

Mean velocity is $-.$