$(30pts)$ Consider fully developed Couette flow $($flow between two infinite plates with the top plate moving and the

bottom plate stationary. We know the velocity profile equation from previous lessons, $u=V\frac{y}{h}.$ Suppose, however, that you

do not know this. Instead, you approach the problem using dimensional analysis and the method of repeating variables. You

set up the problem as $u=u(h,V,,y).$ For consistency, choose your repeating variables in the same order as in the list of

variables above. In other words, if you need two repeating variables, choose $h$ and $V.$ If three, choose $h,V,$ and $,$ etc.

$($a$)$ Go through the step$-$by$-$step procedure, showing all your work, to generate an expression with one or more

nondimensional $$ parameters in the usual fashion, namely, ${}_1=$ function $({}_2,{}_3,$dots$).$

$($b$)$ Show that your result $($if done correctly$)$ is consistent with the known velocity profile equation.