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 $=$ Vy$/$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$,$ mu$,$ 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 mu$,$ etc.

$($a$)$ Go through the step$-$by$-$step procedure, showing all your work, to generate an expression with one or more nondimensional Pi parameters in the usual fashion, namely, Pi$\_(1)=$ function $($Pi$\_(2),$Pi$\_(3),$dots$).$

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

Please show all work for each part.