Question $1[20$ Marks in Total$]$

Working from the expression for flow between parallel plates:

$u(z)=\frac{P}{2L}(h-z)z$

$Q=\frac{h^{3}wP}{12L}$

where the symbols have their usual meanings, using physical reasoning, derive an approximate expression for fully developed flow in a rectangular microchannel, of width w and height h $($you can assume the microchannel is much wider than it is high$).$ Ensure you explain the logic in your reasoning behind each step of the derivation.

$Q=\frac{h^{3}wP}{12L}[1-0\mathrm{.}5\frac{h}{w}]$

$[12$ Marks$]$