Example:

$=850k\frac{g}{m^3}$

An incompressible viscous fluid flows between two horizontal parallel plates as shown. The plates are spaced $0\mathrm{.}5cm$ apart and are very wide perpendicular to page. Flow is laminar and velocity profile at any cross section is given by$,$

$u=-\frac{Y^2}{2}(\frac{P}{L})[1-(\frac{y}{Y}{)}^2]$

where $P$ is the pressure change that occurs in length $L.$ Calculate average mechanical energy loss $h_1$ between the pressure gages. Then show that mechanical energy loss also satisfies the equations

$g{h}_l=\frac{{\displaystyle \underset{CV}{\overset{\phantom{}}{}}}(\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}{)}^2\text{d}\text{A}\text{A}}{(m^{})},$ and $,g{h}_l=Re(\frac{L}{Y})(\frac{\frac{?}{\text{b}\text{a}\text{r}}(V{)}^2}{2})$

where

$Re=\frac{(\frac{?}{\text{b}\text{a}\text{r}}(V))Y}{}$