a$.$ Design a screen that is to be placed in a rectangular channel which transports water from an intake to a water treatment plant. Please use the following data to calculate:

$($i$)$ The coefficient of efficiency of the screen

$($ii$)$ Velocity in the channel upstream of the screen

$($iii$)$Actual velocity through the screen when the screen is clean

$($iv$)$The head loss through the screen when the screen is clean and $50\%$ clogged

$($v$)$ Depth of flow $y_2$ in the channel downstream of the screen

$\begin{array}{cc}\text{D}\text{e}\text{s}\text{i}\text{g}\text{n}\text{f}\text{l}\text{o}\text{w}\text{r}\text{a}\text{t}\text{e}& ?\\ \text{M}\text{a}\text{x}\text{i}\text{m}\text{u}\text{m}\text{v}\text{e}\text{l}\text{o}\text{c}\text{i}\text{t}\text{y}\text{t}\text{h}\text{r}\text{o}\text{u}\text{g}\text{h}\text{t}\text{h}\text{e}\text{s}\text{c}\text{r}\text{e}\text{e}\text{n}& ?\\ \text{U}\text{p}\text{s}\text{t}\text{r}\text{e}\text{a}\text{m}\text{d}\text{e}\text{p}\text{t}\text{h}of\text{f}\text{l}\text{o}\text{w}& ?\\ \text{W}\text{i}\text{d}\text{t}\text{h}of\text{a}\text{s}\text{c}\text{r}\text{e}\text{e}\text{n}\text{b}\text{a}\text{r}& =10mm\\ \text{C}\text{l}\text{e}\text{a}\text{r}\text{s}\text{p}\text{a}\text{c}\text{i}\text{n}\text{g}\text{b}\text{e}\text{t}\text{w}\text{e}\text{e}\text{n}\text{t}\text{w}\text{o}\text{s}\text{c}\text{r}\text{e}\text{e}\text{n}\text{b}\text{a}\text{r}\text{s}& =25mm\end{array}=25mm=10mm=1\mathrm{.}5m=25mm=10mm=1\mathrm{.}5m=0\mathrm{.}9\frac{m}{s}=25mm=10mm=1\mathrm{.}5m=0\mathrm{.}9\frac{m}{s}=2\mathrm{.}0\frac{m^3}{s}$

The following formula can be used to calculate the head loss, $h_h,$ through the screen: channel ubstream of the screen.