$($c$)$ Using the Manning Equation, $\backslash ($ V$=\backslash$frac$\{1\}\{$n$\}$ m$^\{2/3\}$ i$^\{1/2\}\backslash ),$ design a rectangular channel in formed unfinished concrete, having a flow discharge of $\backslash (6\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$sec$\}\backslash ),$ a bed slope of $\backslash (1\mathrm{.}2\backslash \%\backslash )$ and normal depth equal to $\backslash (1/2\backslash )$ the width of the channel. Use the table below to get the Manning's coefficient of roughness.

Channel Description

Glass, copper, plastic, or other smooth surfaces

Smooth, unpainted steel, planed wood

Painted steel or coated cast iron

Smooth asphalt, common clay drainage tile, trowel$-$finished concrete, glazed brick

Uncoated cast iron, black wrought iron pipe, vitrified clay sewer tile

Brick in cement mortar, float$-$finished concrete, concrete pipe

$0\mathrm{.}015$

Formed, unfinished concrete, spiral steel pipe

$0\mathrm{.}017$

Smooth earth

$0\mathrm{.}018$

Clean excavated earth

$0\mathrm{.}022$

Corrugated metal storm drain

$0\mathrm{.}024$

Natural channel with stones and weeds

$0\mathrm{.}030$

Natural channel with light brush

$0\mathrm{.}050$

Natural channel with tall grasses and reeds

$0\mathrm{.}060$

Natural channel with heavy brush

$0\mathrm{.}100$