A rectangular channel has a bottom width $b$ and a channel slope $S_0.$ For steady uniform flow, the normal depth is $y_n.$ Using Manning's equation for open channel flow, write equations for the following for steady uniform flow:

a$)$ The flow area $A$

b$)$ The wetted perimeter $P$

c$)$ The hydraulic radius $R$

d$)$ The flow velocity $V($substitute expressions from above to produce an equation with the normal depth $y_n)$

e$)$ The discharge rate $Q($again$,$ in terms on the normal depth $y_n)$

For steady$-$uniform flow of $30\frac{m^3}{s}$ in a rectangular channel $),$ compute:

f$)$ The normal depth $y_n($in m$)$