$5\mathrm{.}1$ An irrigation channel with a flow depth that is $60\%$ of the bed width conveys $49\mathrm{.}7\frac{m^3}{s}$ of water to an irrigation farm. This excavated earth channel is well maintained with a Manning's coefficient, $n=0\mathrm{.}022.$ The channel has a bed slope of $0\mathrm{.}002$ and side slope of $1$:$4(V$:$H).$ Taking the flow to be uniform, determine the following:

a$)$ Channel bed width and Normal depth.

b$)$ Specific energy in the channel.