Example $4-1$: A $2-$m wide rectangular channel carries water at $20\backslash$deg C at a depth of $0\mathrm{.}5$ m$.$ The channel has a slope of $0\mathrm{.}0004$ and is made of concrete with a surface roughness of $\backslash$epsi $=3\mathrm{.}5$ mm$.$

a$)$ find the hydrodynamic nature of the surface;

b$)$ estimate the discharge of the channel using the Chezy$$s formula.