For the compound channel cross section shown in the $($not to scale$)$ diagram below, assume a channel slope of $0\mathrm{.}0007$ and a Manning's roughness coefficient of $0\mathrm{.}025$ and $0\mathrm{.}14$ for sections $1$ and $2$ respectively.

a$)$ Calculate the velocity in section $1$ and $2$ and total flow rate for the channel.

b$)$ Based on your calculated average velocities for each section, estimate the velocity distribution in the channel by sketching contours of equal velocity across the entire cross section. Provide contours for each whole foot per second, i$.$e$.1fps,2fps,$ etc.