$(10$ pnts$)$ For a certain design, an unlined rectangular wide channel that has a width of $15ft,$ slope of $0\mathrm{.}02$ and a Manning coefficient of $0\mathrm{.}018$ should carry a discharge of $150$ cfs$.$ Will it be possible to carry the required discharge without eroding the bed that is consist of alluvial gravel with a mean diameter size of $1\mathrm{.}8$ in$.$ If not, what should be the new width?