For a certain design, an unlined rectangular wide channel that has a width

of $15$ ft$,$ 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?