$($a$)$ Caiculate the discharge for a flow depth of $0\mathrm{.}85$ m in a trapezoldal open channel with bottom width $1$ m and side slopes of $1$ vertical: $2$ horizontal. The bed slope is $0\mathrm{.}5\frac{m}{100}m$ and Manning's n value is $0\mathrm{.}035.(5$ marks$)$