Q$2.$ A $2m$ circular sewer is laid at a slope of $0\mathrm{.}0007\frac{m}{m}.$ If $n=0\mathrm{.}013$ at all depths of flow, determine:

$($a$)Q$ and $V$ when sewer is flowing full

$($b$)q$ and $v$ when sewer is flowing at a depth of $0\mathrm{.}5m$

$($c$)q$ and $v$ when the flow in the sewer is at $0\mathrm{.}6$ of its capacity

$($d$)v$ and depth of flow when $q=1\frac{m^3}{s}$