A river flows in a $10$m wide rectangular cement channel. Velocity is observed to double in a constriction caused by a bridge $($water level stays the same$).$ During a flood condition, the depth of water upstream of the bridge is measured to be $2$m$,$ and the velocity is estimated to be $1\mathrm{.}5$ m$/$s$.$ What is $($a$)$ the width of the channel at the bridge; $($b$)$ the volume flow rate of water through the bridge $($in m$3/$s$)$ during the flood and $($c$)$ the velocity of flow at the bridge during flood conditions? Assume that the upstream and bridge water depth are the same $($Not necessarily completely true, but a good first assumption$).$