Road A is located parallel to River S$,$ and it cuts one of its tributaries at point M as in Figure $1.$ A $50$ m long pipe culvert crossing is to be used to allow the passage of water below the pavement at pointM. The area is at Dunedin and the rainfall intensity $-$ duration$-$frequency results is in table $3.$a$.$ Given the runoff coefficient c$=0\mathrm{.}3,$ calculate the peak discharge $(*)$ for the culvert at M for flood with an Annual Recurrence Interval of $50$ years.b$.$The pavement is at RL$=58$ m and the minimum height of pavement above head water is $1$ m$.$Assuming the flow through the culvert $($headwall with socket end$)$ is based on inlet control, find the size of pipe culvert to be used. $($suggested trial sizes of $1\mathrm{.}2$ m$,1\mathrm{.}5$ m$,$ and $1\mathrm{.}8$ m$).$The inlet control monograph is in Figure $2.$c$.$ After exiting from the culvert, the water will flow along a $150$ m reinforced concrete drain before discharge into the River S$.$ The drain is $3$m wide and with a freeboard of $0\mathrm{.}2$m$,$ find the size of RC drain to be used, given that the Mannings coefficient n$=0\mathrm{.}013.$