Show me the steps to solve this problem.a$)$ Use the Rational Method to estimate the peak flows$($Q peak in pipes A$,$B$,$C$.$

Assume that the $5-$ears return period duration relationship is i$=2700/$t$+15$ where I is the rainfall intensity in mm$/$hr and t is the rainfall duration in minutes. The inlet time may be calculated using the following correlation: t$=0\mathrm{.}0192$ L$0\mathrm{.}77/$S$0\mathrm{.}385$ where L is the overland travel distance $($m$),$ S is the average slope of tributary are$($m$/$m$)$ and t is the inlet time$($minutes$).$Assume that the pipe flow time is $2$minutes for each pipe.

b$)$ Perform a preliminary design for the pipes A$,$B and C$.$ Determine the pipe internal diameters and the slopes only. Length of Pipe A $=90$m $,$and Ground slope in the direction of flow $=0\mathrm{.}0035($m$/$m$).$ Length of Pipe B $=85$m $,$and Ground slope in the direction of flow $=0\mathrm{.}0025($m$/$m$).$ Length of Pipe C $=100$m $,$and Ground slope in the direction of flow $=0\mathrm{.}0027($m$/$m$).$Do not evaluate cover or invert elevations.

Use reinforced concrete pipes with a manning$$s roughness nf$=0\mathrm{.}015$ at full flow.

Design criteria:

$$ minimum velocity at design flow$=0\mathrm{.}75$m$/$s

$$ maximum velocity at design flow$=3\mathrm{.}5$m$/$s

$$ design pipes to flow approximately full at peak flow

$$ concrete pipes with the following diameters $($mm$)$ are available:$310,380,460,530,610,690,760,840,910,1070,1220,1370,1520,1680,1830,1980,2130,2290,2440,2590,2470,2900$