$(25$ pts$)$ Catchments $1$ and $2$ are the most upstream areas contributing to a storm water collection

system and both enter the inlet to Pipe $1$ as shown. Determine:

a$)$ The design flow rate for Pipe $1$ and its diameter if local regulations specify that all subsurface

pipes must be sized to just fill at runoff generated by the $10-$year return period rainfall, The

pipe is concrete $(n=0\mathrm{.}013)$ and its slope is $0\mathrm{.}5\%.(20$ pts