Homework Problems $(20$ points maximum$)$

$(8$ pts$.)($i$)$ Determine the size of a circular vitrified clay pipe $(n=0\mathrm{.}012)$ to carry $110$ cfs sewage when it is running full. The sewer line is laid at $0\mathrm{.}5\%$ slope. $($ii$)$ Design a pipe $($diameter$)$ if we want the depth of water level at $60\%$ of the pipe diameter $($i$.$e$.\frac{y}{d_0}=0\mathrm{.}6)$ for the same flow.