A $3\mathrm{.}5-$ft diameter concrete pipe $(n=0\mathrm{.}015)$ and longitudinal slope $=0\mathrm{.}0025$ will be used to transport treated sanitary water. Gravitational acceleration is $32\mathrm{.}2\frac{f}{s^2}.$ Design water depth $=0\mathrm{.}75$ times the pipe diameter. Determine $($show all equations and computations$)$:

Water depth $(Y)$ and How dischange $(Q)$ for the required design water depth.

Top width $($T$)$ of the water surface at design water depth.

Hydranlic depth $($D$)$ and hydraulic radius $($R$4)$ at design water depth.

Average velocity $($V$)$ and Froude number $($Fr$)$ at design water depth.

State of the flow in the pipe at design water depth.

Critical depth $($Yc$)$ for the flow discharge already computed in this problem.

Verify if pipe meets requirements : $V_{-2}=2fts($deposition$)$ and $V_{me}=10\frac{f}{s}($erosion$).$

Based on your results decide and explain your answer to justify if the pipe is appropriate for the proposed sanitary system.