$(15$ pts$)$ A earthen trapezoidal canal with a $2-$foot bottom width, $1\mathrm{.}5H$:$1V$ sideslopes, Manning's n of $0\mathrm{.}027,$ and a slope of $\mathrm{.}0018f\frac{t}{f}t$ conveys $30f\frac{t}{s}.$ A portion of the canal is proposed to be piped with PVC pipe with a Manning's n of $0\mathrm{.}011.$ The PVC pipe inside diameters is only available in $0\mathrm{.}5$ foot increments $(2\text{'},{2\mathrm{.}5}^{\text{'}},3^{\text{'}},$ etc.$).$ In order to maintain the same flow depth in the canal upstream and prevent varied flow, the new piped section must have a flow depth approximately the same as the existing trapezoidal canal section. What pipe diameter would be required?