Partially$-$Full Pipe Design

As discussed in class, Manning's equation $($using US Customary Units$)$ for a circular pipe flowing completely full can be rewritten in terms of the diameter $D$ as shown below.

$Q=\frac{0\mathrm{.}463}{n}{D}^{\frac{8}{3}}{S}^{\frac{1}{2}}$

Where $Q$ is the flowrate $(f\frac{t^3}{s}),n$ is Manning's Roughness Coefficient, $D$ is the pipe diameter $(ft),$ and $S$ is the slope of the energy grade line. Using the equation provided above and the attached hydraulic elements chart determine the following:

a$)$ For a pipe made of concrete