Determine the discharge, to the nearest $\backslash (0\mathrm{.}1\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ of a $\backslash (42\mathrm{.}4-\backslash$mathrm$\{$m$\}\backslash )$ long, circular culvert having a projecting inlet. The diameter is $431$ mm $.$ The Manning roughness coefficient is $0\mathrm{.}011.$ The inlet invert elevation is $46\mathrm{.}75$ and the outlet invert elevation is $43\mathrm{.}28.$ The headwater elevation is $50\mathrm{.}52$ and the tailwater elevation is $40\mathrm{.}15.$