A $0\mathrm{.}4$ m high conical plug valve is used to regulate an air flow from a pipe. The air leaves the end of the cone through a section of thickness of $0\mathrm{.}02$ m with a density of $1\mathrm{.}23$ kg$/$m$3.$ If the viscous effects are negligible, and the volumetric flow is $0\mathrm{.}5$ m$3/$s$.$ For air: Cp $=1004$ J$/$kgK$.$ R $=286\mathrm{.}9$ J$/$kgK$,$ consider diatomic air.

Determine.

A$)$ The outlet pressur $($kPa$)$

B$)$ Mach's number at the exit

C$)$ The flow regime at the exit