A supersonic nozzle possessing an area ratio $($exit to throat$)$ of $3\mathrm{.}0$ is supplied from a large reservoir and is allowed to exhaust to atmospheric pressure $(101$ kPa$).$ Determine the range of reservoir pressures over which a normal shock will appear in the nozzle. For what value of reservoir pressure will the nozzle be perfectly expanded, with supersonic flow at the exit plane? Find the minimum reservoir pressure to produce sonic flow at the nozzlethroat. Assume isentropic flow except for shocks, with y $=1\mathrm{.}4.$