$4.$ Air flows through a converging$-$diverging nozzle, with $\backslash ($ A $\backslash$mathrm$\{$e$\}/$ A $\backslash$mathrm$\{$t$\}=3\mathrm{.}5\backslash )$ where $\backslash ($ A $\backslash$mathrm$\{$t$\}=500\backslash$mathrm$\{$~mm$\}^\{2\}\backslash ).$ The upstream stagnation conditions are atmospheric; the back pressure is maintained by a vacuum system. Determine the range of back pressures for which a normal shock will occur within the $/$l nozzle and the corresponding mass flow rate.