The Solid Rocket Boosters $($SRB$)$ on the space shuttle were the most powerful solid$-$propellant rockets ever flown, used to augment the thrust produced by the Space Shuttle Main Engine $($SSME$).$ The nozzles attached to the SRB had an exit$-$to$-$throat area ratio of $7\mathrm{.}5,$ and a throat diameter of $1\mathrm{.}37$ m $.$ The combustion of atomized aluminium with ammonium perchlorate produced a combustion chamber pressure of $6\mathrm{.}3$ MPa and temperature of $\backslash (\backslash$mathrm$\{$T$\}=3500\backslash$mathrm$\{$~K$\}\backslash ).$ For the purposes of this question, assume that the ratio of specific heats can be approximated as $\backslash (\backslash$gamma$=1\mathrm{.}26\backslash ),$ and the gas constant $\backslash ($ R$=0\mathrm{.}219\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}.\backslash$mathrm$\{$K$\}\backslash ).$

a$)$ Calculate the mass flow through the nozzle of an SRB$,$ using the above values.

b$)$ Calculate the Mach number and velocity of the flow at exit.

c$)$ Calculate the pressure at exit. Is this flow ideally expanded, underexpanded, or overexpanded?