Air is drawn through Laval nozzle which passes through section $1,30$ mm diameter with a speed of $70$ m$/$s$,$ while it has an absolute temperature and pressure of $300$ K and $300$ kPa respectively. The sonic flow is produced at the nozzle throat and supersonic flow is occur at section $2,$ where the diameter is $23$ mm$.$ Determine the Mach number at section $1,$ the required area of the throat to produce sonic flow, and the Mach number, temperature, pressure and velocity at section $2.$ Given gas constant $287$ J$/$kg$.$K and specific heat ratio $1\mathrm{.}4$ for air.