Using $2$D$-$irrotational flow approximations, write a Method of Characteristics program to calculate the minimum$-$length nozzle for exit Mach number $=2\mathrm{.}4.$ Follow the discussions in Chapter $11$ of Anderson$$s $$Modern Compressible Flow$$ book. This problem$$s solution for exit Mach number $=2\mathrm{.}4$ is given in the book as Example $11\mathrm{.}1.$

Create a figure similar to what is shown in Figure $11\mathrm{.}4,$ and make a Table similar to the Table $11\mathrm{.}1.$ In your homework submission make sure to include your Method of Characteristics program.

Assume that the incoming flow$$s static pressure and temperature are P$1=1$ atm, and T$1=298\mathrm{.}15$ K$,$ respectively. Use calorically perfect gas assumption with $=1\mathrm{.}4.$ Figure $11\mathrm{.}4$ I Schematic of the effect of grid size on numerical error.