Plot the following in the same figure and compare the results to each other. Assume that the incoming flow$$s static pressure and temperature are P$1=1$ atm, and T$1=298\mathrm{.}15$ K$,$ respectively. Use the calorically perfect gas assumption with $=1\mathrm{.}4.$

a$)$ Following the discussion in Section $4\mathrm{.}6,$ calculate and plot the pressure on a $5$ half angle cone in air using the small disturbance theory, for upstream Mach numbers $($M$1)4$ to $20$ with Mach $=1$ increments. This problem will require you to solve Equation $4\mathrm{.}106,$ using the appropriate boundary conditions.

b$)$ Following the discussion of Chapter $10$ of Anderson$$s $$Modern Compressible Flow$$ book, calculate and plot the pressure on a $5$ half angle cone in air using the inviscid exact theory, for upstream Mach numbers $($M$1)4$ to $20$ with Mach $=1$ increments. This will require you to solve Equation $10\mathrm{.}13$ with the appropriate boundary conditions.

Figure $11\mathrm{.}4$ I Schematic of the effect of grid size on

numerical error.