Final answer:
The deflection angle of a supersonic flow is typically calculated using oblique shock relations involving the initial Mach number, temperatures, pressures, and computational methods or lookup tables.
Step-by-step explanation:
To calculate the deflection angle of a supersonic flow expanding around a sharp corner, we utilize principles of gas dynamics, specifically the oblique shock relations. We have initial conditions with a Mach number M1 = 3.0, temperature T1 = 285 K, and pressure p1 = 1 atm. The pressure downstream of the corner is given as p2 = 0.1306 atm. To find the deflection angle, θ, we could use computational methods or look up the values in oblique shock tables based on the given pressures and Mach number.
However, without specific formulas or methods for solving oblique shocks provided in the question, we typically would use the pressure ratio and Mach number with the oblique shock wave relations or an applicable chart or table to derive the deflection angle. These relations often involve complex equations and are generally beyond the scope of a high school or introductory college physics class, which is why they are primarily dealt with in specialized engineering or aerodynamics courses within a college or university. In practice, advanced software or aerodynamics textbooks are used to assist with these calculations.