The Maximum Conditions

The maximum speed of sound is when the highest temperature is achieved. The maximum temperature that can be achieved is the stagnation temperature

$$U_{max} = \sqrt{{2 k \over k-1} R T_{0}}$$ (5.27)

The stagnation speed of sound is

$$c_{0} = \sqrt{kRT_0}$$ (5.28)

Based on this definition a new Mach number can be defined

$$M_0 = {U \over c_0}$$ (5.29)