expansion of idea of compression is show often the solution
Answers
Explanation:
Pasquale M. Sforza, in Theory of Aerospace Propulsion, 2012
6.13 Hypersonic Flight Considerations
The compression processes discussed in this section are of particular importance as flight Mach numbers in the hypersonic regime, approximately M0 > 5, are considered by Segal (2009). At such flight conditions, high temperatures begin to be encountered as may be inferred from the equation for the free stream stagnation temperature:
Tto=T0(1+γ−12M02).
If M0 = 5, then with γ = 1.4 and the temperature in the stratosphere T0 = 216K, the stagnation temperature Tt0 ∼1300K or over 1000°C. At M0 = 10, the stagnation temperature would appear to be about 4500K! Of course, under increasingly high temperature, the air would dissociate and thermodynamic properties such as γ and cp would vary with the temperature. As a consequence, it is more convenient to avoid the complications due to chemistry and instead examine inlet performance on an enthalpy–entropy plot, as shown in Figure 6.31. The free stream stagnation enthalpy ht0 is constant for an adiabatic process, expressing the balance between internal and kinetic energy as follows:
ht0=h0+12V02.
The real inlet brings the total pressure from the free stream value of pt0 to a value of pt2 at the end of the inlet, but this is at the expense of an entropy increase due to the irreversibility of the shock wave system employed in decelerating the flow. An ideal inlet would act isentropically, leaving the total pressure unchanged. Using Figure 6.38, the inlet kinetic energy efficiency may be defined as follows:

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