Compressible Flow Free Textbook

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Informal Model

Accepting the fact that the shock is adiabatic or nearly adiabatic requires that total energy is conserved, T_0x = T_0y. The relationship between the temperature and the stagnation temperature provides the relationship of the temperature for both sides of the shock.

$\displaystyle {T_y \over T_x} = {{T_y \over {T_0}_y} \over {T_x \over {T_0}_x} } = { {1 + {k-1 \over 2} {M_x}^{2} } \over {1 + {k-1 \over 2} {M_y}^{2} }}$

(5.7)

All the other relationships are essentially derived from this equation. The only issue left to derive is the relationship between M_x and M_y. Note that the Mach number is a function of temperature, and thus for known M_x all the other quantities can be determined, at least, numerically. The analytical solution is discussed in the next section.

Next: Formal Model Up: Solution of the Governing Previous: Solution of the Governing Index

Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21