Page 85 - Mechanical Engineers' Handbook (Volume 4)

74 Fluid Mechanics

Figure 26 Mach numbers across a normal
shock, k 1.4.

1
y k 1 p y p y k 1
x k 1 p x p x k 1
and is plotted in Fig. 27, which shows that weak shocks are nearly isentropic, and that the
density ratio approaches a limit of 6 for gases with k 1.4.
Gas tables show that at an upstream Mach number of 2 for air, M 0.577, the pressure
y
ratio is p /p 4.50, the density ratio is / 2.66, the temperature ratio is T /T 1.68,
x
y
y
x
x
y
and the stagnation pressure ratio is p /p 0x 0.72, which indicates an entropy increase of
0y
s s R ln(p /p ) 94 J/kg.
y
0y
x
0x
10.4 Oblique Shocks
Oblique shocks are inclined from a direction normal to the approaching streamlines. Figure
28 shows that the normal velocity components are related by the normal shock relations.
From a momentum analysis, the tangential velocity components are unchanged through

Figure 27 Rankine–Hugoniot curve, k 1.4.