Page 296 - Aerodynamics for Engineering Students

278 Aerodynamics for Engineering Students

The last of these equations, on taking account of the various ways in which the
acoustic speed can be expressed in isentropic flow (see Eqn (1.6cYd)), i.e.
= 4-
a = E = = u/~;

may be rewritten in several forms for one-dimensional isentropic flow:

or
u:
a: - 4 a;
-+---+- (6.17)
2 7-1 2 (7-1) i
or

6.2.1 Pressure, density and temperature ratios
along a streamline in isentropic flow
Occasionally, a further manipulation of Eqn (6.17) is of more use. Rearrangement
gives successively

since it follows from the relationship (6.1) for isentropic processes that
PlIP2 = (Pl/P2>Y.
Finally, with a; = (7p2/p2) this equation can be rearranged to give,

(6.18)

If conditions 1 refer to stagnation or reservoir conditions, u1 = 0, p1 =PO, the
pressure ratio is

(6.18a)

where the quantity without suffix refers to any point in the flow. This ratio is plotted
on Fig. 6.2 over the Mach number range 0-4. More particularly, taking the ratio
between the pressure in the reservoir and the throat, where M = M* = 1,

Po + 1 d(Y-1)
= 1.89 for air flow
P* -=[TI (6.18b)