Page 302 - Aerodynamics for Engineering Students

284 Aerodynamics for Engineering Students

converted to kinetic energy of linear motion. It follows from the definition that this
state has zero pressure and zero temperature and thus is not practically attainable.
Again applying the energy Eqn (6.17) between reservoir and ultimate conditions

so the ultimate, or maximum possible, velocity

(6.27)

Expressing the velocity as a ratio of the ultimate velocity and introducing the
Mach number:
uz
-
--
C2
or

and substituting Eqn (6.20a) for T/To:

U 7-1 (6.28)
C 2+(y-l)M2

6.2.4 Variation of mass flow with pressure
Consider a converging tube (Fig. 6.3) exhausting a source of air at high stagnation
pressure po into a large receiver at some lower pressure. The mass flow induced in the
nozzle is given directly by the equation of continuity (Eqn (6.22)) in terms of pressure
ratio p/po and the area of exit of the tube A, i.e.

(7-1)l-Y
-- k) "'I [ 1 - k) ] (Eqn(6.22))
2ypopo
-
7-1

Low pressure
P

Fig. 6.3