Page 299 - Aerodynamics for Engineering Students

Compressible flow 281

with the data given,

P - 1 - 7Mk = 0.314
=
Pm
and Eqn (i) gives

M2 = 2.635 giving M = 1.63

6.2.2 The ratio of areas at different sections of the stream tube
in isentropic flow
It is necessary to introduce the mass flow (riz) and the equation of continuity, Eqn
(6.14). Thus riz = puA for the general section, i.e. without suffix. Introducing again
the reservoir or stagnation conditions and using Eqn (6.1):

(6.21)

Now the energy equation (6.17) gives the pressure ratio (6.18) above, which when
referred to the appropriate sections of flow is rearranged to

Substituting d5 a0 and introducing both into Eqn (6.21), the equation of
for
continuity gives

(6.22)

Now, if the general section be taken to be the particular section at the throat,
where in general usage conditions are identified by an asterisk e), the equation of
continuity (6.22) becomes

(6.23)

But from Eqn (6.18b) the ratio p*/po has the explicit value

p* + 1 -7/(7-1)
Po -= [TI