Page 300 - Aerodynamics for Engineering Students

282 Aerodynamics for Engineering Students

and hence

(6.24)
A*

If now the constant quantities m, PO, be eliminated from Eqns (6.22) and (6.24),
the area ratio becomes

and, substituting from Eqns (6.20) and (6.20a),

from Eqn (6. Ha), the expression reduces to

(6.25)

Fig. 6.2 shows this ratio plotted against Mach number over the range 0 < M < 4.

Example 6.3 Derive from first principles the following expression for the rate of change of
stream-tube area with Mach number in the isentropic flow of air, with y = 1.4.
dA 5A M2 - 1
-=--
dM MW+5
At the station where M = 1.4 the area of the stream tube is increased by 1%. Find the
corresponding change in pressure. (Lu)
From Eqn (6.25)

For y = 1.4

or
A (y)3

-=
A* M
Differentiating this expression with respect to M: