Page 314 - Aerodynamics for Engineering Students

296 Aerodynamics for Engineering Students

(a) Stationary wave

( b ) Moving wave

Fig. 6.6
and
au lap
u-=-- (6.32)
ax pax
Eliminating du/ax from these equations leaves

(6.33)

This implies the speed of flow in the stream tube that is required to maintain
a stationary pulse of weak strength, is uniquely the speed given by ,,/= (see
Section 1.2.7, Eqn (1.6~)).
The problem is essentially unaltered if the pulse advances at speed u = z/apiap
through stationary gas and, since this is the (ideal) model of the propagation of weak
pressure disturbances that are commonly sensed as sounds, the unique speed dm
is referred to as the acoustic speed a. When the pressure density relation is isentropic
(as assumed above) this velocity becomes (see Eqn (1.6d))

(6.34)

It will be recalled that this is the speed the gas attains in the throat of a choked
stream tube and it follows that weak pressure disturbances will not propagate
upstream into a flow where the velocity is greater than a, i.e. u > a or A4 > 1.

119.1 Onedimensional flow: plane normal
shook waves

In the previous section the behaviour of gas when acting as a transmitter of waves of
infinitesimal amplitude was considered and the waves were shown to travel at an
(acoustic) speed of a = d= relative to the gas, while the gas properties of
pressure, density etc. varied in a continuous manner.