Page 312 - Aerodynamics for Engineering Students

294 Aerodynamics for Engineering Students

Therefore:
473
Temperature in test section = - = 210 K = -63 "C
2.25
Density in test section = 123 Oo0 = 2.042 kgmP3
287.3 x 210

Speed of sound in test section = (1.4 x 287.1 x 210)f = 293ms-l

Air speed in test section = 2.5 x 293 = 732 m s-'

Using the approximation given in Section 1.4.2 (Example 1.3) for the variation of viscosity
with temperature

p = 1.71 x - = 1.50 x kgm-ls-'
(:::)3'4
p 1.50 x loP5
v=-= = 0.735 x lo-' m2s-'
p 2.042
As a check, the mass flow may be calculated from the above results. This gives

Mass flow = pvA = 2.042 x 732 x 15625 x
= 23.4 kg S-'

6.3 One-dimensional flow: weak waves

To a certain extent the results of this section have already been assumed in that
certain expressions for the speed of sound propagation have been used. Pressure
disturbances in gaseous and other media are propagated in longitudinal waves and
appeal is made to elementary physics for an understanding of the phenomenon.
Consider the air in a stream tube to be initially at rest and, as a simplification,
divided into layers 1, 2, 3, etc., normal to the possible direction of motion. A small
pressure impulse felt on the face of the first layer moves the layer towards the right
and it acquires a kinetic energy of uniform motion in so doing. At the same time,
since layers 1, 2, 3 have inertia, layer 1 converts some kinetic energy of translational
motion into molecular kinetic energy associated with heat, i.e. it becomes com-
pressed. Eventually all the relative motion between layers 1 and 2 is absorbed in
the pressure inequality between them and, in order to ease the pressure difference, the
first layer acquires motion in the reverse direction. At the same time the second layer
acquires kinetic energy due to motion from left to right and proceeds to react on layer
3 in a like manner. In the expansive condition, again due to its inertia, it moves
beyond the position it previously occupied. The necessary kinetic energy is acquired
from internal conditions so that its pressure falls below the original. Reversion to the
status quo demands that the kinetic energy of motion to the left be transferred back to
the conditions of pressure and temperature obtaining before the impulse was felt,
with the fluid at rest and not displaced relative to its surroundings.
A first observation of this sequence of events is that the gas has no resultant mean
displacement velocity or pressure different from that of the initial conditions, and it
serves only to transmit the pressure pulse throughout its length. Secondly, the