Mechanics of Fluids

550 Compressible flow of gases
Fig. 11.32 Mach–Zehnder
interferometer.
each other, making the screen uniformly bright. The beam through the test
section may be retarded by an increase of density there; if this is sufficient
to put the beams out of phase by half a wavelength (or an odd multiple of
half a wavelength), so that the crests of waves in one beam coincide with
troughs in the other, the screen is uniformly dark. Lines of maximum and
minimum brightness therefore represent contours of constant density, and
the density increment between successive contours corresponds to a phase
shift of half a wavelength. Alternatively, the splitter plates P1 and P2 may be
slightly rotated from the position that gives uniform brightness of the screen
at no-flow conditions to one that gives a series of interference fringes parallel
to the axes of rotation. Non-uniform density in the test section then causes
local distortion of these otherwise equally spaced fringes, and measurement
of the fringe displacement permits calculation of the density at that point
relative to the density in an undisturbed part of the flow.
The interferometer is costly and demands very high accuracy of the
optical components and vibration-absorbing supports. It does, however,
yield quantitative information about the density throughout the flow, and
not just where the density changes rapidly.
In association with a heated wire shedding a filament of warmer, less
dense, gas these optical methods may also be used to indicate a filament line
in gas flow otherwise at constant density.
PROBLEMS
(For air take γ = 1.4, R = 287 J · kg −1 · K −1 , cp = 1005 J · kg −1 · K −1 .
All pressures quoted are absolute.)
11.1 Atmospheric air at 101.3 kPa and 15 ◦ C is accelerated isentropically.
What are its velocity and density when the Mach
number becomes 1.0 and what is the maximum velocity theoretically
obtainable? Why could this maximum not be achieved
in practice?
11.2 Air flows isentropically from atmosphere (pressure 101.5 kPa
and temperature 15 ◦ C) to a 600 mm square duct where the
Mach number is 1.6. Calculate the static pressure, the velocity