Mechanics of Fluids

oundaries, both of which are curved, each generates a family of Mach
waves. Flow conditions along a Mach wave of one family are affected by
those of the other family, and so where two families intersect the waves are
no longer straight (Fig. 11.20). A number of special graphical, tabular and
computational techniques have been developed for dealing with problems
of flow between curved boundaries, but these are beyond the scope of this
book.
11.7 THE PITOT TUBE IN COMPRESSIBLE FLOW
When a Pitot-static tube is used to determine the velocity of a constantdensity
fluid the stagnation pressure and static pressure need not be separately
measured: it is sufficient to measure their difference. A high-velocity
gas stream, however, may undergo an appreciable change of density in being
brought to rest at the front of the Pitot-static tube, and in these circumstances
stagnation and static pressures must be separately measured. Moreover, if
the flow is initially supersonic, a shock wave is formed ahead of the tube,
and so results for supersonic flow differ essentially from those for subsonic
flow. We first consider the Pitot-static tube in uniform subsonic flow.
The process by which the fluid is brought to rest at the nose of the tube is
assumed to be frictionless and adiabatic. From the energy equation (11.13)
and from eqn 11.6 we therefore obtain
u 2
2 = cp(T0 − T) = cpT0
� � � �
(γ −1)/γ
p
1 −
p0
The pitot tube in compressible flow 517
SF, I, PG (11.43)
Suffix 0 refers to stagnation conditions (see Fig. 11.21), and T0 and p0 are
referred to as the stagnation temperature and stagnation pressure respectively.
The terms total temperature and total pressure are also sometimes used.
If T0 and the ratio of static to stagnation pressure are known the velocity of
the stream may then be determined from eqn 11.43.
Fig. 11.20 Families of
Mach waves between
curved boundaries.
Fig. 11.21