Page 432 - Introduction to Continuum Mechanics

416 One-Dimensional Flow of a Compressible Fluid

Fig. 6.16

The pressurep given by Eq. (6.29.8) is known as the critical pressure/? . The pressure/? at
2« C £*
section (2) can never be less than/? (which depends only on/? ) because otherwise the flow
will become supersonic at section (2) which is impossible in view of the conclusion reached
earlier that to have M = 1, dA must be zero, and to have M> 1, dA must be increasing(diver-
gent nozzle). Thus, for the case of a convergent nozzle, p can never be less that/?, the
2 K
pressure surrounding the exit jet. When p > p , p - p , and when/? < p , p^ - p . In
A C 2 / \ R. C *" C
other words, the relation between dm /dt and/? //? is given as, for p D^p
R 1 K c

Figure 6.17 shows this relationship.
(ii) Flow in a Convergent-Diverging Nozzle
For a compressible fluid from a large supply tank, in order to increase the speed, a
converging nozzle is needed. From (i), we have seen that the maximum attainable Mach
number is unity in a converging passage. We have also concluded at the beginning of this
section that in order to have the Mach number larger than unity, the cross-sectional area must
increase in the direction of flow. Thus, in order to make supersonic flow possible from a supply