Page 198 - 48Fundamentals of Compressible Fluid Mechanics

160 CHAPTER 9. FANNO FLOW

If the feeding nozzle is a “diverging-converging” then it is has to be dif-
is short or equal to
that associate with
ferentiated between two cases; One case is where the W`XaZ [
entrance Mach number.
the critical length. The critical length is the maximum W`XaZ [

IJLKM IONIQPSR/M
a shock in TUM PSJWVYX Z[/\]D^ _ b `a
the nozzle
fully subsoinic !"$#%'&)(+* ,-/.
01 2 5 34

flow

{

critical Point a 687:9<; =+> ?@/ABDC E H FG
criticalPoint b critical Point c

Fig. 9.12: The pressure distribution as a function of for a long

9.7.2.2 Short W`XaZ [

Figure 9.12 shows different of pressure profiles for different back pressures. before
the flow reach critical point a (in the figure) the flow is subsonic. Up to this stage
the nozzle feeds the tube increases the mass flow rate (with decreasing back pres-
sure). Between point a and point b the shock is in the nozzle. In this range and
further reduction of the pressure the mass flow rate is constant no matter how low
the back pressure is reduced. Once the back pressure is less the point b the su-
personic reaches to the tube. Note however that exit Mach number, N I and is
not 1. A back pressure that is at the critical point c results in a shock wave that
is at the exit. When the back pressure is below point c, the tube is “clean” of any