Fanno Flow Short 4fL/D

Figure (9.12) shows different pressure profiles for different back pressures. Before the flow reaches critical point a (in the Figure) the flow is subsonic. Up to this stage the nozzle feeding the tube increases the mass flow rate (with decreasing back pressure). 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 than point b the supersonic reaches to the tube. Note however that exit Mach number, $M_2 < 1$ 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 shock^9.13. The back pressure below point $c$ has some adjustment as it occurs with exceptions of point $d$ .

Figure 9.13: The effects of pressure variations on Mach number profile