The Pressure Ratio, P2/P1, effects

In this section the studied parameter is the variation of the back pressure and thus, the pressure ratio $P_2 \over P_1$ variations. For very low pressure ratio the flow can be assumed as incompressible with exit Mach number smaller than $<0.3$ . As the pressure ratio increases (smaller back pressure, $P_2$ ), the exit and entrance Mach numbers increase. According to Fanno model the value of $\frac{4fL}{D}$ is constant (friction factor, $f$ , is independent of the parameters such as, Mach number, Reynolds number et cetera) thus the flow remains on the same Fanno line. For cases where the supply come from a reservoir with a constant pressure, the entrance pressure decreases as well because of the increase in the entrance Mach number (velocity).

Again a differentiation of the feeding is important to point out. If the feeding nozzle is converging than the flow will be only subsonic. If the nozzle is ``converging-diverging'' than in some part supersonic flow is possible. At first the converging nozzle is presented and later the converging-diverging nozzle is explained.

Figure: The pressure distribution as a function of 4fL/D for a short 4fL/D