Long 4fL/D

In the case of $\frac{4fL}{D} > \left.\frac{4fL}{D}\right\vert _{max}$ reduction of the back pressure results in the same process as explained in the short $\frac{4fL}{D}$ up to point $c$ . However, point c in this case is different from point c at the case of short tube $\frac{4fL}{D} < \left.\frac{4fL}{D}\right\vert _{max}$ . In this point the exit Mach number is equal to 1 and the flow is double shock. Further reduction of the back pressure at this stage will not ``move'' the shock wave downstream the nozzle. At point c or location of the shock wave, is a function entrance Mach number, $M_1$ and the ``extra'' $\frac{4fL}{D}$ . The is no analytical solution for the location of this point c. The procedure is (will be) presented in later stage.

Figure: Mach number as a function of 4fL/D (total 4fL/D=0.3)