Air with K$=1\mathrm{.}4$K$=1\mathrm{.}4$ and R$=287$Nm$/$kg$*$ K$,$ R$=287$Nm$/$kg$*$K is discharged from a large reservoir through a nozzle. Upon exiting the nozzle, the gas enters a Fanno duct with L$/$D$=10,$ where L is the length of the duct and D is the duct's inner diameter. The conditions of the air inside the reservoir are $500$K and $600$kPa. The back pressure at the outlet of the Fanno duct generates a normal shock wave at a point where L$/$D$=4.$ The area where the shock wave occurs, A$1,$ is twice the area of the throat, A$0.$ The following is required:a$)$ The value of the back pressure in kPa;b$)$ The velocity of the gas after the normal shock in m$/$s;c$)$ The mass flow rate at the outlet of the Fanno duct in kg$/$s$$m$^2$;d$)$ The entropy increase of the gas due to the normal shock in kJ$/$kg$$K;e$)$ The entropy increase of the gas due to friction in the duct in kJ$/$kg$$K$.$