$1.$ Suppose we had two parallel flows mimicking the primary and secondary exhaust flows from a turbofan engine. One flow has a stagnation temperature of $\backslash (1100^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash )$ and the other at $\backslash (2700^\{\backslash$circ$\}\backslash )$ R$.$ Each flow had a stagnation pressure of five atmospheres, a value of $\backslash (\backslash$gamma$=\backslash )1\mathrm{.}4,$ and a value of $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$mathrm$\{$p$\}\}=\mathrm{.}33\backslash$mathrm$\{$Btu$\}/1\backslash$mathrm$\{$bm$\}^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash ).$ The colder flow has five times the mass flow of the hotter flow. Calculate the ratio of total thrust to total mass flow from nozzle expansion in each of the following two cases.

a$)$ The flows are mixed adiabatically at constant pressure and then expanded to ambient pressure of $0\mathrm{.}7$ atmosphere in one nozzle.

b$)$ Each flow is expanded to the $0\mathrm{.}7$ atmosphere ambient pressure through a separate nozzle.