$6\mathrm{.}4.$ On some high$-$speed aircraft an air$-$cycle refrigeration unit is used for cabin cooling, one concept of which is shown in Fig. $6-17.$ Equations available for the compressor are: power $=f_1(t_1,p_1,p_2,(m^{}))$ and $m^{}=f_2(t_1,p_1,,p_2).$ For the turbine the equations are: power $=f_3(t_3,p_3,(m^{}),p_4)$ and $m^{}=f_4(t_3,p_3,,p_4)$ where $f()$ indicates a function or equation in terms of the variables in the parentheses. Assume no pressure drop through the heat exchanger. The compressor$-$turbine combination operates when $p_1$ is greater than $p_4.$ The following data are imposed and known: $p_1,t_1,p_4,$ the UA of the heat exchanger, and the temperature and flow rate of ambient air through the heat exchanger. Construct an information$-$flow diagram to simulate the system using the equations and variables previously listed as well as others that are necessary.

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