$3.$ Consider a turbofan engine flying at a Mach number of $0\mathrm{.}85$ with ambient pressure of $0\mathrm{.}6$ atmosphere and ambient temperature of $\backslash (430^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash ).$ The intake has $\mathrm{.}95$ polytropic efficiency. The air divides with a bypass ratio of $9$ into a primary and a secondary $($or bypass$)$ flow at the air intake exit. The primary flow passes through a fan and compressor with an overall pressure ratio of $22$ and polytropic efficiency of $\mathrm{.}92$ while the secondary flow passes through a fan with pressure ratio of four and efficiency of $95.$

The primary flow burns at constant pressure with liquid kerosene fuel $($heating value $\backslash (=\backslash )\backslash (20,000\backslash$mathrm$\{$Btu$\}/\backslash$mathrm$\{$lbm$\}\backslash ))$ with a final combustor temperature of $\backslash (2500^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash )$ and then expands through a turbine and ultimately through the primary nozzle to ambient pressure. Burner efficiency is $\mathrm{.}98$ while the polytropic efficiencies of the turbine and the nozzle are each $95.$ All work taken from the turbine flow is employed to drive the fan and compressor. The secondary flow expands isentropically to ambient pressure through a secondary nozzle. $\backslash (\backslash$mathrm$\{$cp$\}=0\mathrm{.}24\backslash$mathrm$\{$Btu$\}/1\backslash$mathrm$\{$bm$\}^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash )$ for air; $\backslash (\backslash$mathrm$\{$cp$\}=0\mathrm{.}31\backslash$mathrm$\{$Btu$\}/1\backslash$mathrm$\{$bm$\}^\{\backslash$circ$\}\backslash$mathrm$\{$R$\}\backslash )$ for products; $\backslash (\backslash$gamma$=1\mathrm{.}4\backslash )$ for air; $\backslash (\backslash$gamma $\backslash )\backslash (=1\mathrm{.}25\backslash )$ for products.

a$)$ Calculate the stagnation temperature of the secondary flow at the fan exit.

b$)$ Calculate the stagnation temperature of the primary flow at the compressor exit.

c$)$ What is the temperature at the turbine exit?

d$)$ Calculate the exit jet velocity for the primary flow.

e$)$ Calculate the bypass exit jet velocity.

d$)$ Calculate the thrust and the thrust specific fuel consumption.