problems

$5\mathrm{.}1$ The ideal ramjet engine shown in Fig. P$5\mathrm{.}1$ can be modeled as a turbojet with a compressor pressure ratio of $1.$ For an ideal ramjet engine, do the following:

a$)$ Show that $M_9=M_0.$

b$)$ Develop an expression for specific thrust in terms of ${}_{},{}_r,a_0,M_0,$ and $gc.$

c$)$ Starting with an energy balance of the combustion, show that the fuel$/$air ratio is given by

$f=\frac{c_p{T}_0}{h_{PR}}({}_{}-{}_r)$

d$)$ Once the inlet flow is supersonic, the exit nozzle of the ideal ramjet is choked and $M_8$ is $1.$ Using the mass flow parameter at station $8,$ calculate the variation in $\frac{F}{A_8}$ with flight Mach number at the following conditions:

$T_{t4}=2000K,$ Alt $=15km,=1\mathrm{.}4$

$c_p=1\mathrm{.}004k\frac{J}{kg*K},M_0=2to6$

Fig. P$5\mathrm{.}1$ Ideal ramjet.