$4\mathrm{.}17$ A turbojet engine has the following parameters at

the on$-$design operating point:

$M_0=0,p_0=p_{STD},T_0=T_{STD},=1\mathrm{.}4,c_p=1\mathrm{.}004k\frac{J}{k}g*K$

${}_d=0\mathrm{.}99$

${}_c=30,e_c=0\mathrm{.}9$

${}_x=6\mathrm{.}0,{}_b=0\mathrm{.}98,{}_b=0\mathrm{.}95,$ and $Q_R=42,800k\frac{J}{k}g$

$e_t=0\mathrm{.}90,{}_m=0\mathrm{.}95$

${}_n=0\mathrm{.}98$ and$\frac{p_9}{p_0}=1\mathrm{.}0$

Calculate

$($a$)p_{t3}$ and ${}_c$

$($b$)$ fuel$-$to$-$air ratio $f$ and $p_{t4}$

$($c$){}_t$

Now for the following off$-$design condition:

$M_0=0\mathrm{.}85$ at $20km$ U$.$S$.$ standard altitude and throttle ratio,

$T_{t4}=0\mathrm{.}9T_{t4-\text{d}\text{e}\text{s}\text{i}\text{g}\text{n}},$ assuming that ${}_t$ remains constant

between on$-$design and off$-$design, calculate

$($d$)$ compressor pressure ratio at the off$-$design opera$-$

tion