Unless otherwise noted, use c$\_($p$)=1005($J$)/($k$)$g$-$K$,$R$=287($J$)/($k$)$g$-$K$,$ and $\backslash$gamma $=1\mathrm{.}4.$

$[40$ pts$.]$ A single stage axial flow compressor is to be designed with mean radius conditions:

$\backslash$alpha $\_(1)=20\backslash$deg $,($c$\_($z$))/($U$)=0\mathrm{.}55,$c$\_($z$1)=$c$\_($z$2)=150($m$)/($s$)$

p$\_(01)=101325$Pa$,$T$\_(01)=288\mathrm{.}15$K

aU$.$

bc$\_(\backslash$theta $1).$

cc$\_(1).$

dw$\_(\backslash$theta $1).$

ew$\_(1).$

f$\backslash$beta $\_(1).$

gc$\_(\backslash$theta $2),$ if the design total pressure ratio $($p$\_(02))/($p$\_(01))=1\mathrm{.}50$

and the adiabatic stage efficiency $\backslash$eta $\_($st$)=0\mathrm{.}90.$

hc$\_(2).$

iw$\_(\backslash$theta $2).$

jw$\_(2).$

k$\backslash$alpha $\_(2).$

Calculate the outlet relative flow angle, $\backslash$beta $\_(2).$

m$($U$,$c$\_($z$),$c$\_(1),$c$\_(\backslash$theta $1),$w$\_(1),$w$\_(\backslash$theta $1),$c$\_(2),$c$\_(\backslash$theta $2),$w$\_(2),$w$\_(\backslash$theta $2),\backslash$alpha $\_(1),\backslash$beta $\_(1),\backslash$alpha $\_(2),\backslash$beta $\_(2))$

nT$\_(02)$ and outlet total pressure, P$\_(02).$

oT$\_(1),$T$\_(2).$

pp$\_(1),$p$\_(2).$

q$\backslash$rho $\_(1),\backslash$rho $\_(2).$

r$\backslash$Delta $($h$\_(0))/($U$^(2)).$

sC$\_($p$)=($p$\_(2)-$p$\_(1))/(0\mathrm{.}5\backslash$rho $\_(1)$w$\_(1)^(2)).$ Note that p$\_(1)$

and p$\_(2)$ are static pressures. Is separation of the rotor likely?

tR$.$