$8\mathrm{.}28$ A simple method to establish the annulus geometry

in a multistage compressor is to assume a constant through$-$

flow $($i$.$e$.,$ axial$)$ speed $Cz.$ Calculate

$($a$)$ the density ratio $\frac{{}_3}{{}_2}$

$($b$)$ the exit$-$to$-$inlet area ratio $\frac{A_3}{A_2}$

FIGUREP$8\mathrm{.}28$

for

${}_c=35$

$e_c=0\mathrm{.}90$

$C_z=$ constant

$=1\mathrm{.}4,c_p=1,004\frac{J}{k}g*K$

Also, if the hub radius is constant and for a mass flow

rate of $100k\frac{g}{s}$ and the inlet total pressure of $p_{t2}=100$kPa,

calculate the tip$-$to$-$tip radius ratio $(\frac{r_3}{r_2}{)}_{\text{t}\text{i}\text{p}}$