$8\mathrm{.}17.$ A vane axial fan is characterized by $D=0\mathrm{.}80m,d=0\mathrm{.}49m,$ and $N=1400rpm.$ The performance of the fan is $Q=5\mathrm{.}75\frac{m^3}{s},p_T=750$ Pa $,$ with $=1\mathrm{.}215k\frac{g}{m^3}$ and ${}_T=0\mathrm{.}85.$ Select cascade variables to define the geometry for the blades and vanes. Allow the local diffusion factors, $D_L,$ at hub, mean, and tip station to be $0\mathrm{.}60,0\mathrm{.}45,$ and $0\mathrm{.}30,$ respectively, for the blades and vanes.

a$.$ Choose blade and vane solidity distributions that can satisfy these $D_L$ constraints.

b$.$ Assume that the blades and vanes are very thin. With the solidities and flow angles determined, calculate deviation, camber, and incidence and stagger angles for the blade at hub, mean, and tip stations.

c$.$ Repeat $($b$)$ for the vane row.