$(25$ points$)$ An engineer decides to cut costs by creating a small wind tunnel that has a test

section diameter of $0\mathrm{.}05$ m $.$ The model $($not currently in the tert sectionl will he placed $0\mathrm{.}25$ m

from the entrance to the tert section. At the entrance to the test section the design conditions

are met $($Static prespure $=100$kPa, Static Temperature $=300k,$ Mach number $=3).$ Considering

Fanno flow only, and a constant friction factor of $0\mathrm{.}02$ determine

a$.$ The static temperature $($K$),$ static preswure $($IVa$),$ and Mach number where the model

wili be placed $($no shocks for this problem$).$

b$.$ The $\%$ error in the Mach number when it reaches the pobel $($no shocks$)$