$\backslash$#$6.$ Flow enters an insulated constant$-$area duct at Mach $0\mathrm{.}5,$ and static pressure and temperature of $100$ kPa and $1200$ K $,$ respectively. The duct has a diameter of $3$ cm and an average friction coefficient of $0\mathrm{.}003$ and length of $150$ cm $.$

a$)$ Determine the Exit Mach

b$)$ Determine the loss of stagnation pressure across duct due to friction added

c$)$ Re$-$evaluate flow neglecting all duct friction. Assume heat addition of $\backslash (\backslash$mathrm$\{$q$\}=0\mathrm{.}8\backslash$mathrm$\{$MJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$ Determine the exit Mach.

d$)$ Determine loss of stagnation pressure across duct due to heat addition from part c$)$