PROBLEM $1$:

Consider a steady$-$state compressor with an inlet pressure of $15$ lbf$/$in$2$ and

inlet volumetric flow rate of $10$ ft$3/$s$.$ Assuming that the air undergoes a

polytropic process Pv$1\mathrm{.}5=$const, determine the diameter $($inches$)$ of the exit

pipe for an exit pressure of $160$ lbf$/$in$2$ and exit velocity of $255$ ft$/$s$.$