$5\mathrm{.}19.$ A pitot$-$static tube is placed in a supersonic llow in which the static pressure

and temperature are $60$ kPa and $-20C$ respectively. The difference between the

pitot and static pressures is measured and found to be $449$ kPa $.$ Find the Mach number and velocity in the flow. Discuss the assumptions used in deriving the answers.