Supersonic airflow enters an adiabatic, constant area pipe (inside diameter \(=0.1 \mathrm{~m}\) ) with \(\mathrm{Ma}_{1}=2.0\). The pipe friction factor is 0.02 . If a standing normal shock is located right at the pipe exit, and the Mach number just upstream of the shock is 1.2, determine the length of the pipe.