Applied Aerodynamics (UG & PG) Compressible Flow Assignment 1 Due: 5pm, Friday October 23, 2020 (a) Air flows in a pipe of 50 mm internal diameter. The air enters at supersonic speed at a temperature of 300 K and a flow rate of 1.70 m3/s. The friction coefficient can be assumed constant at Cf = 0.005 ( f= 0.005 in the Anderson text book notation). (i) State any assumptions used to solve this problem. (ii) Find the Mach number of the flow at the pipe entrance. [1 mark] [5 marks] [7 marks] (ii) What is the length of the pipe if the Mach number at exit is 1.5? (b) Consider a convergent-divergent nozzle with an exit-to-throat area ratio of 3.5. The working fluid is air, with k = 1.4. The inlet flow is from a large air storage vessel with a total pressure of 2 atm. The nozzle discharges into ambient air with a static pressure of 1 atm. For this pressure ratio, a normal shock wave stands somewhere inside the divergent section of the nozzle. Using the "direct" or mass-flow-rate matching method, find the exit Mach number of the nozzle. [7 marks] Notes: 1. If using tables, it is acceptable to use the nearest value. 2. For air R = 287 J/kg.K and k = 1.4. 3. Use the problem-solving protocol, state all assumptions, and show all working. 4. Your submission must have a signed cover sheet attached.