A converging-diverging nozzle feeds a long insulated duct before venting into surroundings at atmospheric conditions. The stagnation pressure in the plenum feeding the nozzle is 10 atm, and the nozzle exit to throat area ratio is 1.69. The friction factor is 0.005. a. What is the maximum length to diameter ratio of the duct such that no shocks form? b. Now assume the length to hydraulic diameter ratio of the duct is L/D 10. Calculate the pressure at the exit of the duct and comment on whether the flow is under- expanded or over-expanded.