Aerospace Propulsion Assignment 1 — Ramjet/Scramjet Cycle Analysis
 Instructions
Write your solutions in single column format, with one statement following another vertically. Write your solutions neatly so that they are easy to read and verify. Don't write one line with more than two equal signs. Highlight your answers using a box. Solve the problems starting from the Aerospace Propulsion Tables. Do not use any other document to solve the problems.
 05.22.14
 Problem #1
Consider a ramjet engine flying at Mach 3 and a flight dynamic pressure of 47.65 kPa. The inlet intake area is of 1 m$^2$. The supersonic nozzle is designed such that the pressure at the nozzle exit is equal to the environment pressure. We know that the burning efficiency is of 85% and that the stagnation pressure drops by 15% in the combustor. Knowing that the fuel injected in the combustor is gaseous hydrogen and that the stagnation temperature at the combustor exit is of 2600 K, do the following:
 (a) Find the altitude, the freestream temperature, and the stagnation pressure and temperature at the inlet entrance. (b) Find the fuel/air ratio $\dot{m}_{\rm f}/\dot{m}_{\rm a}$ in the combustor. (c) Find the stagnation pressure at the nozzle exit. (d) Find the stagnation temperature at the nozzle exit.
Assume that the gas constant $R=287~$J/kgK, the specific heat ratio $\gamma=1.4$, and the specific heat at constant pressure $c_p=1000$ J/kgK throughout.
 Problem #2
Consider a ramjet engine flying at Mach 3 and at an altitude of 18 km. The inlet intake area is of 1 m$^2$. We know that the stagnation pressure drops by 19% in the inlet and by an additional 15% in the combustor. Knowing that the fuel injected in the combustor is gaseous hydrogen with a fuel-air ratio of 0.02 and that the stagnation temperature at the combustor exit is of 2600 K, do the following:
 (a) Find the thrust of the engine neglecting external drag should the nozzle be a converging duct only. (b) Find the thrust of the engine neglecting external drag should the nozzle be a converging-diverging nozzle such that the pressure at the nozzle exit matches the environment pressure. (c) Find the overall efficiency of the engine for the thrust found in (b). (d) Find the specific impulse of the engine for the thrust found in (b).
Assume that the gas constant $R=287~$J/kgK, the specific heat ratio $\gamma=1.4$, and the specific heat at constant pressure $c_p=1000$ J/kgK throughout.
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