Jet Propulsion

Derive the fundamental thrust equation for jet propulsion.

A turbojet aircraft is flying with a velocity of $280 \text{ m/s}$ at an altitude of $9150 \text{ m}$, where the ambient conditions are $32 \text{ kPa}$ and $-32^\circ\text{C}$. The pressure ratio across the compressor is $12$, and the temperature at the turbine inlet is $1100 \text{ K}$. Air enters the compressor at $50 \text{ kg/s}$ and the jet fuel has a heating value of $42700 \text{ kJ/kg}$. Assuming ideal operation for all components, and assuming constant specific heats for air at room temperature, determine the velocity of the exhaust gases, the propulsive power, and the rate of fuel consumption.

Derive the fundamental thrust equation for jet propulsion and hence simplify it for a rocket engine.

Consider a rocket engine burning hydrogen and oxygen; the combustion chamber pressure and temperature are 25 atm and 3517 K, respectively. The area of the rocket nozzle throat is 0.1 m$^2$. The area of the exit is designed so that the exit pressure exactly equals ambient pressure at a standard altitude of 30 km. For the gas mixture, assume that $\gamma = 1.22$ and the molecular weight $M = 16$. At a standard altitude of 30 km, determine (i) specific impulse, (ii) thrust, (iii) area of the exit, and (iv) flow Mach number at exit.

What is after-burning? Why it is used?

How does a turboprop engine differ from a turbofan engine?

A turbine aircraft flies with a velocity of $300 \text{ m/sec}$ at an altitude where the air is at $0.35 \text{ bar}$ and $-40^\circ\text{C}$. The compressor has a pressure ratio of $10$, and the temperature of the gases at the turbine inlet is $1100^\circ\text{C}$. Air enters the compressor at a rate of $50 \text{ kg/sec}$. Determine:
(i) the temperature and pressure of the gases at the turbine exit.
(ii) the velocity of the gases at the nozzle exit, and
(iii) the propulsive efficiency of the cycle.