Engine and Nozzle

Consider a rocket engine with a convergent-divergent nozzle operating at sea level. The pressure in the combustion chamber is Pc= 10 MPa, with a combustion temperature of Tc= 2400 K. The static pressure measured in the throat of the rocket nozzle is Pt = 6 MPa. Assume a specific heat ratio (gamma) = 1.4 for the exhaust gases.

a) Calculate the Mach number of the gas flow in the throat of the nozzle.

b) Given this Mach number at the throat, will the gas stream ever reach supersonic speeds in the nozzle? Explain why.

c) If the static pressure at the nozzle throat is to remain unchanged, what must the pressure in the combustion chamber be in order for the flow to reach supersonic velocity in the nozzle?

d) If the temperature in the combustion chamber remains unchanged, what is the temperature at the nozzle throat?

e) From the throat, the stream is isentropic ally expanded until it reaches the exhaust. The static pressure at the exhaust is ambient pressure. Calculate the exhaust temperature.

f) The velocity of the exhaust stream is Ve= 4500 m/s . The rocket exhaust has a cross- sectional area of Ae= 3.8 m^2. Using the area-Mach number relation, calculate the cross- sectional area at the nozzle throat.