An aircraft flies at 850 ft/s through air at -40 F and 5 psia. The turbojet engi

Question

An aircraft flies at 850 ft/s through air at -40 F and 5 psia.  The turbojet engine has a pressure ratio of 10 and the turbine inlet is limited to 2000 F by mass flow of air of 100 pounds per second.  The engine has a diffuser at the inlet and a nozzle at the exit.  Use constant-specific-heat theory, with property values at the cold air standard. Assume that the diffuser slows the inlet flow to zero velocity, find (a) the pressure at the diffuser exit.  (b) the temperature and pressure at the turbine exit (c) the velocity of gases at the nozzle exit (hint: assume the nozzle exit pressure matches the surrounding atmospheric pressure). (d) the engine thrust (newtons) and, (e) the propulsive efficiency of the engine.

Explanation / Answer

Vi = known
Ti = Known
Pi = Known
Ve = ?

Use energy balance for control volume at steady state with no heat transfer,
dEcv/dt = 0 = Q - W + m_dot[(hi-he) + (Vi^2 - Ve^2)], W = 0 and Q = 0
0 = m_dot[(hi-he + Vi^2 - Ve^2)]
(hi-he) + (Vi^2 - Ve^2) = 0
Vi^2 - Ve^2 = he-hi
Ve^2 = Vi^2 - (he-hi)
Ve = [Vi^2 - (he-hi)]^0.5
Vi = known
he(Te,Pe) = known from table
hi(Ti,Pi) = known from table
For certain cases we can use ?h = Cp(Te-Ti)

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