The nozzle in a jet engine takes the high-pressure air exiting the turbine and e

Question

The nozzle in a jet engine takes the high-pressure air exiting the turbine and expands it back to the ambient pressure surrounding the aircraft (i.e., p6= p1). This converts the enthalpy of the hot, compressed gas leaving the turbine into kinetic energy of the exhaust gas. This kinetic energy is what provides the thrust that propels the engine. Assuming an ideal adiabatic expansion of the gas through the nozzle, find the exhaust temperature T6, if the conditions at state 5 are: T5 = 1000 K and p5 = 6 atm. Assume that the kinetic energy entering the nozzle is negligible compared to the enthalpy at State 5 and find the exhaust velocity, Vexhaust.

Explanation / Answer

For ideal adiabatic expansion, T6/T5 = (P6/P5)^(1-1/n) where n = sp. heat ratio = 1.4 for air

T6/1000 = (1/6)^(1-1/1.4)

T6 = 600 K

h5 + V5^2/2 = h6 + V6^2/2

Given that V5 < < h5. Hence, h5 + V5^2/2 ~ h5

So, h5 = h6 + V6^2/2

h5 - h6 = V6^2/2

Cp(T5 - T6) = V6^2/2

Taking Cp (sp. heat at constant pr) for air = 1005 J/kg-K we get,

1005*(1000 - 600) = V6^2/2

V6 = 896.7 m/s

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