A large bypass ratio turbofan engine has the following design and limit parameters:

M0 = 0.8, altitude = 37 kft U. S. standard atmosphere, πd = 0.995, πc = 40, ec = 0.90, α = 6, πf= 1.6, ef = 0.90, πfn= 0.98, fan nozzle is convergent, τλ= 7.0, QR = 42,800 kJ/kg, πb = 0.95, ηb = 0.98, et = 0.90, ηm = 0.975, πn = 0.98, core nozzle is convergent.

Assuming the gas properties may be described by two sets of parameters, namely, cold and hot stream values, i. e.,

Engine cold section: γc = 1 .40, Cpc = 1.004 kJ/kg-K

Engine hot section: γt = 1.33, Cpt = 1.156 kJ/kg-K

Calculate:

the ratio of compressor to fan shaft power Pc/Pf • fuel-to-air ratio, f

a. the ratio of fan nozzle exit velocity to core nozzle exit velocity V19/V9
b. the ratio of two gross thrusts, Fg, fan/Fg, core
c. the engine thermal efficiency and compare it to an ideal Carnot cycle operating between the same temperature limits