Example $2\mathrm{.}6$

A turbofan engine is powering an aircraft flying at Mach number $0\mathrm{.}9,$ at an altitude of $33,000ft,$ where the ambient temperature and pressure are $-50\mathrm{.}4$ and $26\mathrm{.}2$ kPa $.$ The engine BPR is $3,$ and the hot airflow passing through the engine core is $22\mathrm{.}7k\frac{g}{s}.$ Preliminary analysis provided the following results:

Fuel$-to-$air ratio $f=0\mathrm{.}015$

$P_{ec}=55\mathrm{.}26$kPa,$u_{ec}=339\mathrm{.}7\frac{m}{s},A_{ec}=0\mathrm{.}299m^2$

$P_{eh}=32\mathrm{.}56$kPa,$u_{eh}=452\frac{m}{s},A_{eh}=0\mathrm{.}229m^2$

Calculate the thrust force and the propulsive efficiency using the first and second expressions.