Discussion
A turboprop produces \( 1200 \ \mathrm{kW} \) of shaft power and \( 1.5 \ \mathrm{kN} \) of residual jet thrust at \( 100 \ \mathrm{m/s} \). Taking propeller efficiency as 0.85, the equivalent shaft power is approximately
Answer: C
Correct answer: 1376 kW
Equivalent shaft power credits the residual jet thrust by converting it to the shaft power that would have been needed to produce the same thrust through the propeller:
\[ \mathrm{ESHP} = \mathrm{SHP} + \frac{F_j V}{\eta_p} = 1200 + \frac{1500 \times 100}{0.85 \times 1000} \]\[ = 1200 + \frac{150}{0.85} = 1200 + 176 = 1376 \text{ kW} \]Adding the jet power of 150 kW without dividing by the propeller efficiency gives 1350 kW, which under-credits the jet: the propeller would have needed more than 150 kW of shaft power to deliver that thrust.
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