The Efficiencies of Real Engines — Question 1

Question 1

Successive conversion losses multiply before fixed auxiliary loads are subtracted

A plant receives fuel energy at 100 kW. Its thermal stage converts .400 of that input to indicated mechanical power. Mechanical transmission efficiency is .900 and generator efficiency .950. Electrical auxiliaries consume 3.00 kW of generator output. All figures describe steady operation.

1. Find indicated power, shaft power, gross electrical power and net electrical efficiency.

2. Account for every loss channel and verify that net output plus losses equals fuel input. Explain why adding stage efficiencies would be incorrect.

Question 1 - Solution

Successive conversion losses multiply before fixed auxiliary loads are subtracted

(a) Method and calculation

$$P_i=.400(100)=40.0\,\mathrm{kW},\quad P_s=.900(40)=36.0\,\mathrm{kW}.$$$$P_g=.950(36)=34.2\,\mathrm{kW},\quad P_{\mathrm{net}}=34.2-3=31.2\,\mathrm{kW},\quad\eta_{\mathrm{net}}=.312.$$

(b) Interpretation and further calculation

$$L_{\mathrm{thermal}}=60.0,\quad L_{\mathrm{mechanical}}=4.00,\quad L_{\mathrm{generator}}=1.80,\quad L_{\mathrm{auxiliary}}=3.00\quad\mathrm{kW}.$$$$31.2+60+4+1.8+3=100\,\mathrm{kW}.$$Each fractional efficiency acts on the reduced input from the previous stage. The fixed auxiliary load is subtracted after those multiplications.

Physical check

Stage boundaries must be specified to avoid counting a loss twice.