The mechanical efficiency of a single-cylinder, four-stroke engine is 90%. The frictional power is 30 kW. What will be the brake power developed by the engine?

Concept:

The work input to the piston is due to the expansion of hot gases. Thus the work input to the piston is found by the pressure and volume changes in the p-v diagram, known as the indicator diagram. Thus the work input to the piston is known as indicator work done (IWD).

The work output from the piston is found by a brake mechanism attached to the shaft of the engine, this mechanism is known as a dynamometer. Hence the work output of the piston is known as brake work done (BWD).

The ratio of brake work done to indicated work done is known as mechanical efficiency.

\({\eta _m} = \frac{{BWD}}{{IWD}}= \frac{{{b_{mep}} \times {V_s}}}{{{i_{mep}} \times {V_s}}} = \frac{{brake~power\left( {BP} \right)}}{{indicated~power\left( {IP} \right)}}\)

where   

b_mep = Break mean effective pressure,

i_mep = Indicated mean effective pressure,

V_s = Stroke volume                                         

IP = BP + FP

FP = Frictional Power

Calculation:

Given:

Mechanical efficiency η_m = 90 %

Frictional power, FP = 30 kW

IP = BP + FP

\(\frac{{BP}}{{0.9}} = BP + 30\)

∴ BP = 270 kW.