Example $4\mathrm{.}1$:

The following data refer to a four $-$ cylinder internal $-$ combustion engine operating on a four $-$ stroke cycle at $4400re\frac{v}{m}in$ : volume compression ratio $7\mathrm{.}6$:$1$; cylinder diameter $78$ mm ; stroke $105$ mm ; brake power $38$ kW ; indicated power $47\mathrm{.}5$ kW ; air consumption $21k\frac{g}{k}g$ fuel; fuel consumption $13\mathrm{.}6k\frac{g}{?}$ hour; energy release of $1$ kg of fuel, $41800$ kJ $.$ Determine.

$($i$)$ the mechanical efficiency

$($ii$)$ the mean effective pressure

$($iii$)$ the volumetric efficiency $($referred to $1$atm$=\frac{1\mathrm{.}01325}{b}ar,0C)$

$($iv$)$ the brake thermal efficiency

$($v$)$ the brake thermal efficiency ratio relative to the air$-$standard cycle.

Assume $R=0\mathrm{.}287k\frac{J}{k}gK.$