The inline six engine has been extensively used in small and midsize sedans. A

$2$ VSOHC inline six manufactured by BMW $($M$20$B$25)$ produced $126$ kW at

$5800$ RPM and peak torque of $226$ Nm at $4000$RPM operating on gasoline. The

M$20$B$25$ has a stroke of $75$ mm and a bore of $84$ mm and operates at a

compression ratio of $9\mathrm{.}7$:$1.$ The intake conditions at the operation condition are

$(100$kPa,$60$C$).$ The lambda value is $1\mathrm{.}05$ at peak torque conditions and $0\mathrm{.}92$ at

peak power conditions.

Analyze the engine at the peak torque operating condition and answer the

following questions. Assume that $92\%$ of the fuel is burned during combustion.

The scavenging efficiency is $96\%$ at $4000$RPM resulting in $4\%$ residual exhaust

gas in the cylinder at the start of the compression stroke.

$1.$ Mean Piston Speed?

$2.$ Brake Work?

$3.$ mechanical efficiency?

$4.$ reasonable?

$5.($fmep$)?$

$6.($bsfc$)?$