Q$5$: $[9$ marks $]$ A four$-$stroke cycle, $2L,$ four$-$cylinder, square, $CI$ engine, operating at $3500$ rpm $,$ produces $62$ kW of brake power. If the combustion efficiency is $0\mathrm{.}95,$ volumetric efficiency is $0\mathrm{.}82,$ mechanical efficiency is $0\mathrm{.}75,$ connecting rod length $=28cm,$ and air$-$fuel ratio $AF=19$:$1.$ Assume that the injection started $15$ degrees $bTDC$ and ends at $23$ crank angle degree aTDC Use $air=1\mathrm{.}21k\frac{g}{m^3},[Q_{HV}]=43500k\frac{J}{k}g.$ Calculate:

a$.$ Mean piston speed.

b$.$ Rate of air flow into engine.

c$.$ The amount of the fuel that didn't burned in the combustion

d$.$ Brake specific fuel consumption in $[$gm$/$kW$-$hr$].$

e$.$ Brake thermal efficiency.

f$.$ Output per displacement.

g$.$ How many injection process for the whole engine in $1$ sec $.$