$(100$ points$)$ A single cylinder, four stroke, diesel engine has following parameters:

Bore: $B=10\mathrm{.}6cm$

Stroke: $S=12\mathrm{.}7cm$

Connecting rod length: $r=20\mathrm{.}43cm$

Compression ratio: $13\mathrm{.}5$

Use MATLAB $($attach your MATLAB script to the solution$)$ to:

a$.(25$ points$)$ Calculate the displacement $V_d$ and clearance $V_c$ of the engine in liters.

b$.(40$ points$)$ Calculate and plot the variation of cylinder volume with changes in crank

angle, in $0\mathrm{.}1CA($crank angle$)$ increments, for one engine cycle

c$.(35$ points$)$ Calculate the mass of air ingested per cycle in $k\frac{g}{c}$ycle if the volumetric

efficiency is $80\%.$ Use standard air properties.

Show MatlLab Code please