P$5$: Using the equation which relates the Mach index to volumetric efficiency $($Equation $1),$ plot the volumetric efficiency for an intake valve opening event of $15$ BTDC and an exhaust closing event of $15$ ABDC assuming a gas mixture with a specific heat ratio of $1\mathrm{.}32.$ Superimpose the experimental data given in table $1$ and limit the $y-$axis scale to $100\%.$

a$)$ State the differences between the model prediction and experimental results.

b$)$ Based on these results, identify the Mach Index range you would use as a starting point in valvetrain design.

${}_v=[\frac{2}{+1}{]}^{\frac{+1}{2(-1)}}\frac{({}_{\text{I}\text{V}\text{C}}-{}_{\text{I}\text{V}\text{O}})}{}\frac{1}{Z}$

$\backslash$table$[[$Experimental Data$],[$Mach Index,Volumetric Efficiency $(\%)],[0\mathrm{.}4,92],[0\mathrm{.}5,90],[0\mathrm{.}6,85],[0\mathrm{.}7,75],[0\mathrm{.}8,65],[0\mathrm{.}9,59],[1\mathrm{.}0,55]]$

Table $1$: Experimental data for Problem $5$