Correct Answer - Option 3 : 9.38
Concept:
Compression ratio (r):
It is defined as the ratio of the sum of clearance volume and swept volume to the clearance volume.
It is given by
\({\bf{r}} = \frac{{{{\bf{v}}_{\bf{c}}} + {{\bf{v}}_{\bf{s}}}}}{{{{\bf{v}}_{\bf{c}}}}} = \frac{{{{\bf{v}}_1}}}{{{{\bf{v}}_2}}}\)
where
\({{\bf{v}}_{\bf{s}}} = Swept ~volume= \;\frac{{\bf{\pi }}}{4}\; × \;{{\bf{d}}^2}\; × \;{\bf{l}}\times n\)
Calculation:
Given:
Number of cylinder (n) = 6, bore (d) = 20 cm, stroke length (l) = 40 cm, vc = 2000 cm3, r = ?
Now, we know that
Swept volume is:
\({{\bf{v}}_{\bf{s}}} = \;\frac{{\bf{\pi }}}{4}\; × \;{{\bf{d}}^2}\; × \;{\bf{l}}\times n\) = 0.7854 × 202 × 40 × 6
∴ vs = 75398.22 cm3
Compression ratio is:
\({\bf{r}} = \frac{{{{\bf{v}}_{\bf{c}}} + {{\bf{v}}_{\bf{s}}}}}{{{{\bf{v}}_{\bf{c}}}}}= \;\frac{{9000\; + \;75398.22}}{{9000}} \)
∴ r = 9.38