An engine cylinder has clearance volume of 20 cc and compression ratio of 14. The mechanical and volumetric efficiencies are 88% and 80%, respectively. The actual volume of charge in cc inducted per stroke is:

Explanation:

Concept: 

Volumetric efficiency: It is defined as the ratio of the actual volume of charge inducted per stroke to the actual volume displaced by the system.

\(Volumetric \space efficiency \space(\eta_{v})=\frac{Actual\space volume\space intake}{Swept\space volume}\)

Compression ratio: It is defined as the ratio of the total volume of the cylinder to the clearance volume of the cylinder.

\(Compression\space ratio\space (r)=\frac{Total\space volume}{Clearance\space volume}\) = \(\frac{V_s+V_c}{V_c}=\frac{V_s}{V_c}+1\)

Total volume = Swept volume(V_s) + Clearance volume(V_c)

Calculation:

Given:

V_c = 20 cc, r = 14, \(\eta_{v} \) = 80%, \(\eta_{m}\) = 88%.

\(r=\frac{V_{s}}{20}+1\)\(\Longrightarrow\) \(V_{s}=260\space cc\)

\(\eta_{v}=\frac{Actual\space volume\space intake}{V_{s}}\) \(\Rightarrow\) \(0.8=\frac{Actual\space volume\space intake}{260}\)

\(\therefore Actual\space volume\space intake=260\times 0.8=208\space cc\).

Thus, option (2) is the correct answer.