How is the swept volume of a cylinder calculated?

The calculation of the swept volume of a cylinder, often referred to as the displacement volume, is achieved by multiplying the area of the piston crown by the stroke length. This is because the swept volume represents the volume displaced by the piston as it moves through its stroke within the cylinder.

To understand this better, the area of the piston crown is computed using the formula for the area of a circle (πr²), where 'r' is the radius of the piston. The stroke length is the distance the piston travels from the top of its travel (top dead center) to the bottom of its travel (bottom dead center). When you multiply the piston area by the stroke, you obtain the volumetric displacement of the cylinder for one complete stroke.

In contrast, the other options do not accurately describe the relationship between the volumes in a reciprocating engine's cylinder. The area of the cylinder cross-section multiplied by cylinder length would represent total cylinder volume, which includes both swept volume and clearance volume. Half of the clearance volume does not have a direct relation to swept volume. Lastly, adding total volume and piston volume does not yield any meaningful metric in this context. Thus, focusing on the product of piston area and stroke length highlights the nature of swept volume