Total displacement

Calculate the total displacement of the 12-cylinder engine with the diameter of the piston bore B = 8.9 cm and stroke S=1.9 cm of the piston.

Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back to the top. The piston is connected to the crankshaft. We can note the movement of the piston by the angle of rotation of the crankshaft.

Zero degrees occur when the piston is at the top of the cylinder. Since there are 360 degrees in one revolution, the piston is at the bottom when the crank angle is 180 degrees. The piston's distance from zero to 180 degrees is called the stroke S of the piston. The piston makes four strokes, and the crankshaft completes two revolutions between combustion firings. The piston's diameter, and the cylinder's inside diameter, are called the bore B.

Correct answer:

V =  1418.4 cm³

Step-by-step explanation:

$$\begin{gathered} B=8.9\text{cm} \\ r=B/2=8.9/2=\frac{89}{20}=4.45\text{cm} \\ S=1.9\text{cm} \\ n=12 \\ {V}_1=\pi \cdot r^2\cdot S=3.1416\cdot 4.45^2\cdot 1.9\doteq 118.2016{\text{cm}}^3 \\ V=n\cdot V_1=12\cdot 118.2016=1418.4{\text{cm}}^3 \end{gathered}$$

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