Engine Capacity Calculation Explained

This question asks us to find the total engine capacity in cubic centimeters (cc) for a specific reciprocating engine. We are given the number of cylinders, cylinder diameter, stroke length, and clearance volume. It's important to note that engine capacity typically refers to the total swept volume of the cylinders.

Understanding Engine Capacity Components

• Number of Cylinders (N): The engine has 4 cylinders.
• Cylinder Diameter (d): The diameter of each cylinder is given as 4 cm.
• Stroke Length (l): The length of the piston's stroke is given as 7 cm.
• Clearance Volume ($V_c$): The volume remaining above the piston when it's at the top dead center is 2 cm³. This value is used for calculating the compression ratio but is not directly needed to calculate the engine's swept capacity.

Formula for Swept Volume

The swept volume ($V_s$) of a single cylinder in a reciprocating engine is the volume displaced by the piston as it moves from the bottom dead center (BDC) to the top dead center (TDC). The formula is based on the volume of a cylinder:

$$V_s = \frac{\pi}{4} d^2 l$$

Where:

• $V_s$ = Swept volume of one cylinder
• $d$ = Cylinder diameter
• $l$ = Stroke length

Step-by-Step Calculation

First, we calculate the swept volume for a single cylinder:

1. Substitute the given values into the formula:

   $$V_s = \frac{\pi}{4} (4 \text{ cm})^2 (7 \text{ cm})$$

2. Calculate the square of the diameter:

   $$d^2 = (4 \text{ cm})^2 = 16 \text{ cm}^2$$

3. Plug this back into the formula:

   $$V_s = \frac{\pi}{4} \times 16 \text{ cm}^2 \times 7 \text{ cm}$$

4. Simplify the expression:

   $$V_s = \pi \times 4 \text{ cm}^2 \times 7 \text{ cm}$$

   $$V_s = 28\pi \text{ cm}^3$$

5. Approximate the value using $\pi \approx 3.14159$:

   $$V_s \approx 28 \times 3.14159 \text{ cm}^3$$

   $$V_s \approx 87.96 \text{ cm}^3$$

Calculating Total Engine Capacity

The total engine capacity is the swept volume of one cylinder multiplied by the total number of cylinders.

Total Engine Capacity = $N \times V_s$

Using the calculated swept volume for one cylinder:

Total Engine Capacity = $4 \times 28\pi \text{ cm}^3$

Total Engine Capacity = $112\pi \text{ cm}^3$

Now, let's calculate the approximate numerical value:

Total Engine Capacity $\approx 4 \times 87.96 \text{ cm}^3$

Total Engine Capacity $\approx 351.84 \text{ cm}^3$

Since engine capacity is usually rounded to the nearest whole number, the total capacity is approximately 352 cc.

Final Engine Capacity Result

Based on the calculations, the engine capacity for the given 4-stroke, 4-cylinder engine is approximately 352 cc. The clearance volume of 2 cm³ was provided but not needed for this specific calculation of swept volume.