If stroke volume of engine = 300 cc, clearance volume of engine = 20 cc. The compression ratio of engine will be:
16
Calculating Engine Compression Ratio
The compression ratio is a fundamental parameter of an internal combustion engine. It is defined as the ratio of the maximum volume of the cylinder (when the piston is at the bottom dead center, BDC) to the minimum volume (when the piston is at the top dead center, TDC). This minimum volume is also known as the clearance volume.
The total volume of the cylinder when the piston is at BDC is the sum of the stroke volume (or swept volume) and the clearance volume.
- Stroke Volume ($\text{V}_\text{s}$): This is the volume swept by the piston as it moves from TDC to BDC.
- Clearance Volume ($\text{V}_\text{c}$): This is the volume remaining in the cylinder when the piston is at TDC.
- Total Volume ($\text{V}_\text{t}$): This is the volume of the cylinder when the piston is at BDC, calculated as $\text{V}_\text{t} = \text{V}_\text{s} + \text{V}_\text{c}$.
The formula for compression ratio (CR) is:
$$ \text{CR} = \frac{\text{Total Volume}}{\text{Clearance Volume}} = \frac{\text{Stroke Volume} + \text{Clearance Volume}}{\text{Clearance Volume}} $$
Given values:
Stroke Volume ($\text{V}_\text{s}$) = 300 cc
Clearance Volume ($\text{V}_\text{c}$) = 20 cc
First, calculate the Total Volume:
$$ \text{V}_\text{t} = \text{V}_\text{s} + \text{V}_\text{c} = 300 \text{ cc} + 20 \text{ cc} = 320 \text{ cc} $$
Now, calculate the Compression Ratio using the formula:
$$ \text{CR} = \frac{\text{V}_\text{t}}{\text{V}_\text{c}} = \frac{320 \text{ cc}}{20 \text{ cc}} $$
$$ \text{CR} = 16 $$
Let's summarize the values in a table:
| Parameter | Value |
|---|---|
| Stroke Volume ($\text{V}_\text{s}$) | 300 cc |
| Clearance Volume ($\text{V}_\text{c}$) | 20 cc |
| Total Volume ($\text{V}_\text{t} = \text{V}_\text{s} + \text{V}_\text{c}$) | 320 cc |
| Compression Ratio ($\text{CR} = \text{V}_\text{t} / \text{V}_\text{c}$) | 16 |
Therefore, the compression ratio of the engine is 16.
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