1.1 Calculate the cylinder diameter of an
engine with a compression ratio of
, a stroke length of 150 mm and a
clearance volume of .

Ask by Simmons Hills. in South Africa

Mar 25,2025

Question

1.1 Calculate the cylinder diameter of an engine with a compression ratio of $$ 15: 1 $$, a stroke length of 150 mm and a clearance volume of $$ 230 \mathrm{~cm}^{3} $$.

UpStudy AI · Accepted Answer

**Step 1. Compute the Swept Volume**

The compression ratio is given by  
$$
\text{CR} = \frac{V_s + V_c}{V_c},
$$  
where $$ V_s $$ is the swept volume and $$ V_c $$ is the clearance volume. Rearranging for $$ V_s $$, we have  
$$
V_s = V_c \times (\text{CR} - 1).
$$

Given:  
- $$ \text{CR} = 15 $$,
- $$ V_c = 230\,\text{cm}^3 $$.

Thus,  
$$
V_s = 230 \times (15 - 1) = 230 \times 14 = 3220\,\text{cm}^3.
$$

---

**Step 2. Relate Swept Volume to Cylinder Dimensions**

The swept volume of a cylinder is also given by  
$$
V_s = \frac{\pi}{4}d^2 L,
$$  
where $$ d $$ is the cylinder diameter and $$ L $$ is the stroke length.

Given:  
- $$ L = 150\,\text{mm} $$.

It is convenient to work in consistent units. Convert the stroke length to centimeters:  
$$
150\,\text{mm} = 15\,\text{cm}.
$$

So the formula becomes  
$$
3220 = \frac{\pi}{4}d^2 \times 15.
$$

---

**Step 3. Solve for the Cylinder Diameter $$ d $$**

Isolate $$ d^2 $$ in the equation:
$$
d^2 = \frac{4 \times 3220}{\pi \times 15}.
$$

Calculate the numerator:  
$$
4 \times 3220 = 12880.
$$

Thus,
$$
d^2 = \frac{12880}{15\pi}.
$$

Taking the square root gives  
$$
d = \sqrt{\frac{12880}{15\pi}}.
$$

Now, approximate the value. First, compute the denominator:
$$
15\pi \approx 15 \times 3.1416 \approx 47.124.
$$

Then,  
$$
\frac{12880}{47.124} \approx 273.6.
$$

Taking the square root:  
$$
d \approx \sqrt{273.6} \approx 16.54\,\text{cm}.
$$

---

**Step 4. Convert the Result to Millimeters**

Since $$ 1\,\text{cm} = 10\,\text{mm} $$,  
$$
d \approx 16.54\,\text{cm} \times 10 \approx 165.4\,\text{mm}.
$$

---

**Final Answer**

$$
\boxed{d \approx 165\,\text{mm}}
$$
The cylinder diameter is approximately 165 mm.

1.1 Calculate the cylinder diameter of an
engine with a compression ratio of
, a stroke length of 150 mm and a
clearance volume of .

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1.1 Calculate the cylinder diameter of an engine with a compression ratio of , a stroke length of 150 mm and a clearance volume of .