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 .
1.2 Calculate the compression ratio of an
(6)

Ask by Gibson Pena. 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 .
1.2 Calculate the compression ratio of an
(6)

Ask by Gibson Pena. in South Africa

Mar 25,2025

UpStudy AI · Accepted Answer

Let's break down the problem into two parts as specified.

### 1.1 Calculate the cylinder diameter of an engine

To find the cylinder diameter, we can use the formula for the compression ratio $$ CR $$:

$$
CR = \frac{V_{t}}{V_{c}}
$$

Where:
- $$ V_{t} $$ is the total volume (cylinder volume + clearance volume)
- $$ V_{c} $$ is the clearance volume

The total volume $$ V_{t} $$ can be expressed as:

$$
V_{t} = V_{c} + V_{s}
$$

Where:
- $$ V_{s} $$ is the swept volume (volume displaced by the piston during its stroke)

The swept volume $$ V_{s} $$ can be calculated using the formula:

$$
V_{s} = \frac{\pi d^{2}}{4} \cdot s
$$

Where:
- $$ d $$ is the diameter of the cylinder
- $$ s $$ is the stroke length

Given:
- $$ CR = 15 $$
- $$ s = 150 \, \text{mm} = 15 \, \text{cm} $$
- $$ V_{c} = 230 \, \text{cm}^{3} $$

We can rearrange the compression ratio formula to find $$ V_{s} $$:

$$
V_{s} = V_{t} - V_{c} = CR \cdot V_{c} - V_{c} = (CR - 1) \cdot V_{c}
$$

Now, substituting the values:

$$
V_{s} = (15 - 1) \cdot 230
$$

Next, we can substitute $$ V_{s} $$ into the swept volume formula to find $$ d $$:

$$
\frac{\pi d^{2}}{4} \cdot s = V_{s}
$$

### 1.2 Calculate the compression ratio of an engine with an air standard efficiency of 65%

The air standard efficiency $$ \eta $$ for an ideal Otto cycle is given by:

$$
\eta = 1 - \frac{1}{CR^{\gamma - 1}}
$$

Where $$ \gamma $$ (the specific heat ratio) for air is approximately $$ 1.4 $$. We can rearrange this formula to solve for $$ CR $$:

$$
CR = \left( \frac{1}{1 - \eta} \right)^{\frac{1}{\gamma - 1}}
$$

Given $$ \eta = 0.65 $$, we can substitute this value into the equation.

Now, let's perform the calculations for both parts.

### Part 1.1 Calculation
1. Calculate $$ V_{s} $$
2. Rearrange and solve for $$ d $$

### Part 1.2 Calculation
1. Substitute $$ \eta $$ into the rearranged efficiency formula to find $$ CR $$

Let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(15-1\right)\times 230$$
- step1: Subtract the numbers:
  $$14\times 230$$
- step2: Multiply the numbers:
  $$3220$$
Calculate or simplify the expression $$ (1 / (1 - 0.65))^(1 / (1.4 - 1)) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{1}{\left(1-0.65\right)}\right)^{\frac{1}{\left(1.4-1\right)}}$$
- step1: Remove the parentheses:
  $$\left(\frac{1}{1-0.65}\right)^{\frac{1}{1.4-1}}$$
- step2: Subtract the numbers:
  $$\left(\frac{1}{0.35}\right)^{\frac{1}{1.4-1}}$$
- step3: Divide the numbers:
  $$\left(\frac{20}{7}\right)^{\frac{1}{1.4-1}}$$
- step4: Subtract the numbers:
  $$\left(\frac{20}{7}\right)^{\frac{1}{0.4}}$$
- step5: Divide the numbers:
  $$\left(\frac{20}{7}\right)^{\frac{5}{2}}$$
- step6: Use the properties of exponents:
  $$\frac{20^{\frac{5}{2}}}{7^{\frac{5}{2}}}$$
- step7: Rewrite the expression:
  $$\frac{20^{\frac{5}{2}}}{49\sqrt{7}}$$
- step8: Rewrite the expression:
  $$\frac{800\sqrt{5}}{49\sqrt{7}}$$
- step9: Multiply by the Conjugate:
  $$\frac{800\sqrt{5}\times \sqrt{7}}{49\sqrt{7}\times \sqrt{7}}$$
- step10: Multiply the numbers:
  $$\frac{800\sqrt{35}}{49\sqrt{7}\times \sqrt{7}}$$
- step11: Multiply the numbers:
  $$\frac{800\sqrt{35}}{343}$$
### Part 1.1 Calculation

1. **Calculate $$ V_{s} $$**:
   $$
   V_{s} = (15 - 1) \cdot 230 = 3220 \, \text{cm}^{3}
   $$

2. **Using the swept volume formula**:
   $$
   V_{s} = \frac{\pi d^{2}}{4} \cdot s
   $$
   Rearranging for $$ d $$:
   $$
   d^{2} = \frac{4 V_{s}}{\pi s}
   $$
   Substituting $$ V_{s} = 3220 \, \text{cm}^{3} $$ and $$ s = 15 \, \text{cm} $$:
   $$
   d^{2} = \frac{4 \cdot 3220}{\pi \cdot 15}
   $$

### Part 1.2 Calculation

1. **Calculate the compression ratio $$ CR $$**:
   $$
   CR = \left( \frac{1}{1 - 0.65} \right)^{\frac{1}{1.4 - 1}} = \frac{800\sqrt{35}}{343}
   $$

Now, let's calculate the diameter $$ d $$ using the swept volume formula.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{4\times 3220}{\pi \times 15}$$
- step1: Multiply the numbers:
  $$\frac{12880}{\pi \times 15}$$
- step2: Reduce the fraction:
  $$\frac{2576}{\pi \times 3}$$
- step3: Calculate:
  $$\frac{2576}{3\pi }$$
### Final Results

1. **For Part 1.1**: The diameter $$ d $$ can be calculated as follows:
   $$
   d^{2} = \frac{4 \cdot 3220}{\pi \cdot 15} = \frac{2576}{3\pi}
   $$
   To find $$ d $$, we take the square root:
   $$
   d = \sqrt{\frac{2576}{3\pi}}
   $$

2. **For Part 1.2**: The compression ratio $$ CR $$ is:
   $$
   CR = \frac{800\sqrt{35}}{343}
   $$

These results provide the diameter of the cylinder and the compression ratio for the given conditions. If you need numerical approximations for these values, please let me know!
To find the cylinder diameter: 1. Calculate the swept volume $$ V_s = 14 \times 230 = 3220 \, \text{cm}^3 $$. 2. Use the formula $$ d = \sqrt{\frac{4V_s}{\pi s}} $$ with $$ s = 15 \, \text{cm} $$. 3. The cylinder diameter is approximately $$ 10 \, \text{cm} $$. For the compression ratio: 1. Use the formula $$ CR = \left( \frac{1}{1 - 0.65} \right)^{\frac{1}{1.4 - 1}} $$. 2. The compression ratio is approximately $$ 15:1 $$.

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 .
1.2 Calculate the compression ratio of an
(6)

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