In car engines, write out what SI stands for. A four-stroke 2 -cylinder internal combustion engine running at the speed of $$ 240 \mathrm{r} / \mathrm{min} $$, has a bore and stroke length of $$ 0,380 \mathrm{~m} $$ and $$ 0,585 \mathrm{~m} $$ respectively. The engine develops a brake torque of $$ 11,860 \mathrm{kNm} $$, while the volumetric efficiency is 0,85 . The air-fuel ratio by volume is $$ 7: 1 $$. The fuel used in this engine has a calorific value of $$ 38600 \mathrm{~kJ} / \mathrm{m}^{3} $$. Calculate: 5.2.1 The engine's brake power in kW 5.2.2 The mean speed of the engine's pistons in $$ \mathrm{m} / \mathrm{s} $$ 5.2 The engine's swept volume in $$ \mathrm{m}^{3} / \mathrm{s} $$ $$ 5.2 \quad $$ The engine's induced volume in $$ \mathrm{m}^{3} / \mathrm{s} $$ $$ 5.2 .5 \quad $$ The brake thermal efficiency

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### 5.2.1 The Engine's Brake Power in kW

The brake power (BP) of an engine can be calculated using the formula:

$$
BP = \frac{2 \pi N T}{60}
$$

where:
- $$ N $$ = engine speed in revolutions per minute (rpm)
- $$ T $$ = brake torque in Nm

Given:
- $$ N = 240 \, \text{r/min} $$
- $$ T = 11,860 \, \text{kNm} = 11,860,000 \, \text{Nm} $$

Substituting the values:

$$
BP = \frac{2 \pi (240) (11,860,000)}{60}
$$

Calculating:

$$
BP = \frac{2 \pi (240) (11,860,000)}{60} \approx \frac{2 \times 3.14159 \times 240 \times 11,860,000}{60}
$$

$$
BP \approx \frac{2 \times 3.14159 \times 240 \times 11,860,000}{60} \approx 1,507,000 \, \text{W} \approx 1507 \, \text{kW}
$$

### 5.2.2 The Mean Speed of the Engine's Pistons in $$ \mathrm{m/s} $$

The mean speed of the pistons can be calculated using the formula:

$$
\text{Mean Speed} = \frac{2 \times \text{Stroke Length} \times N}{60}
$$

Given:
- Stroke Length = $$ 0.585 \, \text{m} $$
- $$ N = 240 \, \text{r/min} $$

Substituting the values:

$$
\text{Mean Speed} = \frac{2 \times 0.585 \times 240}{60}
$$

Calculating:

$$
\text{Mean Speed} = \frac{2 \times 0.585 \times 240}{60} = \frac{280.8}{60} \approx 4.68 \, \text{m/s}
$$

### 5.2.3 The Engine's Swept Volume in $$ \mathrm{m}^3 $$

The swept volume (V_s) of a cylinder can be calculated using the formula:

$$
V_s = \frac{\pi}{4} \times \text{Bore}^2 \times \text{Stroke}
$$

Given:
- Bore = $$ 0.380 \, \text{m} $$
- Stroke = $$ 0.585 \, \text{m} $$

Calculating the swept volume for one cylinder:

$$
V_s = \frac{\pi}{4} \times (0.380)^2 \times (0.585)
$$

Calculating:

$$
V_s = \frac{3.14159}{4} \times 0.1444 \times 0.585 \approx 0.067 \, \text{m}^3
$$

Since there are 2 cylinders:

$$
\text{Total Swept Volume} = 2 \times V_s \approx 2 \times 0.067 \approx 0.134 \, \text{m}^3
$$

### 5.2.4 The Engine's Induced Volume in $$ \mathrm{m}^3/s $$

The induced volume (V_i) can be calculated using the formula:

$$
V_i = V_s \times N \times \text{Volumetric Efficiency}
$$

Given:
- Volumetric Efficiency = $$ 0.85 $$
- $$ N = 240 \, \text{r/min} $$

Calculating the induced volume per second:

$$
V_i = 0.134 \, \text{m}^3 \times \frac{240}{60} \times 0.85
$$

Calculating:

$$
V_i = 0.134 \times 4 \times 0.85 \approx 0.456 \, \text{m}^3/s
$$

### 5.2.5 The Brake Thermal Efficiency

The brake thermal efficiency ($$ \eta_b $$) can be calculated using the formula:

$$
\eta_b = \frac{BP}{\dot{Q}}
$$

Where $$ \dot{Q} $$ is the heat input, calculated as:

$$
\dot{Q} = V_i \times \text{Air-Fuel Ratio} \times \text{Calorific Value}
$$

Given:
- Air-Fuel Ratio = $$ 7:1 $$
- Calorific Value = $$ 38600 \, \text{kJ/m}^3 $$

Calculating $$ \dot{Q} $$:

$$
\dot{Q} = V_i \times \left( \frac{1}{7} \right) \times 38600
$$

Substituting $$ V_i $$:

$$
\dot{Q} = 0.456 \, \text{m}^3/s \times \left( \frac{1}{7} \right) \times 38600
$$

Calculating:

$$
\dot{Q} \approx 0.456 \times 0.142857 \times 38600 \approx 0.456 \times 5514.29 \approx 2515.71 \, \text{kW}
$$

Now, substituting $$ BP $$ and $$ \dot{Q} $$ into the efficiency formula:

$$
\eta_b = \frac{1507}{2515.71} \approx 0.597 \text{ or } 59.7\%
$$

### Summary of Results
- **Brake Power**: $$ 1507 \, \text{kW} $$
- **Mean Speed of Pistons**: $$ 4.68 \, \text{m/s} $$
- **Swept Volume**: $$ 0.134 \, \text{m}^3 $$
- **Induced Volume**: $$ 0.456 \, \text{m}^3/s $$
- **Brake Thermal Efficiency**: $$ 59.7\% $$
### 5.2.1 The Engine's Brake Power in kW The brake power (BP) of an engine is approximately 1507 kW. ### 5.2.2 The Mean Speed of the Engine's Pistons in $$ \mathrm{m/s} $$ The mean speed of the pistons is approximately 4.68 m/s. ### 5.2.3 The Engine's Swept Volume in $$ \mathrm{m}^3 $$ The engine's swept volume is approximately 0.134 m³. ### 5.2.4 The Engine's Induced Volume in $$ \mathrm{m}^3/s $$ The engine's induced volume is approximately 0.456 m³/s. ### 5.2.5 The Brake Thermal Efficiency The brake thermal efficiency is approximately 59.7%.

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