In car engines, write out what $$ S / $$ stands for. A four-stroke 2 -cylinder internal combustion engine running at the sp of $$ 240 \mathrm{r} / \mathrm{min} $$, has a bore and stroke length of $$ 0,380 \mathrm{~m} $$ and $$ 0,585 \mathrm{~m} $$ respectiv The engine develops a brake torque of $$ 11,860 \mathrm{kNm} $$, while the volume efficiency is 0,85 . The air-fuel ratio by volume is $$ 7: 1 $$. The fuel used in this ens 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 $$ \mathrm{m} / \mathrm{s} $$ 5.2.3 The engine's swept volume in $$ \mathrm{m}^{3} / \mathrm{s} $$ i.2.4 The engine's induced volume in $$ \mathrm{m}^{3} / \mathrm{s} $$ 2.5 The brake thermal efficiency

Question

UpStudy AI · Accepted Answer

To solve the problems related to the four-stroke 2-cylinder internal combustion engine, we will use the following formulas and steps:

### Given Data:
- Engine speed, $$ N = 240 \, \text{r/min} $$
- Bore, $$ D = 0.380 \, \text{m} $$
- Stroke length, $$ L = 0.585 \, \text{m} $$
- Brake torque, $$ T = 11.860 \, \text{kNm} = 11,860 \, \text{Nm} $$
- Volume efficiency, $$ \eta_v = 0.85 $$
- Air-fuel ratio, $$ \text{AFR} = 7:1 $$
- Calorific value of fuel, $$ CV = 38,600 \, \text{kJ/m}^3 $$

### 5.2.1 The Engine's Brake Power in kW
The brake power (BP) can be calculated using the formula:
$$
BP = \frac{2 \pi N T}{60}
$$
Where:
- $$ N $$ is the engine speed in r/min
- $$ T $$ is the brake torque in Nm

Substituting the values:
$$
BP = \frac{2 \pi (240) (11,860)}{60}
$$
$$
BP = \frac{2 \pi (240) (11,860)}{60} \approx  15,000 \, \text{W} \approx 15 \, \text{kW}
$$

### 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:
$$
v = \frac{N \cdot L}{2 \cdot 60}
$$
Where:
- $$ L $$ is the stroke length in meters

Substituting the values:
$$
v = \frac{240 \cdot 0.585}{2 \cdot 60} = \frac{240 \cdot 0.585}{120} \approx 2.87 \, \text{m/s}
$$

### 5.2.3 The Engine's Swept Volume in $$ \mathrm{m}^3 $$
The swept volume (V_s) for a 2-cylinder engine can be calculated using the formula:
$$
V_s = \frac{\pi D^2 L}{4} \cdot n
$$
Where:
- $$ n $$ is the number of cylinders

Substituting the values:
$$
V_s = \frac{\pi (0.380)^2 (0.585)}{4} \cdot 2
$$
$$
V_s \approx \frac{\pi (0.1444) (0.585)}{4} \cdot 2 \approx 0.067 \, \text{m}^3
$$

### 5.2.4 The Engine's Induced Volume in $$ \mathrm{m}^3/s $$
The induced volume (V_i) can be calculated using the formula:
$$
V_i = V_s \cdot \frac{N}{2 \cdot 60} \cdot \eta_v
$$
Substituting the values:
$$
V_i = 0.067 \cdot \frac{240}{2 \cdot 60} \cdot 0.85
$$
$$
V_i \approx 0.067 \cdot 2 \cdot 0.85 \approx 0.114 \, \text{m}^3/s
$$

### 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 per second, calculated as:
$$
\dot{Q} = \frac{V_i \cdot \text{Density of air} \cdot \text{Calorific value}}{\text{AFR}}
$$
Assuming the density of air is approximately $$ 1.225 \, \text{kg/m}^3 $$:
$$
\dot{Q} = \frac{0.114 \cdot 1.225 \cdot 38,600}{7}
$$
Calculating $$ \dot{Q} $$:
$$
\dot{Q} \approx \frac{0.114 \cdot 1.225 \cdot 38,600}{7} \approx 0.114 \cdot 1.225 \cdot 5,514.29 \approx 0.114 \cdot 6760.71 \approx 770.5 \, \text{kW}
$$
Now substituting into the efficiency formula:
$$
\eta_b = \frac{15}{770.5} \approx 0.0194 \text{ or } 1.94\%
$$

### Summary of Results:
- **5.2.1 Brake Power:** $$ \approx 15 \, \text{kW} $$
- **5.2.2 Mean Speed of Pistons:** $$ \approx 2.87 \, \text{m/s} $$
- **5.2.3 Swept Volume:** $$ \approx 0.067 \, \text{m}^3 $$
- **5.2.4 Induced Volume:** $$ \approx 0.114 \, \text{m}^3/s $$
- **5.2.5 Brake Thermal Efficiency:** $$ \approx 1.94\% $$

Please verify the calculations and assumptions, especially regarding the density of air and the calorific value, as they can vary based on conditions.
- 5.2.1 The engine's brake power is approximately 15 kW. - 5.2.2 The mean speed of the engine's pistons is approximately 2.87 m/s. - 5.2.3 The engine's swept volume is approximately 0.067 m³. - 5.2.4 The engine's induced volume is approximately 0.114 m³/s. - 5.2.5 The brake thermal efficiency is approximately 1.94%.

Upstudy AI Solution

Answer

Solution

Given Data:

5.2.1 The Engine’s Brake Power in kW

5.2.2 The Mean Speed of the Engine’s Pistons in

5.2.3 The Engine’s Swept Volume in

5.2.4 The Engine’s Induced Volume in

5.2.5 The Brake Thermal Efficiency

Summary of Results:

Mind Expander

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