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

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.