ESTION 5 In car engines, write out what SI stands for. A four-stroke 2 -cylinder internal combustion engine running at the spee of 240 r/min, has a bore and stroke length of \( 0,380 \mathrm{~m} \) and \( 0,585 \mathrm{~m} \) respectivel The engine develops a brake torque of \( 11,860 \mathrm{kNm} \), while the volumetr efficiency is 0,85 . The air-fuel ratio by volume is \( 7: 1 \). The fuel used in this engir has a calorific value of \( 38600 \mathrm{~kJ} / \mathrm{m}^{3} \). Calculate: \( 5.2 .1 \quad \) The engine's brake power in kW \( 5.2 .2 \quad \) The mean speed of the engine's pistons in \( \mathrm{m} / \mathrm{s} \) \( 5.2 .3 \quad \) The engine's swept volume in \( \mathrm{m}^{3} / \mathrm{s} \) \( 5.2 .4 \quad \) The engine's induced volume in \( \mathrm{m}^{3} / \mathrm{s} \) \( 5.2 .5 \quad \) The brake thermal efficiency

To solve this problem, we need to calculate the engine's brake power, mean speed of the pistons, swept volume, induced volume, and brake thermal efficiency. Let's go step by step. **5.2.1 The engine's brake power in kW** The brake power (P) can be calculated using the formula: \[ P = \frac{T \cdot \omega}{9.549 \cdot 10^3} \] where: - \( T \) is the brake torque (11,860 kNm) - \( \omega \) is the angular speed (in radians per second) First, we need to convert the angular speed from rpm to radians per second: \[ \omega = \frac{2 \pi \cdot n}{60} \] where: - \( n \) is the engine speed (240 rpm) \[ \omega = \frac{2 \pi \cdot 240}{60} = 8 \pi \, \text{rad/s} \] Now, we can calculate the brake power: \[ P = \frac{11,860 \cdot 10^3 \cdot 8 \pi}{9.549 \cdot 10^3} \] \[ P \approx 1,011.5 \, \text{kW} \] **5.2.2 The mean speed of the engine's pistons in m/s** The mean speed of the pistons (v) can be calculated using the formula: \[ v = \frac{2 \cdot \pi \cdot d \cdot n}{60} \] where: - \( d \) is the bore diameter (0.380 m) - \( n \) is the engine speed (240 rpm) \[ v = \frac{2 \cdot \pi \cdot 0.380 \cdot 240}{60} \] \[ v \approx 7.54 \, \text{m/s} \] **5.2.3 The engine's swept volume in m³/s** The swept volume (V) can be calculated using the formula: \[ V = \pi \cdot d^2 \cdot l \] where: - \( d \) is the bore diameter (0.380 m) - \( l \) is the stroke length (0.585 m) \[ V = \pi \cdot (0.380)^2 \cdot 0.585 \] \[ V \approx 0.069 \, \text{m}^3 \] To find the swept volume per second, we multiply by the engine speed: \[ V_{\text{per second}} = V \cdot n \] \[ V_{\text{per second}} = 0.069 \cdot 240 \] \[ V_{\text{per second}} \approx 16.56 \, \text{m}^3/\text{s} \] **5.2.4 The engine's induced volume in m³/s** The induced volume (V_induced) can be calculated using the formula: \[ V_{\text{induced}} = V_{\text{swept}} \cdot \left(1 - \frac{1}{n}\right) \] where: - \( V_{\text{swept}} \) is the swept volume per second (16.56 m³/s) - \( n \) is the engine speed (240 rpm) \[ V_{\text{induced}} = 16.56 \cdot \left(1 - \frac{1}{240}\right) \] \[ V_{\text{induced}} \approx 16.56 \cdot 0.996 \] \[ V_{\text{induced}} \approx 16.53 \, \text{m}^3/\text{s} \] **5.2.5 The brake thermal efficiency** The brake thermal efficiency (η) can be calculated using the formula: \[ \eta = \frac{P}{Q_{\text{in}}} \] where: - \( P \) is the brake power (1,011.5 kW) - \( Q_{\text{in}} \) is the total heat input (in kW) The total heat input (Q_in) can be calculated using the formula: \[ Q_{\text{in}} = \frac{V_{\text{induced}} \cdot \rho \cdot C_p \cdot T_a}{\eta_v} \] where: - \( V_{\text{induced}} \) is the induced volume per second (16.53 m³/s) - \( \rho \) is the density of air (1.225 kg/m³) - \( C_p \) is the specific heat capacity of air (1.005 kJ/kg·K) - \( T_a \) is the air temperature (in K) - \(