A four stroke automobile engine operates at a fuel-air ratio of 0.05, volumetric efficiency of 90% and indicated thermal efficiency of 30%. Given that the calorific value of the fuel is 45 MJ/kg and the density of air at intake is 1 kg/m³, the indicated mean effective pressure for the engine is

Concept:

• Fuel-air ratio, \( \frac{F}{A} = 0.05 \)
• Volumetric efficiency, \( \eta_v = 90\% = 0.9 \)
• Indicated thermal efficiency, \( \eta_{ith} = 30\% = 0.3 \)
• Calorific value of fuel, \( CV = 45 \, \text{MJ/kg} = 45,000 \, \text{kJ/kg} \)
• Density of air at intake, \( \rho_{air} = 1 \, \text{kg/m}^3 \)

Step 1: Calculate mass of air inducted per cycle

Assuming displacement volume = 1 m³ (for simplification):

\( m_{air} = \eta_v \times \rho_{air} \times V_d = 0.9 \times 1 \times 1 = 0.9 \, \text{kg} \)

Step 2: Calculate mass of fuel supplied per cycle

\( m_{fuel} = \left( \frac{F}{A} \right) \times m_{air} = 0.05 \times 0.9 = 0.045 \, \text{kg} \)

Step 3: Calculate energy input per cycle

\( E_{in} = m_{fuel} \times CV = 0.045 \times 45,000 = 2,025 \, \text{kJ} \)

Step 4: Determine indicated work output per cycle

\( W_i = \eta_{ith} \times E_{in} = 0.3 \times 2,025 = 607.5 \, \text{kJ} \)

Step 5: Calculate Indicated Mean Effective Pressure (IMEP)

For a four-stroke engine (work per full cycle = 2 revolutions):

\( \text{IMEP} = \frac{W_i}{V_d} = \frac{607.5 \, \text{kJ}}{1 \, \text{m}^3} = 607.5 \, \text{kPa} = 6.075 \, \text{bar} \)