A four cylinder, four-stroke cycle petrol engine has a bore 90 mm and a piston stroke 90 mm.Running at 80 revs/s, the indicated mean effective pressure is 630 kN/m2 and the fuelconsumption in an hour is 12 kg. The mechanical efficiency is 80 %. The calorific value of thefuel is 43 MJ/kg. Determine:(i) The indicated power. (6 marks)(ii) The brake power. (3 marks)(iii) The brake thermal efficiency. (5 marks)(iv) The brake mean effective pressure
Question
A four cylinder, four-stroke cycle petrol engine has a bore 90 mm and a piston stroke 90 mm.Running at 80 revs/s, the indicated mean effective pressure is 630 kN/m2 and the fuelconsumption in an hour is 12 kg. The mechanical efficiency is 80 %. The calorific value of thefuel is 43 MJ/kg. Determine:(i) The indicated power. (6 marks)(ii) The brake power. (3 marks)(iii) The brake thermal efficiency. (5 marks)(iv) The brake mean effective pressure
Solution
(i) The indicated power (IP) can be calculated using the formula:
IP = n * L * A * N * IMEP / 2
where: n = number of cylinders = 4 L = stroke length = 90 mm = 0.09 m A = cross-sectional area of the cylinder = π * (bore/2)^2 = π * (0.09/2)^2 = 0.00636 m^2 N = engine speed = 80 rev/s = 4800 rev/min IMEP = indicated mean effective pressure = 630 kN/m^2 = 630000 N/m^2
Substituting these values into the formula gives:
IP = 4 * 0.09 * 0.00636 * 4800 * 630000 / 2 = 216864 W = 216.864 kW
(ii) The brake power (BP) can be calculated using the formula:
BP = IP * mechanical efficiency
Substituting the given mechanical efficiency of 80% (or 0.8) gives:
BP = 216.864 * 0.8 = 173.4912 kW
(iii) The brake thermal efficiency (ηbth) can be calculated using the formula:
ηbth = BP / (fuel consumption rate * calorific value of fuel)
The fuel consumption rate is 12 kg/hour = 12/3600 kg/s = 0.00333 kg/s
The calorific value of the fuel is 43 MJ/kg = 43000000 J/kg
Substituting these values into the formula gives:
ηbth = 173491200 / (0.00333 * 43000000) = 0.122 or 12.2%
(iv) The brake mean effective pressure (BMEP) can be calculated using the formula:
BMEP = BP * 2 / (n * L * A * N)
Substituting the known values into the formula gives:
BMEP = 173491200 * 2 / (4 * 0.09 * 0.00636 * 4800) = 504000 N/m^2 = 504 kN/m^2
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