During a dynamometer test a 4 cylinder, 4 stroke diesel engine develops an indicated meaneffective pressure of 850 KN/m2 at an engine speed of 2000rpm. The engine has a bore of93mm and stroke of 91mm. The test runs for 5 min, during which time 0.8kg of fuel isconsumed. Mechanical efficiency is 83%. Calorific value of the fuel is 43MJ/kg.Calculatei) The indicated power and Brake power (6 marks)ii) The energy supplied from the fuel per second. (5 marks)iii) The indicated and brake thermal efficiency. (6 marks)iv) The Brake specific fuel consumption in kg/KWh.
Question
During a dynamometer test a 4 cylinder, 4 stroke diesel engine develops an indicated meaneffective pressure of 850 KN/m2 at an engine speed of 2000rpm. The engine has a bore of93mm and stroke of 91mm. The test runs for 5 min, during which time 0.8kg of fuel isconsumed. Mechanical efficiency is 83%. Calorific value of the fuel is 43MJ/kg.Calculatei) The indicated power and Brake power (6 marks)ii) The energy supplied from the fuel per second. (5 marks)iii) The indicated and brake thermal efficiency. (6 marks)iv) The Brake specific fuel consumption in kg/KWh.
Solution
Sure, let's break down the problem step by step.
i) The indicated power (IP) and Brake power (BP)
The indicated power can be calculated using the formula:
IP = n * N * A * L * IMEP / (60 * 1000)
where: n = number of power strokes per minute = 2 (for a 4-stroke engine) N = engine speed in RPM = 2000 A = cylinder area = π * (bore/2)^2 = π * (0.093/2)^2 m^2 L = stroke length = 0.091 m IMEP = indicated mean effective pressure = 850 kN/m^2 = 850 * 10^3 N/m^2
Substituting the values, we get the indicated power.
The brake power can be calculated using the mechanical efficiency (ηm):
ηm = BP / IP
Rearranging for BP gives:
BP = ηm * IP
Substitute the values to get the brake power.
ii) The energy supplied from the fuel per second
This can be calculated using the formula:
Energy supplied = mass of fuel consumed per second * calorific value of fuel
The mass of fuel consumed per second can be calculated as:
mass of fuel consumed per second = total mass of fuel consumed / total time = 0.8 kg / (5 * 60) seconds
Substitute the values to get the energy supplied from the fuel per second.
iii) The indicated and brake thermal efficiency
The indicated thermal efficiency (ηith) can be calculated as:
ηith = IP / (Energy supplied per second)
The brake thermal efficiency (ηbth) can be calculated as:
ηbth = BP / (Energy supplied per second)
Substitute the values to get the indicated and brake thermal efficiencies.
iv) The Brake specific fuel consumption in kg/KWh
This can be calculated using the formula:
BSFC = mass of fuel consumed per hour / BP
The mass of fuel consumed per hour can be calculated as:
mass of fuel consumed per hour = total mass of fuel consumed / total time * 3600 = 0.8 kg / (5 * 60) * 3600 kg/h
Substitute the values to get the brake specific fuel consumption.
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