2 Estimate the fuel that would be required to travel in a di

2. Estimate the fuel that would be required to travel in a diesel powered speed boat on a trip from Port Huron, Michigan to Mackinaw Island, Michigan. The boat has two 400 kW engines (max power is 400kW) that operate at 75% power, near the peak efficiency point of the engines. The average speed is 40 miles per hour. How much fuel in gallons must be onboard to make the trip with a 10% reserve? Make the necessary assumptioms.

Port Huron to Mackinaw City (240 miles)

Solution

The power that is supplied by the two engines is,

Power, P = 2*(75% of 400kW) = 600 kW = 600 kJ/s,

since the engines operate at 75% of max. power which is 400kW.

The average speed is given to be 40 miles per hour and the distance to be travelled is 240 miles. Thus,

Time of trip, T = Distance / Average Speed = 6 hours = 6*3600 seconds

us, the total energy required for the trip is, E = P*T = 300*6*3600 kJ.

The higher calorific value of the diesel fuel is, HCV = 44800 kJ/kg (please check on your own). Assuming we utilise the fuel with a 100% efficiency and all the energy of the fuel is converted into mechanical energy, the amount of fuel required to supply the energy for the trip is = E / HCV = 300*6*3600/44800 kg = 144.64 kg approximately

We need a 10% reserve, hence, the actual amount of fuel required is = 1.1 * 144.64 kg = 159.10 kg

Now, 1 gallon equals 3.79 kilograms (kg) approximately. Hence, the amount of fuel in gallons is = 159.10 / 3.79 = 41.98 gallons.

Hence, we need approx. 42 gallons of diesel fuel to make the trip from Port Huron to Mackinaw City.