Find the jet fuel mileage (mpg) of a Boeing 787 Dreamliner if: C=0.024, v=900 km/h, 1 gallon=3.8 liters, 1 mile= 1.6 km, energy conversion efficiency=30%, A=2060 ft^2, 1 ft^2=0.093 m^2, drag force = 1/2(CApv^2), p=0.41 kg/m^3 at 10,000 m, jet fuel energy density=35 MJ/liter. I have calculated the drag force using the given information, but cannot figure out how to get from there to the mpg. Every formula I can find uses the mass of the plane and that isn't given as part of the problem.

Question

Find the jet fuel mileage (mpg) of a Boeing 787 Dreamliner if: C=0.024, v=900 km/h, 1 gallon=3.8 liters, 1 mile= 1.6 km, energy conversion efficiency=30%, A=2060 ft^2, 1 ft^2=0.093 m^2, drag force = 1/2(CApv^2), p=0.41 kg/m^3 at 10,000 m, jet fuel energy density=35 MJ/liter. I have calculated the drag force using the given information, but cannot figure out how to get from there to the mpg. Every formula I can find uses the mass of the plane and that isn't given as part of the problem.

Answer 1

To find the jet fuel mileage (mpg) of a Boeing 787 Dreamliner, we need to calculate the fuel consumption rate first and then convert it to miles per gallon. Although the mass of the plane is not given in the problem, we can still proceed by assuming a constant mass and using the energy conversion efficiency.

Here's the step-by-step approach:

1. Start by calculating the fuel consumption rate in liters per hour. We can obtain this value by finding the power consumed by the engines.
- Given: C = 0.024 (drag coefficient), v = 900 km/h (velocity), A = 2060 ft^2 (wing area), p = 0.41 kg/m^3 (air density), and energy conversion efficiency = 30%

2. Calculate the drag force using the formula: drag force = 1/2 * C * A * p * v^2.
- Convert A from square feet to square meters: A = 2060 ft^2 * 0.093 m^2/ft^2.
- Now plug in the given values into the drag force formula to find the force in Newtons (N).

3. Calculate the power consumed by the engines using the formula: power = force * velocity.
- Convert v from km/h to m/s: v = 900 km/h * 1000 m/km * 1/3600 h/s.
- Now multiply the drag force (in N) by the velocity (in m/s) to obtain the power consumed (in Watts).

4. Calculate the fuel consumption rate in liters per hour using the power consumed.
- Given: jet fuel energy density = 35 MJ/liter
- Convert energy density from MJ/liter to Ws/liter by multiplying by 10^6.
- Divide the power consumed by the energy density to get the fuel consumption rate (in liter/s).
- Convert the fuel consumption rate from liter/s to liter/hour.

5. Lastly, convert the fuel consumption rate from liters per hour to miles per gallon (mpg).
- Given: 1 gallon = 3.8 liters, 1 mile = 1.6 km
- Convert the fuel consumption rate from liters per hour to gallons per hour.
- Multiply the fuel consumption rate (in gallons per hour) by the conversion factor (miles/km) to obtain mpg.

By following these steps, you should be able to calculate the jet fuel mileage (mpg) of a Boeing 787 Dreamliner.