Question

In 1923, the United States Army (there was no U.S. Air Force at that time) set a record for in-flight refueling of airplanes. Using two refueling planes, an Airco DH-4B biplane was able to remain in flight for 35 hours. During the flight, the refueling planes were able to air-transfer a total of 687 gallons of fuel to the plane in 9 refueling transfers. Assume that the refueling nozzle had a diameter of 1.75 inches and each refueling took 2.41 minutes to perform. Calculate the velocity of the fuel through the nozzle. Assume that the fuel filled the entire cross-sectional area of the nozzle.

Answer 1

Total fuel transferred = V₀ = 687 gallons = 2.6 m³

Number of refueling transfers = 9

Fuel transferred in 1 refueling transfer = V₁ = 2.6/9 = 0.289 m³

Time for 1 refueling transfer = t = 2.41 minutes = 144.6 sec

Diameter of refueling nozzle = d = 1.75 inches = 4.445 x 10^-2 m²

Velocity of fuel through the refueling nozzle = v

Area of refueling nozzle = A = d²/4

A = (4.445 x 10^-2)²/4

A = 1.551 x 10^-3 m²

Flow rate of fuel through the refueling nozzle = Q

Q = V₁/t

Q = 0.289/144.6

Q = 2 x 10^-3 m³/s

Q = Av

2 x 10^-3 = (1.551 x 10^-3)v

v = 1.29 m/s

Velocity of fuel through the refueling nozzle = 1.29 m/s