Question

In 1923, the United States Army (there was no United States 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 39 h. 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 in and each refueling took 2.45 min 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 volume of fuel transfer = V = 687 gallons = 2.6 m³

Diameter of refueling nozzle = d = 1.75 in = 4.445 x 10^-2 m

Number of refueling transfers = n = 9

Time taken for one refueling transfer = t = 2.45 min = 147 sec

Velocity of fuel through the nozzle = v

Cross-sectional area of the nozzle = A

A = d²/4

A = (4.445x10^-2)²/4

A = 1.552 x 10^-3 m²

The total volume transferred is equal to the volumetric flow rate times the total time taken.

V = (Av)(nt)

2.6 = (1.552x10^-3)v(9)(147)

v = 1.266 m/s

Velocity of the fuel through the nozzle = 1.266 m/s