In 1923, the United States Army 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 37 h. During the flight, the re

Question

In 1923, the United States Army 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 37 h. During the flight, the refueling planes were able to air-transfer a total of 687 of fuel to the plane in 9 refueling transfers.

Assume that the refueling nozzle had a diameter of 1.55 in and each refueling took 2.51 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

Hi Elena!

The first thing to do for this problem is to calculate the cross-sectional area of the nozzle. To do this we use the formula

A = pi*r^2

where,

A = cross-sectional area

r = radius

We know,

r = D/2

where,

D = diameter

therefore

A = (1/4)*pi*D^2.

A = (1/4)*pi*(1.55 in)^2

Now let's figure out how much time total it took to refuel the plane.

t[total] = #refuels*time[refuel]

t[total] = 9*(2.51 mins)

Now let's calculate the velocity of the fuel in the nozzle.

The units are not clear for the amount of fuel, let's just assume gallons.

Flow rate = Volume/t[total]

Flow Rate = 687 gallons/(22.59 mins)

Flow Rate = 30.4 gallons/min

Now we convert gallons to cubic inches to help later.

1 gallon = 231 cubic inches

Flow rate = 30.4*231 = 7022 cubic inches/min

From this point, you calculate velocity.

Flow rate = A*velocity

velocity = Flow Rate/A

velocity = 7022 cubic inches per min/(.25*pi*1.55^2)

velocity = inches/min