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 1.45 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.

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Answer:

the velocity of the fuel through the nozzle v= 6.45 ft/s

Explanation:

Given values

Volume =  687 gallons= [tex]2.6 m^3[/tex]

9 refueling transfers

dia of nozzle d= 1.45 inches

each refueling took 2.41 minutes to perform. t= 2.41×60×9= 1247.4 sec

Volume of fuel pumped in time t is give by

V= Avt

A= area of mouth of pipe

v= flow rate

t= time

A= πr^2

A= [tex]\pi\times (\frac{0.0368}{2} )^2 = 0.00106 m^2[/tex]

now substituting the values in equation 1 we get

[tex]2.6= 0.00106\times v \times1247.4[/tex]

v= 1.966 m/sec

v= 6.45 ft/s

the velocity of the fuel through the nozzle v= 6.45 ft/s