Your car\'s fuel efficiency is e = 26 miles per gallon. The fuel pump pulls fuel

Question

Your car's fuel efficiency is e = 26 miles per gallon. The fuel pump pulls fuel from the tank at the same speed v at which the car itself moves (so if the car is moving 1 mile per hour, the fuel moves through the pump at 1 miles per hour). The fuel pump pulls fuel at speed v through a hose with cross-sectional area A. What is the cross-sectional area of the hose in square inches? What is it in square millimeters? (1 gallon = 231 in3. You need to find the volume of fuel pumped per time in terms of v and A. Fuel efficiency is distance traveled per fuel pumped, which is equal to speed v divided by fuel pumped per time. The time dependence cancels out. Fuel efficiency has units distance per volume.)

in^2

mm^2

Explanation / Answer

1 gallon = 231 in^3

efficiency = e = 26 miles / gallon = 26 / 231 = 0.11255 miles / in^3

1 mile = 63360 inch

efficiency = e =  0.11255 x 63360 in / in^3 = 7131.428 in^-2

efficiency = e = v / ( Area x v )

Area = 1 / e = 1/7131.428 = 0.00014022 in^2

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cross-sectional area of the hose = A =  0.00014022 in^2

1 inch = 25.4 mm

cross-sectional area of the hose =  0.00014022 x 25.4^2 = 0.0905 mm^2

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