o reduce the drag coefficient and thus to improve the fuel efficiency, the frontal area of a car is to be reduced. Determine the amount of fuel and money saved per year as a result of reducing the frontal area from 18 to 14 ft2. Assume the car is driven 12,000 mi a year at an average speed of 55 mi/h. Take the density and price of gasoline to be 50 lbm/ft3 and $3.10/gal, respectively; the density of air to be 0.075 lbm/ft3, the heating value of gasoline to be 20,000 Btu/lbm; and the overall efficiency of the engine to be 30 percent. Take the drag coefficient as CD

Complete question

To reduce the drag coefficient and thus to improve the fuel efficiency, the frontal area of a car is to be reduced. Determine the amount of fuel and money saved per year as a result of reducing the frontal area from 18 to 14 ft2. Assume the car is driven 12,000 mi a year at an average speed of 55 mi/h. Take the density and price of gasoline to be 50 lbm/ft3 and $3.10/gal, respectively; the density of air to be 0.075 lbm/ft3, the heating value of gasoline to be 20,000 Btu/lbm; and the overall efficiency of the engine to be 30 percent. Take the drag coefficient as CD=0.3 for a passenger car.

22.22%

$57

Explanation:

From the question we are told that

Initial area of frontal area

Final area of frontal area

Distance covered a year

Average speed a year

Density

Price

Density of air

Heating value of gasoline

Efficiency

Drag coefficient

Generally the equation for drag force is mathematically given as

where

Generally the equation for work done W is mathematically given as

where

Generally the equation for overall efficiency is mathematically given as

where

Generally the equation for reduction fee with change in frontal area is mathematically given as

Where

if

Therefore

if

Generally the equation for reduction of fuel is mathematically given as

where

Fuel reduction price by reducing front area is 22.22%

Money saved per year is $57

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