Question

1. (25pts) A car has a drag coefficient of C_D=0.3 The area of the car is 24ft². The weight of the car is 3000lbf. The car is travelling at V=75mph through air at sea level (ρ=0.0024 slug/ft³). Treat the rolling friction as μ=0.015. Model the power needed to move the car per the lecture as: . Watch your units.
   1. What is the power needed to travel at 75mph, in units of horsepower (hp)?
   2. How long does it take to travel one mile at a speed of 75mph?
   3. How much energy is used to travel 1 mile at 75mph in this car? Give answer in ft∙lbf and in BTU.
   4. If the car uses 1 gallon of gasoline to travel 20 miles, and if gasoline has an energy density of 129000BTU/gal, what is the efficiency of the car’s engine?

Answer 1

calculate velocity en ft/s :) V=75% 1.4667 ttle = v= loft/s @ Pewer required :- bf7 49.8) X 550 eb fost P= PCOAV3 - tly wor -P- 6.9024) (Lug) XD-3 * 24 (+3)x 103(+4%) 0.015*390° X10 ft 2 (11499-8+ 4950) 350) Islug.ft effoft/sec lo7 1 52 - p = 1 16 449.8 l ebfoft It is asked to calculate in Up :- - p = (16449.8) × t he x ebf.ft P = 29.9 hp? time required to travel I mile :- t = distance travelled at= » t = 475hr speed 75 to Lx3600 sec ③ Energy consumed to 48 sec trand Imile :- 1 t= E = (Power) & (time) E = (16449-8) ebfift X48 rel) E = 789590.4 lbf.ft . ebfift E = 789590.4 debt.tt x 0.001285 Bte TE = 1014.62 Btuel

e calculate Year O .. n = car 1014 - 6 Btu x 100 fuel is required. the efficiency of car :- Energy consumed to travel I müle x100 Energy given up by fuel for samedistance - When I gallon of gal 129000) Btugal El 1. travel 2oniles thers for a mile to gallons is required 15-73) Mar