Question

Problem 2 (40%). While driving, some of a car's kinetic energy is lost to air drag. We would like to estimate the importance of air drag using dimensional analysis and the Buck- ingham a theorem. The relevant parameters are the drag force (FD), the frontal surface area (A) and velocity of the car (v), as well as the density of air (Pair = 1 kg/m3). Answer the following questions: 1. Derive the expression of the drag force as a function of the other relevant parameters using the table method. You can assume the constant that emerges in the dimensional analysis to be equal to 1. 2. The amount of energy lost to air drag (Ed) is given by the drag force multiplied by distance travelled (d), while the car's kinetic energy is given by Ek = mcar v2. Given that the car has mass mcar = 103 kg, frontal area A = 3 m², and length 1 = 4 m, calculate the ratio between Ed and Ek as a function of d. 3. Given the average distance between city stop signs is d = 50 m, does air drag matter in city driving? Given the average distance between highway exits is d = 2000 m, does air drag matter in highway driving?

Answer 1

Joon- Griven data - Pair = 1 kg/m² According to Bucking ham - Theorem Drag force (F) = f of (A, 6, 8) dependable Total number of fundamental variable (m) no. of fundamental variable ) 80 Number of IT-term = m-h = 4-3 - irst it-term T = A & B G C FD (1) writting the dimension on both sides [MUR] = [12] @ (LT-173 (ML. 37 [ MLT-2] [mper'1 - [1784+b=3C' Crib-mjet! comparing the power of the dimension on both sidei (+1=0 -b-2=0 gatb-3ct1=0 gat2 ga-2 +3+1 =0 =0 a =-1) substitutes the value of a, b, c inequal o T = A 6 -2 -1 FD Fo Fo = IT. AS42 = K SA 02 ie

put the value of constaut K=1 Amount of energy Lost to drag (Ed = drag for at drogforo x distan - Foxd = Auxd = 1x 3x2²xd carls kinetic energy (EK) = I meart = 1 x 103 262 = 5008² Ratio = 3ud 5000 3) For city stop sign d= 50m Aug distance between highway d = 2000m For airdrag & Ed = 30²,50 = 15002 which is less than care driving kinetic energy so the air drag matter is possible to driving in highway,