Question

A vehicle which is equipped with a 6 cylinder, 2000 cc spark ignition engine is cruising at an average speed of 150 km/h from Ankara to Istanbul on the highway. The mass of the vehicle with single driver is 1200 kg and its projected frontal area is 3 m2. The coefficient of rolling resistance is 0.015 and the discharge coefficient is 0.3. The distance between Istanbul and Ankara is approximately 450 km. Assuming an average brake specific fuel consumption of 250 g/hp-h, calculate how many liters of fuel will be used during this journey ( r fuel = 0.73 g/cc and ambient air density r a=1.2 kg/m3).

Answer 1

Air resistnace acting on the vehicle is:

where r_a is density of ambient air,

c_w is discharge coefficient

A is frontal area of car and

v is vehicle speed in m/s

Rolling resistance is:

where f_r is rolling resistance coefficient,

m is mass of the vehicle with driver

g is gravitaitonal constant

Total resistance force (F) = F_air +F_r = 937.5+176.58 = 1114.08N

Power required by the vehicle (P) = F*v = 1114.08*150/3.6 = 46.420kW = 62.25 hp

Time required for entire journey = distance/speed = 450/150 = 3 h

Mass of fuel consumed = (break specific fuel consumption)*(Power)*(Time) = 250*62.25*3 = 46687.5g

Volume of fuel consumed = (mass of fuel consumed)/(density of fuel) = 46687.5/0.73 = 63955.48 cc = 63.955 liters.

Therefore, 63.955 liters of fuel will be used during this journey