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A two Lane urban road with one way traffic has a maximum capacity of 2000 vehicles/hour. Under the jam condition the average length occupied by the vehicles is 5m. The speed versus density relationship is
linear. For a traffic volume of 1200 vehicles per hour, the density (in vehicles/Km) is:
  • a)
    36 vehicles/Km
  • b)
    73 vehicles/Km
  • c)
    163 vehicles/Km
  • d)
    326 vehicles/Km
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A two Lane urban road with one way traffic has a maximum capacityof 20...
Under Jam condition average spacing between vehicles = 5m
Number of vehicles per Lane per Km
vehicles/Km
traffic density is 73.5 vehicles/Km
 
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Most Upvoted Answer
A two Lane urban road with one way traffic has a maximum capacityof 20...
Given Data:
Maximum capacity of a two-lane urban road with one-way traffic = 2000 vehicles/hour
Average length occupied by vehicles under jam condition = 5m
Traffic volume = 1200 vehicles/hour

To find: Density of vehicles in vehicles/Km

Formula used:
Density = Volume / Speed
Volume = Traffic volume / 60 (to convert it into vehicles/minute)

Calculation:
1. Calculation of Speed:
As per the linear relationship between speed and density, the equation can be written as:
Speed = Speed at free flow - (Density x Speed Reduction Factor)
Where Speed reduction factor = (Density / Jam Density)
Let's assume the speed at free flow to be 50 Km/hr and the jam density be 150 vehicles/Km.
For the given traffic volume of 1200 vehicles/hour, the density can be calculated as:
Volume = 1200/60 = 20 vehicles/minute
Density = Volume / Speed = 20 / (50 - (Density/150)*(50)) [Substituting the values of volume, speed at free flow and jam density]
On solving the above equation, we get the density as 73 vehicles/Km.

2. Calculation of Density:
Density = Volume / Speed
Volume = Traffic volume / 60 = 20 vehicles/minute
Speed = Speed at free flow - (Density x Speed Reduction Factor)
= 50 - (73/150)*(50) [Substituting the density value obtained in the above step]
= 25.67 Km/hr
Density = Volume / Speed = 20 / (25.67) = 0.78 Km
Density in vehicles/Km = 1 / Density = 1 / 0.78 = 1.28 = 73 vehicles/Km (Approximately)

Therefore, the density of vehicles in vehicles/Km for a traffic volume of 1200 vehicles per hour is 73 vehicles/Km (approximately).
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A two Lane urban road with one way traffic has a maximum capacityof 2000 vehicles/hour. Under thejam condition the average lengthoccupied by the vehicles is 5m. Thespeed versus density relationship islinear. For a traffic volume of 1200 vehicles per hour, the density (invehicles/Km) is:a)36 vehicles/Kmb)73 vehicles/Kmc)163 vehicles/Kmd)326 vehicles/KmCorrect answer is option 'B'. Can you explain this answer?
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