GATE CE 2025 Set 1 — Question 40
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Transportation Engineering → Traffic Studies & Flow → Speed-Density-Flow
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Question
The speed-density relation on a one-way, single lane road is shown in the figure, where speed is in km/hour and density is in vehicles/km. The maximum flow (in vehicles/hour) on this road is
Correct answer
(A) 2500
Solution
Flow is given by .
From the graph:
To find the maximum flow, set :
vehicles/km.
Since lies within the range , the maximum flow is:
vehicles/h.
Comparing the two ranges, the overall maximum flow is 2500 vehicles/h.
From the graph:
1.For , km/h. Thus, . The maximum flow in this range is vehicles/h.
2.For , the relation is linear: .
In this range, .To find the maximum flow, set :
vehicles/km.
Since lies within the range , the maximum flow is:
vehicles/h.
Comparing the two ranges, the overall maximum flow is 2500 vehicles/h.
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