GATE CE 2026 Set 1 — Question 42
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Transportation Engineering → Traffic Studies & Flow → Fundamental Flow Relationships
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Question
A road is divided into four sections having varying widths as shown in the figure. Section-2 () represents a capacity constrained condition with respect to the traffic flow passing through Section-1 (). Section-3 () and Section-4 () do not face any such capacity constraint with respect to the flow. A flow-density relationship for unconstrained and constrained flow conditions is shown in the figure. 
If Section-1 observes density , the option representing the correct state of density in Sections 2, 3 and 4 is:
Correct answer
(D) S2 - D4; S3 - D3; S4 - D1
Solution
In Section-1 (), the observed density is on the unconstrained flow curve, corresponding to a flow rate (point 2). Section-2 () is a bottleneck and operates under capacity constrained conditions. For the flow to pass through , it must follow the constrained flow curve. The point on the constrained curve with flow is point 4, which has density . Thus, is at density . Sections 3 and 4 are unconstrained. is wider than , so for the same flow , the density will decrease in the uncongested regime. Point 3 on the unconstrained curve has flow and density . is even wider than , so the density decreases further to (point 1) for the same flow. Therefore, the correct state of density is ; ; .
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