GATE CE 2020 Set 1 — Question 44
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Transportation Engineering → Traffic Studies & Flow → Fundamental Flow Relationships
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Question
The relationship between traffic flow rate () and density () is shown in the figure
The shock wave condition is depicted by
The shock wave condition is depicted by
Correct answer
(B) flow changing from point 2 to point 6 (q₂ q₆)
Solution
A shock wave in traffic flow occurs when there is a discontinuity in the flow-density relationship, often due to a sudden change in capacity or demand. This leads to a propagation of the change in traffic conditions (the 'shock wave').Let's analyze the options in the context of the given flow-density () curve:
- Point 1: Represents the maximum flow rate (), which is the capacity of the road. While important, it doesn't directly depict a shock wave condition itself, but rather a state of flow.
- Points 4 and 5: These points have the same flow rate () but different densities. This scenario represents a condition where a shock wave exists, as it indicates a transition between two different traffic states (e.g., free flow to congested flow) at the same flow rate. However, the question asks what depicts the shock wave condition, and option B describes a change in flow that leads to a shock wave.
- Option B: flow changing from point 2 to point 6 (): If traffic conditions change from point 2 to point 6, it means the flow rate decreases () while the density increases (as point 6 is to the right of point 2 on the curve). This situation, where upstream flow (at point 2) is greater than downstream flow (at point 6), implies that vehicles are arriving faster than they can depart, leading to a build-up of vehicles and a backward-moving shock wave (a queue formation). This is a classic depiction of a shock wave forming or propagating.
- Option C: flow changing from point 3 to point 7 (): This implies an increase in flow rate. If , and point 7 is at a higher density, this could represent a transition from a less congested state to a more congested state, but the condition itself doesn't directly describe the formation or propagation of a shock wave as clearly as .
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