A road is divided into four sections having varying widths as shown in the figure. Section-2 (S2) represents a capacity constrained condition with respect to the traffic flow passing through Section-1 (S1). Section-3 (S3) and Section-4 (S4) do not face any such capacity constraint with respect to the flow. A flow-density re lationship for unconstrained and constrained flow conditions is shown in the figure.

If Section-1 observes density D2, the option representing the correct state of den sity in Sections 2, 3 and 4 is:

The correct option/answer is: S2- D4 ; S3- D3 ; S4- D1

Detailed Step-by-Step Explanation:

1. Analysis of the Road Sections and Graph:
From the given schematic, the road is divided into four sections with varying widths:
• Section-1 (S1) is the wide approach section operating under unconstrained flow conditions.
• Section-2 (S2) is a narrow bottleneck representing a capacity-constrained section.
• Section-3 (S3) has a width between S2 and S1, operating under unconstrained conditions.
• Section-4 (S4) is wider, returning to the width of S1, also operating under unconstrained conditions.

Looking at the flow-density graph:
• There are two curves: the upper curve representing Unconstrained flow and the lower curve representing Constrained flow.
• S1, S3, and S4 operate on the unconstrained curve, while S2 operates on the constrained curve.
• Density _D1 corresponds to a low-density, free-flow state on the unconstrained curve.
• Density _D2 corresponds to the incoming flow state on the unconstrained curve, which has a higher flow rate _q2.
• Density _D3 corresponds to the peak capacity (maximum flow rate _q3) of the constrained flow curve (representing S2).
• Density _D4 corresponds to a high-density, congested state on the unconstrained curve.

2. Traffic State Transitions:
• For Section-1 (S1): The input state is given as density _D2. The corresponding flow rate _q2 is higher than the capacity _q3 of the constrained section S2.

• For Section-2 (S2): Since the incoming flow demand _q2 exceeds the capacity of Section-2 (which is _q3), Section-2 acts as a bottleneck. This capacity constraint forces the traffic in Section-2 to operate under congested, forced flow conditions. Because the bottleneck restricts the flow to its maximum limit and creates a queue, Section-2 experiences a highly congested state. In the given system, this congested state corresponds to the maximum density point _D4.

• For Section-3 (S3): Downstream of the bottleneck, the traffic begins to transition back. S3 is wider and unconstrained. The flow passing through S3 is the restricted flow _q3 coming from the bottleneck. At this flow rate _q3, the intermediate section S3 experiences density _D3.

• For Section-4 (S4): In the final, widest section, the flow remains _q3 but the road width has fully opened up. Under unconstrained free-flow conditions, the traffic recovers completely, resulting in a low density state corresponding to _D1.

Thus, the correct states of density in Sections 2, 3, and 4 are:
• Section-2 (S2): D4
• Section-3 (S3): D3
• Section-4 (S4): D1