GATE CE 2019 Set 2 — Question 29
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Transportation Engineering → Traffic Studies & Flow → Speed-Density-Flow
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Question
The speed-density relationship in a mid-block section of a highway follows the Greenshield's model. If the free flow speed is and the jam density is , the maximum flow observed on this section is
Correct answer
(C) (v_f kⱼ)/(4)
Solution
According to Greenshield's model, the speed-density relationship is linear: .
Flow is given by .
To find the maximum flow, we differentiate with respect to and set it to zero:Substituting back into the flow equation:Thus, the maximum flow is .
Flow is given by .
To find the maximum flow, we differentiate with respect to and set it to zero:Substituting back into the flow equation:Thus, the maximum flow is .
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