GATE CE 2022 Set 2 — Question 28
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Transportation Engineering → Traffic Studies & Flow → Fundamental Flow Relationships
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Question
For a traffic stream, is the space mean speed, is the density, is the flow, is the free flow speed, and is the jam density. Assume that the speed decreases linearly with density.Which of the following relation(s) is/are correct?
Correct answer
(B) q = v_f k - ((v_f)/(kⱼ)) k²; (D) q = kⱼ v - ((kⱼ)/(v_f)) v²
Solution
According to the Greenshields linear speed-density model:Flow is defined as the product of density and speed: .Case 1: Expressing in terms of
Substituting the expression for :This matches option (B).Case 2: Expressing in terms of
From the speed-density relationship, we can express as:Substituting this into :This matches option (D).Therefore, both (B) and (D) are correct.
Substituting the expression for :This matches option (B).Case 2: Expressing in terms of
From the speed-density relationship, we can express as:Substituting this into :This matches option (D).Therefore, both (B) and (D) are correct.
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