GATE CE 2026 Set 2 — Question 60
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Transportation Engineering → Traffic Studies & Flow → Speed-Density-Flow
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Question
For a given traffic stream, the speed-density relationship is given as:where is the mean speed (in km/h), and is the density (in veh/km).Considering as , and as , the maximum flow (in veh/h) for the given stream is __________ (rounded off to the nearest integer).
Correct answer
3300 to 3350
Solution
The relationship between flow (), density (), and speed () is .
1.Expression for Flow:
2.Finding Maximum Flow:
To find the density at maximum flow, differentiate with respect to and set to zero:3.Calculating Maximum Flow ():
Substitute back into the flow equation:Given and :Rounding to the nearest integer, the maximum flow is .Continue learning with Success Tracker
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