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On an urban road, the free mean speed was measured as 70 kmph and the average spacing between the vehicles under jam condition as 7.0 m. The speed-flow-density equation is given by
U = Usf 1 - k and q = UK k1
where, U → space-mean speed (kmph); Usf → free mean speed (kmph); k → density (veh/km); kj → jam density (veh/ km); q → flow (veh/hr). The maximum flow (veh/hr) per lane for this condition is equal to
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- 2000
- 2500
- 3000
- None of these
- 2000
Correct Option: B
u = usf | ![]() | 1 - | ![]() | ||
kj |
q = uk
= usf | ![]() | 1 - | ![]() | |||
k | kj |
⇒ q = usf | ![]() | 1 - | ![]() | k | |
kj |
Diff. w.r.t.k,
= 0 ⇒ usf | ![]() | 1 - | ![]() | = 0 | ||
dk | kj |
⇒ k = | ||
2 |
∴ qmax = usf = | ![]() | 1 - | ![]() | × | = usf × | ||||
2 | 2 | 4 |
= 70 × | = 2500 | |
7 × 4 |