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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
-
- 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 |
