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Unformatted text preview: CIV ENG 376: Homework #8 Due on Friday, Dec. 2 Instructor: Marco Peng Chen Peng Chen CIV ENG 376 (Instructor: Marco ): Homework #8 Problem 1 When the accident happened at 8:00 am, the capacity would drop to 2000 vph, which caused a shock wave from downstream to upstream. According to the triangular flow-density relation as shown in the Figure 1,we can calculate the speed of the shock wave, which is w s = 3000- 2000 60- 240 =- 50 9 mph Figure 1: Flow-density Relationship When the accident was cleared, the capacity at downstream would return back to 4000 vph, which would issue an acceleration wave at the speed of 12.5 mph from downstream to upstream. The acceleration wave would eventually catch up with the shock wave, then the queue was cleared. The critical state was that the queue would be cleared just at the Point A, which was shown in Figure 2.According to the figure, we can calculate that the accident was cleared at t =- 5- 50 / 9 60-- 5- 12 . 5 60 = 30 min Thus, the accident must be clear before 8:30 am in order to prevent the congestion caused by the accident affecting the diverging traffic at point A....
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- Fall '11