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The relation between speed u (in km/h) and density k (number of vehicles / km) for a traffic stream on a road is u = 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).
Correct answer is between '1740,1760'. Can you explain this answer?
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The relation between speedu(in km/h) and densityk(number of vehicles /...
Traffic volume,
q = uk
q = (70 – 0.7 k) k= 70k – 0.7 k2
Maximum possible volume is capacity of road.
For maximum volume
⇒ 70 – 1.4 k = 0
⇒ k = 50 Veh /km
Hence, capacity
C = (70 – 0.7 × 50) × 50
C = 1750 Veh/hr
Most Upvoted Answer
The relation between speedu(in km/h) and densityk(number of vehicles /...
Relation between speed and density:
- The relation between speed (u) and density (k) for the traffic stream on the road is given by the equation u = 70 - 0.7k.
Calculating capacity:
- Capacity is the maximum number of vehicles that can pass a point on the road in one hour.
- The capacity can be calculated by finding the maximum flow rate when speed is at its maximum.
- To find the maximum flow rate, we need to find the point where the gradient of the speed-density curve is zero.
- Taking the derivative of u = 70 - 0.7k with respect to k and setting it to zero, we get 0 = -0.7.
- Solving for k, we get k = 0.
- Substituting k = 0 into u = 70 - 0.7k, we get u = 70 km/h.
- Therefore, the capacity of the road is 70 km/h * 25 vehicles/km = 1750 vehicles/hour.
Validating the answer:
- The given range for the capacity is between 1740 and 1760 vehicles/hour.
- The calculated capacity of 1750 vehicles/hour falls within this range.
- Hence, the correct capacity for the road is between 1740 and 1760 vehicles/hour.
- The relation between speed (u) and density (k) for the traffic stream on the road is given by the equation u = 70 - 0.7k.
Calculating capacity:
- Capacity is the maximum number of vehicles that can pass a point on the road in one hour.
- The capacity can be calculated by finding the maximum flow rate when speed is at its maximum.
- To find the maximum flow rate, we need to find the point where the gradient of the speed-density curve is zero.
- Taking the derivative of u = 70 - 0.7k with respect to k and setting it to zero, we get 0 = -0.7.
- Solving for k, we get k = 0.
- Substituting k = 0 into u = 70 - 0.7k, we get u = 70 km/h.
- Therefore, the capacity of the road is 70 km/h * 25 vehicles/km = 1750 vehicles/hour.
Validating the answer:
- The given range for the capacity is between 1740 and 1760 vehicles/hour.
- The calculated capacity of 1750 vehicles/hour falls within this range.
- Hence, the correct capacity for the road is between 1740 and 1760 vehicles/hour.
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The relation between speedu(in km/h) and densityk(number of vehicles / km) for a traffic stream on a road isu= 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).Correct answer is between '1740,1760'. Can you explain this answer?
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The relation between speedu(in km/h) and densityk(number of vehicles / km) for a traffic stream on a road isu= 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).Correct answer is between '1740,1760'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The relation between speedu(in km/h) and densityk(number of vehicles / km) for a traffic stream on a road isu= 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).Correct answer is between '1740,1760'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The relation between speedu(in km/h) and densityk(number of vehicles / km) for a traffic stream on a road isu= 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).Correct answer is between '1740,1760'. Can you explain this answer?.
The relation between speedu(in km/h) and densityk(number of vehicles / km) for a traffic stream on a road isu= 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).Correct answer is between '1740,1760'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The relation between speedu(in km/h) and densityk(number of vehicles / km) for a traffic stream on a road isu= 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).Correct answer is between '1740,1760'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The relation between speedu(in km/h) and densityk(number of vehicles / km) for a traffic stream on a road isu= 70 – 0.7k. The capacity on this road is _______________ vph (vehicles/hour).Correct answer is between '1740,1760'. Can you explain this answer?.
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