Assume that the flow-density on a roadway looks as follows: (0,0) (kamax ¹9max) k (kjam, 0) If the capacity, qmax, is 2,286 veh/hour, jam density, Kjam, is 167 veh/mi and the free flow speed (maximum speed) is 64 mi/hr, what is the density (in veh/mi) at a congested flow of 1200 veh/hour?
Assume that the flow-density on a roadway looks as follows: (0,0) (kamax ¹9max) k (kjam, 0) If the capacity, qmax, is 2,286 veh/hour, jam density, Kjam, is 167 veh/mi and the free flow speed (maximum speed) is 64 mi/hr, what is the density (in veh/mi) at a congested flow of 1200 veh/hour?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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#### Graph Description
The graph demonstrates the flow-density relationship where the horizontal axis (k) represents the density of vehicles (in vehicles per mile, veh/mi), and the vertical axis (q) represents the flow of vehicles (in vehicles per hour, veh/hour).
Key Points on the Graph:
- (0,0): Indicates no vehicles on the road, resulting in zero flow.
- \((k_{q_{max}}, q_{max})\): Represents the maximum flow point \((q_{max})\), where the road's capacity is reached.
- \((k_{jam}, 0)\): Represents the jam density \((k_{jam})\), where the roadway is at full capacity, and the flow drops to zero due to a traffic jam.
#### Problem Statement
Given the following parameters:
- Capacity, \( q_{max} \) = 2,286 veh/hour
- Jam density, \( k_{jam} \) = 167 veh/mi
- Free flow speed (maximum speed) = 64 mi/hr
**Question:** What is the density (in veh/mi) at a congested flow of 1200 veh/hour?
To solve this problem, use the following linear relationship between flow and density on the congested side of the graph.
#### Steps to Solve:
1. **Identify the Parameters:**
- \( q = 1200 \) veh/hour
- \( q_{max} = 2,286 \) veh/hour
- \( k_{jam} = 167 \) veh/mi
2. **Use the Linear Equation for Congested Flow:**
The linear equation relating flow (q) and density (k) in the congested region is derived from the two points \((k_{q_{max}}, q_{max})\) and \((k_{jam}, 0)\).
The equation of the line is:
\[
q = q_{max} - \frac{q_{max}}{k_{jam}}(k - k_{q_{max}})
\]
Simplify and solve for k when \( q = 1200 \) veh/hour:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42c7cd09-242c-4485-83c6-76fce27f0b64%2F639c5d10-2f73-4747-9403-1e428a26ed9b%2Fhdhxncq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Flow-Density Relationship on a Roadway
Understanding the flow-density relationship on a roadway is crucial for traffic engineering and management. The following graphical representation outlines this important relationship:
#### Graph Description
The graph demonstrates the flow-density relationship where the horizontal axis (k) represents the density of vehicles (in vehicles per mile, veh/mi), and the vertical axis (q) represents the flow of vehicles (in vehicles per hour, veh/hour).
Key Points on the Graph:
- (0,0): Indicates no vehicles on the road, resulting in zero flow.
- \((k_{q_{max}}, q_{max})\): Represents the maximum flow point \((q_{max})\), where the road's capacity is reached.
- \((k_{jam}, 0)\): Represents the jam density \((k_{jam})\), where the roadway is at full capacity, and the flow drops to zero due to a traffic jam.
#### Problem Statement
Given the following parameters:
- Capacity, \( q_{max} \) = 2,286 veh/hour
- Jam density, \( k_{jam} \) = 167 veh/mi
- Free flow speed (maximum speed) = 64 mi/hr
**Question:** What is the density (in veh/mi) at a congested flow of 1200 veh/hour?
To solve this problem, use the following linear relationship between flow and density on the congested side of the graph.
#### Steps to Solve:
1. **Identify the Parameters:**
- \( q = 1200 \) veh/hour
- \( q_{max} = 2,286 \) veh/hour
- \( k_{jam} = 167 \) veh/mi
2. **Use the Linear Equation for Congested Flow:**
The linear equation relating flow (q) and density (k) in the congested region is derived from the two points \((k_{q_{max}}, q_{max})\) and \((k_{jam}, 0)\).
The equation of the line is:
\[
q = q_{max} - \frac{q_{max}}{k_{jam}}(k - k_{q_{max}})
\]
Simplify and solve for k when \( q = 1200 \) veh/hour:
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