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 Inspection of a freeway data set reveals a free flow speed of 60 mph, a jam density of 180 vehicles per mile per lane, and an observed maximum flow of 2000 vehicles per hour. Determine the linear equation for velocity for these conditions, and determine the speed and density at maximum flow conditions. How do the theoretical and observed conditions compare? [Solution Shown Below]
Solution vs= vf – vf/kj k (mph) vs = 60 – 60/180 k = 60 – 0.333k q = vsk q = 60k-0.333k2 dq/dk = 60 –2(0.333)k 60 = 2(0.333)k k= 90. 0 = kj/2 half of jam density vm= 60-60/180 (90) = 30 mph = vf/2 = half of free flow speed q= vs k q = 30 (90) = 2700vph > 2000 vph The theoretical value does not account for the field conditions that influence maximum flow.
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