Question

A section of highway has a free-flow speed of 55 mph and a capacity of 3300 veh/hr. In a given hour, 2100 vehicles were counted at a specified point along this highway section. If the linear speed density relationship applies, what would you estimate the space-mean speed of the vehicles to be?

Answer 1

Answer:

Space mean speed = 44 mi/h

Explanation:

Using Greenshield's linear model

q = Uf ( D - $D^{2}$/Dj )

qcap = capacity flow that gives Dcap

Dcap = Dj/2

qcap = Uf. Dj/4

Where

U = space mean speed

Uf =  free flow speed

D = density

Dj = jam density

now,

Dj = 4 × 3300/55

    = 240v/h

q = Dj ( U - $U^{2}$/Uf)

2100 = 240 ( U - $U^{2}$/55)

Solve for U

U = 44m/h