Question

Given a Greenshields linear density speed-relationship, S = 55.0 - 0.45 D. Flow-speed relationship is Flow=1100S-S^2/g and flow-density relationship is Flow=55D-0.45D^2

1.What are the values for the following:

a) free flow speed __________________________

b) jam density ____________________

c) capacity _______________________

Answer 1

S = 55.0 - 0.45 D

the greenshield model

$S=S_f-\frac{S_f}{Dj}D$

thus

free flow speed (S_f): 55

jam density (D_j)=55/0.45=122

To determine the capacity of the site need to determine the maximum flow:

$\frac{d q}{dD}=55-0.9D=0$

$D=\frac{55}{0.9}=61.1$

density at maximum flow 61

Flow= $55D-0.45D^2$

$=55(61.1)-0.45(61.1)^2=1680.5$

capacity=1680.5