GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 65 of 65

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The space mean speed (kmph) and density (vehicles/km) of a traffic stream are linearly related. The free flow speed and jam density are

80 {kmph}

and 100 vehicles/km respectively. The traffic flow (in vehicles/h, up to one decimal place) corresponding to a speed of

40 {kmph}

Solution:

V_{f}=

Free mean speed

=50 {kmph}

k_{j}=

Jam density

=100 {veh} {/} {km}

As per linear model (green-shield)

V=V_{f}(1-\;{k}/{k_{j}})

\Rightarrow

Density @ speed

=40 {kmph}

40=80(1-\;{k}/{100})=50 {veh} {/}{km}

Traffic flow @ density 50 veh/km @ speed

40 {kmph}

q \;\; =V k

q \;\; =v_{f}(k-\;{k^{2}}/{k_{j}}) ⇒ 80(50-\;{50^{2}}/{100})

\;\; =2000 {veh}{/} {km}

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