GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 61 of 65

Marks: +1, -0

The speed-density relationship of a highway is given as

{u}=100-0.5 {k}

where,

{u}=

speed in

{km}

per hour,

{k}=

density in vehicles per

{km}

. The maximum flow (in vehicles per hour, round off to the nearest integer) is ________

Solution:

Given that,

{u}=100-0.5 {k}

Maximum flow

=\;{u_{ {f}} k_{\;\text "jam "\;}}/{4}

{u} = {u}_{ {f}}(1- {k}{/} {k}_{ {j}})

{u} \;\; =100(1-(0.5 {k} {/} 100))

=100(1- {k} {/} 200)

therefore,

u_{f}=100

and

k_{j}=200

so, maximum flow

=\;{200 × 100}/{4}

=5000

vehicles /hr

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