GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 31 of 65

Marks: +1, -0

The speed-density relationship in a mid-block section of a highway follows the Greenshield's model. If the free flow speed is

{V}_{ {f}}

and the jam density is

{k}_{ {j}}

, the maximum flow observed on this ection is

Solution:

{Q}=[\;{-V_{f}}/{ {K}_{ {j}}} {K}+ {V}_{ {f}}] {K}

....(i)

\;{d Q}/{d K}=\;{-V_{f}}/{K_{j}} × 2 K+V_{f}=0

⇒ \;\; {K}=\;{ {K}_{ {1}}}/{2}

∴ \;\; Q=[\;{-V_{f}}/{K_{j}} × \;{K_{j}}/{2}+V_{f}] \;{K_{1}}/{2}=\;{V_{f} K_{j}}/{4}

Go to Question:

Prev Question

Next Question