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GATE 2023 CE (CE1) – Question 46

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 2 marks · Multiple choice

A plot of speed-density relationship (linear) of two roads (Road A and Road B) is shown in the figure.

[Figure: speed against density. Road A is a straight line from the free speed $u_A$ on the speed axis to the jam density $k_A$ on the density axis. Road B is another straight line from $u_B$ to $k_B$, with $u_A > u_B$ and $k_A < k_B$.]

If the capacity of Road A is $C_A$ and the capacity of Road B is $C_B$, what is $\frac{C_A}{C_B}$ ?

Diagram for GATE 2023 CE (CE1) question 46
  1. $\frac{k_A}{k_B}$
  2. $\frac{u_A}{u_B}$
  3. $\frac{k_Au_A}{k_Bu_B}$
  4. $\frac{k_Au_B}{k_Bu_A}$

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Show answer and explanation

Correct answer: (C) $\frac{k_Au_A}{k_Bu_B}$

Explanation

For a linear speed-density relation the capacity is $q_{max} = \frac{u_fk_j}{4}$. So $C_A = \frac{u_Ak_A}{4}$ and $C_B = \frac{u_Bk_B}{4}$, and the ratio is $\frac{k_Au_A}{k_Bu_B}$.