5.2. Consider the situation of when two lanes of traffic merge down to one lane, as shown in Figure 5.36. The densities and velocites at the far left and right are known. Assume a steady flow, so the density and velocity do not depend on time, and assume all variables are non-negative. (a) Using the result of Exercise 5.1(a), find an equation that relates the values on the right with those on the left. P2,V2 P3;V3 Figure 5.36 Configuration of roadway used for Problem 5.2.

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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5.2. Consider the situation of when two lanes of traffic merge down to one
lane, as shown in Figure 5.36. The densities and velocites at the far left and
right are known. Assume a steady flow, so the density and velocity do not
depend on time, and assume all variables are non-negative.
(a) Using the result of Exercise 5.1(a), find an equation that relates the values
on the right with those on the left.
P1,V1
P2;V2
P3;V3
Figure 5.36 Configuration of roadway used for Problem 5.2.
5.1. This problem considers various consequences of the traffic flow equation.
(a) Show that given any two points a and b on the x-axis, with a < b,
p(x, t)dx = J(pa) – J(p6),
dt
where pa = p(a, t) and
ical terms.
Pb = p(b, t). Interpret the above equations in phys-
Transcribed Image Text:5.2. Consider the situation of when two lanes of traffic merge down to one lane, as shown in Figure 5.36. The densities and velocites at the far left and right are known. Assume a steady flow, so the density and velocity do not depend on time, and assume all variables are non-negative. (a) Using the result of Exercise 5.1(a), find an equation that relates the values on the right with those on the left. P1,V1 P2;V2 P3;V3 Figure 5.36 Configuration of roadway used for Problem 5.2. 5.1. This problem considers various consequences of the traffic flow equation. (a) Show that given any two points a and b on the x-axis, with a < b, p(x, t)dx = J(pa) – J(p6), dt where pa = p(a, t) and ical terms. Pb = p(b, t). Interpret the above equations in phys-
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