Thursday, September 3, 2009

Fluid Traffic Dynamics

I encounter a traffic flow problem everyday on my commute to work. For several miles in Farmington Hills, eastbound I-696 has four lanes. A mile or so after Orchard Lake Road the highway expands into six lanes. Every day, without fail, the half mile leading up to the expansion and through the first mile of the expansion the speed of traffic slows down. One would think that with more lanes the rate of travel would increase, but that is not the case. Every day I angrily wonder why that is. I decided to turn to engineering and fluid dynamics to explain this phenomenon.

The volumetric flow rate of a system is a measure of the volume of fluid passing a point in the system per unit time. The volumetric flow rate (V) can be calculated as the product of the cross- sectional area (A) for flow and the average flow velocity (v). V=Av or V/A=v. The velocity of a fluid through a pipe is inversely proportional to the area. As the area gets bigger, the velocity gets smaller.

Does this apply to traffic, treating the road as a pipe, or area, and the cars as fluid? The volume of cars is constant. The area increases with more lanes. And the result can be seen is that the flow decreases when the area increases.

Is this accurate? Is this a good idea to make these assumptions? Probably not. I suspect the issue is more a result of idiot drivers (it is Michigan, although bad drivers are universal). Oh well, it is a fun theory to think about and makes the drive go by quicker.

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