Background on Turbulent Flow

It is fairly safe to state that, except for flow through porous media, the environment experiences turbulent flow. The reason that we have not used a river, lake, or the atmosphere as an application in an example in Chapter 2 is that these flows are always turbulent. The example simply would not have been realistic. To emphasize this point, we will consider the constriction of a water or air flow that would be required to have the other option, laminar flow. 

An experimentally based rule-of-thumb is that laminar flow often occurs when the pipe Reynolds number, Vdjv, is less than 2,000, or when an open channel Reynolds number, Vhjv, is less than 500, where V is the cross-sectional mean velocity, d is the pipe diameter, v is the kinematic viscosity of the fluid, and h is the channel depth. The diameter or depth that would not be exceeded to have laminar flow by these experimental criteria is given in Table 5.1. 

It is convenient to divide the velocity and concentration traces into temporal mean values and fluctuating components  

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