##### Page 2, Turbulence & Rheology, Dr. D. Penney

__Reynolds Number (continued..)__

Much work with physiologic systems has been done using Reynold's equations in attempting to determine which type of flow will occur. In some cases, however, Reynolds numbers of 3,000-4,000 are reached before **turbulent flow** develops. In other cases, turbulent flow may develop at a Reynolds number of 500 or less. The reasons for this have to do with the fact that the equation doesn't take into account several important variables.
There is no expression of wall surface character. A rough wall predisposes to turbulence. Tube configuration is not included; whether the conduit is perfectly straight or makes sharp turns. Sharp turns predispose to turbulence.

Time is not included in the equation, in terms of the duration of time over which high flow velocity or rate occur. It takes a certain amount of time for turbulence to develop, and also for it to disappear. A condition may exist where there is a high Reynolds number, much higher than the critical number, but laminar flow continues. Then gradually turbulence develops over a period of time.

As flow velocity and the Reynolds number are falling, turbulence may persist past the critical number. Turbulence once initiated tends to be self perpetuating. [SEE MISCONCEPTION 20]

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