Four factors are used to calculate the Reynolds number (**Table 1.02**). The preferred equation is one that incorporates mean velocity of flow, times tube radius, times the specific gravity of the liquid, and this quantity is divided by the viscosity.

In 1883 Sir Osborne Reynolds, using a purely physical system, found that for a Reynolds number below 1000, streamline or laminar flow usually was present. When the Reynolds number was above 1000, turbulent flow was usually present. One thousand seems to be the critical value when radius is used to calculate the Reynolds number, but the critical value is really more like a zone.

Much work with physiologic systems has been done using Reynold's equations attempting to determine which type of flow will occur. Unfortunately, the Reynolds equation ignores some important variables. In some cases, the Reynolds number can reach values of 3,000-4,000 before turbulent flow develops. In other cases, turbulent flow may develop at a Reynolds number of 500 or less.

This is because 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.