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It is named after Osborne Reynolds ( 1842 – 1912 ), who proposed it in 1883 . Typically it is given as follows for flow through a pipe: : or : where:
Laminar Flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion, while Turbulent Flow , on the other hand, occurs at high Reynolds numbers and is dominated by inertial forces, producing random eddies, vortices and other flow fluctuations. The transition between laminar and turbulent flow is often indicated by a critical Reynolds number (''Recrit''), which depends on the exact flow configuration and must be determined experimentally. Within a certain range around this point there is a region of gradual transition where the flow is neither fully laminar nor fully turbulent, and predictions of fluid behaviour can be difficult. For example, within circular pipes the critical Reynolds number is generally accepted to be 2300, where the Reynolds number is based on the pipe diameter and the mean velocity ''v''s within the pipe, but engineers will avoid any pipe configuration that falls within the range of Reynolds numbers from about 2000 to 4000 to ensure that the flow is either laminar or turbulent. THE SIMILARITY OF FLOWS In order for two flows to be similar they must have the same geometry, have equal Reynolds numbers and Euler Numbers . When comparing fluid behaviour at homologous points in a model and a full-scale flow, the following holds: : :
REYNOLDS NUMBER SETS THE SMALLEST SCALES OF TURBULENT MOTION In a turbulent flow, there is a range of scales of the fluid motions, sometimes called eddies. A single packet of fluid moving with a bulk velocity is called an Eddy . The size of the largest scales (eddies) are set by the overall geometry of the flow. For instance, in an industrial smoke-stack, the largest scales of fluid motion are as big as the diameter of the stack itself. The size of the smallest scales is set by the Reynolds number. As Reynolds number increases, smaller and smaller scales of the flow are visible. In the smoke-stack, the smoke may appear to have many very small bumps or eddies, in addition to large bulky eddies. In this sense, the Reynolds number is an indicator of the range of scales in the flow. The higher the Reynolds number, the greater the range of scales. What is the explanation for this phenomenon? A large Reynolds number indicates that viscous forces are not important to the flow. With a low level of Viscosity , the smallest scales of fluid motion are undamped -- there is not enough viscosity to dissipate their motions. In contrast, a low Reynolds number indicates that viscosity is important to the flow dynamics. The smallest scales are damped out, and only the larger scales remain. Next time you look at a turbulent flow, try to pick out the smallest and biggest scales of fluid motion. Is the Reynolds number big or small? EXAMPLE ON THE IMPORTANCE OF REYNOLDS NUMBER If an airplane needs testing of its wing, one can make a scaled down model of the wing and test it as a table top model in the lab with the same Reynolds number the actual airplane is subjected to. For example, if a scale model is one quarter that of the full size, the flow velocity would have to be ''increased'' four times. Alternatively, the tests may be conducted in a water tank (water has a higher dynamic viscosity than air), thus maintaining the same Reynolds number. The results of the laboratory model will be similar to that of the actual plane wing results. Thus we need not bring a full scale plane into the lab and actually test it. This is an example of "dynamic similarity".
TYPICAL VALUES OF REYNOLDS NUMBER
Onset of turbulent flow ~ 2.3×103
SEE ALSO REFERENCES
pp. 107-152
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