The Reynolds Number is a ratio that defines the rate of fluid flow in pipes. It characterizes the particular flow regimes that can occur in the circuit.
The onset of turbulence in water is between 2300-4000. A Reynolds number of 4000, or higher, represents turbulent flow, and turbulent flow is preferred for cooling applications. However the higher the Reynolds number in the circuit, the more energy is required to pump it through the circuit. Hence the ideal Reynolds number for cooling circuits is 10,000. The pumping losses associated with Reynolds higher than 10,000 outweigh the heat transfer gains that can be achieved with higher Reynolds numbers.
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