Reynolds number
Flow in a pipe

For flow in a pipe or tube, the Reynolds number is generally defined as

where

For shapes such as squares, rectangular or annular ducts where the height and width are comparable, the characteristic dimension for internal-flow situations is taken to be the hydraulic diameter, D, defined as

where A is the cross-sectional area, and P is the wetted perimeter. The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the flow. This means that the length of the channel exposed to air is not included in the wetted perimeter.

For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter:

For an annular duct, such as the outer channel in a tube-in-tube heat exchanger, the hydraulic diameter can be shown algebraically to reduce to

where

For calculation involving flow in non-circular ducts, the hydraulic diameter can be substituted for the diameter of a circular duct, with reasonable accuracy, if the aspect ratio AR of the duct cross-section remains in the range 1 / 4 < AR < 4.
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