For flow in a pipe or tube, the Reynolds number is generally defined as
where
*  is the hydraulic diameter of the pipe (the inside diameter if the pipe is circular) (m),
*  is the volumetric flow rate (m/s),
*  is the pipes cross-sectional' area () (m),
*  is the mean velocity of the fluid (m/s),
*  (mu) is the dynamic viscosity of the fluid (Pa·s = N·s/m = kg/(m·s)),
*  (nu) is the kinematic viscosity () (m/s),
*  (rho) is the density of the fluid (kg/m),
*  is the mass flowrate of the fluid (kg/s).
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, , defined as
where  is the cross-sectional area, and  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
* is the inside diameter of the outer pipe,
* is the outside diameter of the inner pipe.
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  < AR < 4.