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Reynold’s Number

The Reynold’s number is a dimensionless number that characterises the flow of a fluid and is represented by:

(1)

Where Re = Reynold’s number, = density, u = fluid velocity, = characteristic length or hydraulic diameter, = dynamic viscosity. It can be alternatively written in terms of the kinematic visocity:

(2)

Where = kinematic visocity and is equivalent to .

The Reynold’s Number characterises the flow as laminar when Re < 2000, as transient when 2000 < Re < 4000 and as turbulent when Re > 4000.

Characteristic Length / Hydraulic Diameter

The characteristic length, also known as the hydraulic diameter, is the ratio of cross-sectional area to the ‘wetted’ perimeter of the tube or channel the flow is moving through. It is defined as:

(3)

Where A = cross-sectional area and P = perimeter of the channel or tube in contact with the fluid.

For example, the characteristic length for a fully filled tube with internal diameter, D, is:

(4)

For a fully filled square channel with side length, L, the characteristic length is:

(5)

A partially filled rectangular open channel with width, a, and height, b, is shown below:

Here, only 3 surfaces are in contact with the fluid and are ‘wetted’. The ‘wetted’ perimeter is therefore only (a + 2b). As such the the characteristic length is:

(6)

Reynold’s Number Calculator from Dynamic Viscosity

Reynold’s Number Calculator from Kinematic Viscosity

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