Darcy friction factor formulae

The pipe friction factor λ (lambda ) is a dimensionless number used to calculate the pressure drop at a flow in a pipe.

Definition

The resistance of pipe flows could in this case be written as pressure loss coefficient ζ (zeta ), but further dissolve (D = inner diameter, L = length) can be:

For the laminar, fully developed flow in a circular pipe, the pipe friction factor can be determined by the Reynolds number as follows exactly:

For turbulent flow, there is approximate formulas for determining the pipe friction factor. The following cases can be distinguished:

• Hydraulically smooth tube, that is, the unevenness of the wall of the tube are covered entirely by a viscous sublayer. The value of is calculated with the formula of Prandtl:

• Hydraulically rough pipe, that is, the unevenness of the wall of the pipe will no longer be covered by a viscous sublayer. The value of is calculated with the formula of Nikuradse:

• The transition region between the above-mentioned conditions. This applies Colebrook:

Notes

The boundary between transitional and rough area goes according to Moody at

The so-called absolute Rauheitsbeiwerte k be, eg, 1.0 mm for straight duct sections or 0.1 mm for pure water - pressure pipelines. In order to compare different roughness, one can use the equivalent sand roughness.

The loss coefficients can be calculated or taken from tables or diagrams.

In correspondence of the calculation of loss coefficients for full pipes, this can also be determined for partially filled pipes or any Gerinnequerschnitte. Here, in the calculation instead of the pipe diameter d of the so-called hydraulic diameter:

Be used. The application of this method for the calculation of runoff in open channels has not been enforced, and is only used to calculate the drain pipes in use. To calculate the discharge in open channels is usually on the empirically derived flow formula by Strickler ( in the English language to Manning ), resorted, after which the rate of runoff can be calculated as follows:

The Strickler coefficient kst is to be selected depending on the surface condition and does not change in principle with the flow depth.

When referring to the dimension of the hydraulic radius, typical kst are in:

It has been found that were used at inquiries carried out in the past Gerinneberechnungen sometimes too optimistic coefficients and insufficient drainage capacity was available for review in the nature. This is exacerbated by emerging vegetation in the channel.

In natural channels kst is partially adopted in respect to different cross sections and partial cross sections.