The Fanning friction factor, named after
John Thomas Fanning, is a
dimensionless number used as a local parameter in
continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such m ...
calculations. It is defined as the ratio between the local
shear stress and the local flow kinetic energy density:
:
where:
*
is the local Fanning friction factor (dimensionless)
*
is the local
shear stress (unit in
or
or Pa)
*
is the bulk
flow velocity (unit in
or
)
*
is the
density of the fluid (unit in
or
)
In particular the shear stress at the wall can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area (
for a pipe with circular cross section) and dividing by the cross-sectional flow area (
for a pipe with circular cross section). Thus
Fanning friction factor formula
This friction factor is one-fourth of the
Darcy friction factor, so attention must be paid to note which one of these is meant in the "friction factor" chart or equation consulted. Of the two, the Fanning friction factor is the more commonly used by chemical engineers and those following the British convention.
The formulas below may be used to obtain the Fanning friction factor for common applications.
The
Darcy friction factor can also be expressed as
where:
*
is the shear stress at the wall
*
is the density of the fluid
*
is the flow velocity averaged on the flow cross section
For laminar flow in a round tube
From the chart, it is evident that the friction factor is never zero, even for smooth pipes because of some roughness at the microscopic level.
The friction factor for laminar flow of
Newtonian fluids in round tubes is often taken to be:
where Re is the
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
of the flow.
For a square channel the value used is:
For turbulent flow in a round tube
Hydraulically smooth piping
Blasius developed an expression of friction factor in 1913 for the flow in the regime