Fanning friction factor - Alchetron, the free social encyclopedia

The Fanning friction factor, named after John Thomas Fanning, is a dimensionless number used as a local parameter in continuum mechanics calculations. It is defined as the ratio between the local shear stress and the local flow kinetic energy density:

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 ( 2 π R L for a pipe with circular cross section) and dividing by the cross-sectional flow area ( π R 2 for a pipe with circular cross section). Thus Δ P = f L R ρ u 2

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 formula below may be used to obtain the Fanning friction factor for common applications.

The Darcy friction factor can also be expressed as

f = 8 τ ¯ ρ u ¯ 2

where:

τ is the shear stress at the wall

ρ is the density of the fluid

u ¯ is the flow velocity averaged on the flow cross section

For laminar flow in a round tube

The friction factor for laminar flow of Newtonian fluids in round tubes is often taken to be:

f = 16 R e

where Re is the Reynolds number of the flow.

For a square channel the value used is:

f = 14.227 R e

Hydraulically smooth piping

Blasius developed an expression of friction factor in 1913 for the flow in the regime 2100 < R e < 10 5 .

f = 0.0791 R e 0.25

Koo introduced another explicit formula in 1933 fora turbulent flow in region of 10 4 < R e < 10 7

f = 0.0014 + 0.125 R e 0.32

Pipes/tubes of general roughness

Haaland (1983) 4 ⋅ 10 4 < R e < 10 7 , k D < 0.05

1 f = − 3.6 log 10 ⁡ [ 6.9 R e + ( k / D 3.7 ) 10 / 9 ]

Commercial standard steel piping

Drew (1936) 10 4 < R e < 10 7 ; k D ≈ 0.0015

f = 0.0014 + 0.090 R e 0.27

Fully rough conduits

Nikuradse and Reichert (1943) R e > 10 4 ; k D > 0.01

1 f = 2.28 − 4.0 log 10 ⁡ ( k D )

For the turbulent flow regime, the relationship between the Fanning friction factor and the Reynolds number is more complex and is governed by the Colebrook equation which is implicit in f :

1 f = − 2.0 log 10 ⁡ ( ϵ d 3.7 + 2.51 R e f ) , turbulent flow

Various explicit approximations of the related Darcy friction factor have been developed for turbulent flow.

Stuart W. Churchill developed a formula that covers the friction factor for both laminar and turbulent flow. This was originally produced to describe the Moody chart, which plots the Darcy-Weisbach Friction factor against Reynolds number. The Darcy Weisbach Formula f D is 4 times the Fanning friction factor f and so a factor of 1 4 has been applied to produce the formula given below.

Re, Reynolds number (unitless);

ε, roughness of the inner surface of the pipe (dimension of length);

D, inner pipe diameter;

f = 2 ( ( 8 R e ) 12 + ( A + B ) − 1.5 ) 1 12 A = ( 2.457 ln ⁡ ( ( ( 7 R e ) 0.9 + 0.27 ϵ D ) − 1 ) ) 16 B = ( 37530 R e ) 16

Application

The friction head can be related to the pressure loss due to friction by dividing the pressure loss by the product of the acceleration due to gravity and the density of the fluid. Accordingly, the relationship between the friction head and the Fanning friction factor is:

Δ h = f u 2 L g R = 2 f u 2 L g D

where:

Δ h is the friction loss (in head) of the pipe.

f is the Fanning friction factor of the pipe.

u is the flow velocity in the pipe.

L is the length of pipe.

g is the local acceleration of gravity.

D is the pipe diameter.

References

Fanning friction factor Wikipedia

(Text) CC BY-SA

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