The Fanning friction factor, named after John Thomas Fanning (1837–1911), is a dimensionless number used in fluid flow calculations. It is related to the shear stress at the wall as:
- is the shear stress at the wall
- is the Fanning friction factor of the pipe
- is the fluid velocity in the pipe
- is the density of the fluid
The wall shear stress can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area ( for a pipe) and dividing by the cross-sectional flow area ( for a pipe).
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:
- is the friction loss (in head) of the pipe.
- is the Fanning friction factor of the pipe.
- is the fluid velocity in the pipe.
- is the length of pipe.
- is the local acceleration of gravity.
- is the pipe diameter.
... equation are the heat capacity ratio, γ, the Fanning friction factor, f, and the hydraulic diameter, Dh Assuming the Fanning friction factor is a constant along the duct wall ... in mind, however, that the value of the Fanning friction factor can be difficult to determine for supersonic and especially hypersonic flow velocities ... This means that a subsonic flow entering a duct with friction will have an increase in its Mach number until the flow is choked ...
... The Darcy–Weisbach friction factor, fD is 4 times larger than the Fanning friction factor,f, so attention must be paid to note which one of these is meant in any "fricti ... Of the two, the Darcy–Weisbach factor, fD is more commonly used by civil and mechanical engineers, and the Fanning factor, f, by chemical engineers, but care should be taken to identify the correct factor ... Note that Most charts or tables indicate the type of friction factor, or at least provide the formula for the friction factor with laminar flow ...
... 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 ... Of the two, the Fanning friction factor is the more commonly used by Chemical Engineers and those following the British convention ... formulae below may be used to obtain the Fanning friction factor for common applications ...
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