Fanning friction factor

where:

• τ is the shear stress at the wall
• f is the Fanning friction factor of the pipe
• v is the fluid velocity in the pipe
• ρ is the density of the fluid

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The wall shear stress can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area (2πRL for a pipe) and dividing by the cross-sectional flow area (πR² 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:

where:

• h_f is the friction loss (in head) of the pipe.
• f is the fanning friction factor of the pipe.
• v is the fluid velocity in the pipe.
• L is the length of pipe.
• g_c is a conversion factor.
• D is the pipe diameter.

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, this is the more commonly used by Chemical Engineers and those following the British convention.