Early approximations for smooth pipes by Paul Richard Heinrich Blasius in terms of the Darcy–Weisbach friction factor are given in one article of 1913:
Johann Nikuradse in 1932 proposed that this corresponds to a power law correlation for the fluid velocity profile.
Mishra and Gupta in 1979 proposed a correction for curved or helically coiled tubes, taking into account the equivalent curve radius, R:
with,
where f is a function of:
* Pipe diameter, D (m, ft)
* Curve radius, R (m, ft)
* Helicoidal pitch, H (m, ft)
* Reynolds number, Re (dimensionless)
valid for:
* Re 
* 6.7 /D < 346.0
* 0 < H/D < 25.4