Darcy Weisbach 
DarcyWeisbach formulaThe DarcyWeisbach equation is an empirical approach for the calculation of pressure losses related to frictional flow in straight open channels and piping. The analytical approach with a system of differential equations provided by [Navier 1822] can only be integrated for a few particular cases. Specialized software packages provide iterative solutions. In everyday life of engineers the DarcyWeisbach equation has established itself due to easy handling. Table 1 shows equations of major authors from the first half of the 19th century regarding pressure loss in straight piping. The empirical equations were derived from experiments with turbulent water flow in iron and cast iron pipes. Table 1 [Weisbach 1850, page 529] noted equation (1) as we know it today. Darcy Friction Factors f in Table 1 become dimensionless by the dimensions of their constants. The approach of Eytelwein features a constant Darcy Friction Factor. Weisbach, Prony and Aubuisson show that Dracy Friction Factor f falls in value with rising velocity. Darcy points out that Friction Factor f falls in value with rising diameters. Both observations are true. The absolute Darcy Friction Factor values provided by equations of Table 1 match the range of Frictions Factors shown in the Moody diagram. In his equations Colebrook used dimensionless values for describing the Darcy Friction Factor f (roughness/diameter and Reynolds number). Moody diagram The work of Navier, Stokes, Hagen, Poiseuille, Reynolds, Karman, Prandtl and Colebrook  to name the most famous  led to the formulation of the Dracy Friction Factor as we know it today (diagram by Moody). It comprises flow regimes from laminar to completely turbulent for all Newtonian fluids.
For Re < 2320 (laminar flow) the Darcy Friction Factor is calculated according to HagenPoiseuille:
For Re > 2320 (turbulent flow) the Darcy Friction Factor is calculated according to [Colebrook 1939, page 137]: For Re => ∞ (completely turbulent flow) the equation of Colebrook converges to the equation of [Prandtl 1933, page 110] according to Kármán: and for ε/d => 0 (smooth pipe) to the equation of [Prandtl 1933, page 111]:
Laminar flow is possible for Re < 8000 [VDI 1984, page Lb1]. In the critical transition
zone (2320 <= Re < 8000) the value of the Darcy Friction Factor might be overestimated
by the means of calculation presented above.
