Field Assessment of Friction Head Loss and Friction Correction Factor Equations

Abstract

Friction head loss equations and friction correction factors were evaluated and compared to field observations collected from thirty center pivots with laterals made of PVCs. The friction head loss equations include Darcy-Weisbach (D-W), Hazen-Williams (H-W), and Scobey, in addition to a proposed equation valid for smooth and rough pipe types and for all turbulent flow types. The proposed equation was developed by combining the equations of D-W and H-W, along with the multiple nonlinear regression technique. The friction correction factors were computed by using the typical Christiansen, modified Christiansen, Anwar, and Alazba formulae. The evaluation has been based on statistical error techniques with observed values as a reference. With the combination of modified Christiansen, Anwar, and Alazba formulae, the results revealed that the magnitudes of friction head loss calculated by using the D-W, H-W, and proposed equations were in agreement with field observations. The root mean square deviation (RMSD) values ranged from 1.6 to 1.7 m. As expected, and when the typical Christiansen friction correction factor was used with the D-W, H-W, and proposed equations, the results showed poor agreement between observed and computed friction head loss values. This was clearly reflected by the high RMSD values that ranged from 5.4 to 5.9 m. On the other hand, agreement occurred between observed friction head loss values and those calculated by using the Scobey equation, invalid for PVC pipe type, when combined with the typical Christiansen formula. This interesting finding led to improved results of the Scobey equation through a developed $C_s$ coefficient suitably valid for PVC pipe type through analytically mathematical derivation; accordingly, the RMSD value dropped from approximately 8.6 to 1.6 m.