Fitting Hazen-Williams Roughness Coefficient to the Head Loss Obtained by Darcy-Weisbach Equation in PVC Pipes

There are still today discussions about what formula shall be used to calculate head loss in water pipelines. Especially in academic circles, the Darcy-Weisbach (DW) equation is highly recommended, with a series of articles and scientific evidence on the subject. In the context of water supply companies, the Hazen-Williams (HW) equation gains a lot of strength, possibly even because, within the speed ranges that the systems operate, it can provide acceptable results. Thus, the present research provides a series of curves to adjust the HW roughness coefficients C, in order to make the obtained head loss results to be very similar to those derived from the DW equation. For the diameters of 50, 75, 100, 150, and 200 mm, spreadsheets were prepared, which indicated which value of C was generated for each flow rate, whose variation ranged from 0.05 to 287.00 L/s. It was verified in the spreadsheets, for each same value ​​of C, which were the combinations of flow and diameter ​​that produced it, and the same procedure was repeated for all C. Thus, each curve of C could be plotted. In order to assess the accuracy of the fit curves, points generated by the combination of flow and diameter outside the Hazen-Williams region of application were taken. Such points were plotted in the curves to obtain the adjusted C. This procedure made the results of HW much closer to those of DW, which when such a comparison was made using the values ​​of C from the literature.