Comparison of Traditional Methods With The Developed Empirical Equation In Determination of Minor Losses
Abstract
Traditional methods principally used for the determination of secondary or minor losses in irrigation systems are the Equivalent Length, Resistance Coefficient and Valve Flow Coefficient methods. The problem or challenge with using these methods during irrigation system design is the unreliability of their accuracy considering the shortfalls identified in each method. These are, respectively, the fixed flow coefficient (length, L, to diameter, D ratio (L/D ratio)), the thorough knowledge of the development of coefficients required for application, and the reliance on conversion parameters. This research provides a comparison of these traditional methods to the Dayton Equation considering their shortfalls for the extent of error involved in their estimation of minor losses. The Dayton Equation is deemed the best approximation tool for determining secondary losses, as it caters for all the shortfalls identified in the traditional methods.
The degree of accuracy or error involved in the use of each traditional method was achieved by comparison (% difference) of the frictional losses as determined for the 19.05 mm diameter pipe published and those adopted for each traditional method, to the theoretical 19.05 mm pipe (Dayton Equation), as reference. This was also expanded to different friction coefficients on the same pipe diameter. The choice of pipe diameter was mainly due to availability of data points (friction coefficients) for comparison compared to other pipe diameters.
The Equivalent Length method was found to be fairly accurate (tolerance with reference to the Dayton Equation for short radius: 53.23% to 50.41%, standard radius: -35.09% to 62.27%, long radius: -32.33% to 35.34%) for determining the secondary losses during the irrigation design stage, provided the bend length to pipe diameter, (L/D), ratio relative to the flow velocity was considered in the determination of the equivalent lengths. The Resistance Coefficient method was confirmed to be the best method due to the closeness of the published friction coefficients to the Dayton Equation values (tolerance with reference to the Dayton Equation for short radius: 0.27%, standard radius: 1.42% to 35.23%, long radius: 0.25% to 25.31%). The Valve Flow Coefficient method is largely dependent on the values from the Equivalent Length and the Resistance Coefficient for conversion if not found with respect to the changing pipe bend, curvature, and flow velocity (tolerance with reference to the Dayton Equation for standard radius: -0.54% to 32.77%, long radius: -1.57%). Frictional loss estimation with nearly all traditional methods was generally poor with bend angles less than 90°. Comparison of the Dayton Equation to the traditional methods (Equivalent Length, Resistance Coefficient and Valve Flow Coefficient method) was achieved. Since the Dayton's equation is consistent when determining the minor losses, it is recommended for more accurate and efficient irrigation system design that includes bends with different length-to-diameter (L/D) ratios.
