The development of an empirical equation for determining minor losses due to bends in smooth pipes for irrigation system design
Abstract
As pipe networks get to shorter lengths or the number of bends increase, the proportion of losses due to bends increases contributing significantly to possible over- and under-sizing of pumps, especially for low operating pressure systems. Methods used for determining minor losses in smooth pipes for irrigation system design consist primarily of the Equivalent Length, Resistance Coefficient and Valve Flow Coefficient method. Without a thorough knowledge of their development, the methods do not offer easy, quick, accurate and precise determination of minor losses as bend parameters change in the design process. The resulting incorrect use of methods and estimations of 30 to 50 pipe-diameters in length of equivalent straight pipe, 10% to 15% and at times 25% of mainline losses by designers in industry, leaves room for error.
An Empirical Equation for determining minor losses based on the Resistance Coefficient method deemed the most accurate, was derived from analysis, association and amalgamation of behavioural patterns of pressure drop due to change of individual bend parameters that contribute to pressure drop. Changing bend angles and key components defining bends, pipe diameter per radius of curvature (relative radius of curvature), Rc, and the flow coefficient, bend length per pipe diameter ratio (L/D ratio) were used in the derivation of the Empirical Equation. Behavioural patterns at Rc values of 13.545, 27.679 and 79.578 were obtained experimentally and the Short, Standard and Long radius, from published data.
The derived Empirical Equation (based on the theoretical 19.05 mm Standard radius for friction coefficient, = 0.7395) dynamically determined the best estimate of minor losses due to bend angles 0° to 90° without need of a thorough knowledge, eliminating error. It catered for finding for pipe diameters outside the experimental and published data. The pragmatic basis for its derivation catered for all the constant parameters, easily measured and the unseen or immeasurable parameters also validating the equation. The equation allowed for the identification of the phenomenon of saturation as Rc continued beyond experimental values. It confirmed the difference between the Short and Standard radius bends ( = 0.8976) often confused in the literature reviewed by close approximation of at Rc = 0.5. The derived Empirical Equation can satisfactorily be used in irrigation system design procedures and software for correctly estimating the minor losses.
