Variability of Darci Friction Factor in Differential Equation for Enforced Flow in Collector-Pipeline

Enforced streams with discrete along the path inflow of jets are implemented in collector-pipelines of the following systems: horizontal water-intake; radial water-collectors; purifying structures in water-supply and water-removal; drainage systems in hydromelioration; exhaust ventilation, etc. The fluid inflow into a collector-pipeline through orifices in its wall is variable and increases along the path. The cause of this is the decrease in piezometric head in the collector-pipeline caused by hydraulic resistance of the pipeline and by the increase in kinetic head in it. Reliable and adequate methods of calculation of collector-pipelines are lacking, though such pipelined are widespread. It is known that high accuracy in hydraulic calculation can be achieved basing on methods of differential equation of variable flow rate fluid flow. All authors accept that the hydraulic friction factor and the mean speed along the collector-pipeline are constant. In effect, because jet inflows along the path, they vary. Incomplete taking into account the hydrodynamic characteristics of the variable flow rate fluid flow causes essential errors in designing the collector-pipeline. In this article, relationships for calculation of head losses for overcoming the friction forces along the collector-pipelines are obtained in differential form; zone of laminar flow and three segments of turbulent flow zone, which in sequence emerge along the path, are considered. The variable hydraulic friction factor is expressed in differential form in terms of variable working head in the collector-pipeline.