Abstract
The article presents the results of tests of minor head losses through PVC and PP elbows for a flow of water and mixtures of water and sand with grain sizes of up to 0.5 mm and concentrations of 5.6 g·L−1, 10.84 g·L−1, and 15.73 g·L−1. The tests were carried out at variable flow velocities for three elbow diameters of 63 mm, 75 mm, and 90 mm. The flow rate, pressure difference in the tested cross-sections, and temperature of the fluids were measured and automatically recorded. The results of the measurements were used to develop mathematical models for determining the minor head loss coefficient as a function of elbow diameter, sand concentration in the liquid, and Reynolds number. The mathematical model was developed by cross validation. It was shown that when the concentration of sand in the liquid was increased by 1.0 g∙L−1, the coefficient of minor head loss through the elbows increased, in the Reynolds number range of 4.6 × 104–2.1 × 105, by 0.3–0.01% for PP63, 0.6–0.03% for PP75, 1.1–0.06% for PP90, 0.8−0.01% for PVC63, 0.8–0.02% for PVC75, and 0.9–0.04% for PVC90. An increase in Re from 5 × 104 to 2 × 106 for elbows with diameters of 63, 75 and 90 mm caused a 7.3%, 6.8%, and 6.0% decrease in the minor head loss coefficient, respectively.
Highlights
Easy and quick determination of head losses through fittings in a piping system is important, because it allows to select pumps for proper operation of the system
Grains with a maximum diameter of 0.5 mm could sediment at a flow velocity lower than that determined by the simplified Newitt equation Vo = 17Vs = 17∙0.062 = 1.05 m∙s-1 [32]
When analyzing the location and the variability of location of the observation points shown in Figure 7, we looked for a function that could describe the variability in coefficient ζ as a function of Reynolds number and concentration of suspended solids
Summary
Easy and quick determination of head losses through fittings in a piping system is important, because it allows to select pumps for proper operation of the system. The essential components of a piping system are elbows; because, as a rule, pipes in a system are connected by many elbows, these fittings strongly affect the overall head losses of the entire system. Where: v – mean flow velocity upstream of the fitting, m∙s-1, ζ – dimensionless coefficient of minor head loss, ρ – fluid density, kg∙m-3. Formula (1) is divided by ρ∙g to transform it into another formula which gives the difference in pressure. It has the form (2), where g is the acceleration of gravity in m∙s-2. Investigations of the behavior of liquids flowing through elbows show that flow involves very complex phenomena, with many factors affecting head loss.
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