Friction factor for small diameter polyethylene pipes

On this paper, the results of an experimental study oil the hydraulic friction loss for small-diameter polyethylene pipes are reported. The experiment was carried out using a range of Reynolds number between 6000 to 72000, obtained by varying discharge at 20 degrees C water temperature, with internal pipe diameters of 10.0 mm, 12.9 mm, 16.1 mm, 17.4 mm and 19.7 mm. According to the analysis results and experimental conditions, the friction factor 0 of the Darcy-Weisbach equation call be estimated with c = 0.300 and m = 0.25. The Blasius equation (c = 0.316 and m = 0.25) gives an overestimate of friction loss, although this fact is non-restrictive for micro-irrigation system designs. The analysis shows that both the Blasius and the adjusted equation parameters allow for accurate friction factor estimates, characterized by low mean error (5.1%).

LOCAL HEAD LOSS OF NON-COAXIAL EMITTERS INSERTED IN POLYETHYLENE PIPE

The design of a lateral line for drip irrigation requires accurate evaluation of head losses in not only the pipe but in the emitters as well. A procedure was developed to determine localized head losses within the emitters by the formulation of a mathematical model that accounts for the obstruction caused by the insertion point. These localized losses can be significant when compared with tire total head losses within the system due to the large number of emitters typically installed along the lateral line. Air experiment was carried out by altering flow characteristics to create Reynolds numbers (R) from 7,480 to 32,597 to provide turbulent flow and a maximum velocity of 2.0 m s(-1). The geometry of the emitter was determined by an optical projector and sensor An equation was formulated to facilitate the localized head loss calculation using the geometric characteristics of the emitter (emitter length, obstruction ratio, and contraction coefficient). The mathematical model was tested using laboratory measurements on four emitters. The local head loss was accurately estimated for the Uniram (difference of +13.6%) and Drip Net (difference of +7.7%) emitters, while appreciable deviations were found for the Twin Plus (-21.8%) and Tiran (+50%) emitters. The head loss estimated by the model was sensitive to the variations in the obstruction area of the emitter However, the variations in the local head loss did not result in significant variations in the maximum length of the lateral lines. In general, for all the analyzed emitters, a 50% increase in the local head loss for the emitters resulted in less than an 8% reduction in the maximum lateral length.

Characterization of the microtube emitters used in a novel micro-sprinkler

The microtube is a simple and cheap emitter that was widely used throughout the world in the early days of drip irrigation. Its length can be adjusted according to the pressure distribution along the lateral line and the discharge from the microtube can be adjusted by its length. This not only counters the pressure loss due to pipe friction but also makes it suitable for undulating and hilly conditions, where pressure in the lateral line varies considerably according to the differences in elevation. This is the major problem facing the designer, i.e., emitter flow changes as the acting pressure head changes. In this study, a novel micro-sprinkler system is proposed that uses microtube as the emitter and where the length of the microtube can be varied in response to pressure changes along the lateral to give uniformity of emitter discharges. The objective of this work is to develop and validate empirical and semi-theoretical equations for the emitter hydraulics. Laboratory testing of two microtube emitters of different diameter over a range of pressures and discharges was used in the development of the equations relating pressure and discharge, and pressure and length for these emitters. The equations proposed will be used in the design of the micro-sprinkler system, to determine the length of microtube required to give the nominal discharge for any given pressure. The semi-theoretical approach underlined the importance of accurate measurements of the microtube diameter and the uncertainty in the estimation of the friction factor for these tubes.

Leak detection by inverse transient analysis in an experimental PVC pipe system

Leakage reduction in water supply systems and distribution networks has been an increasingly important issue in the water industry since leaks and ruptures result in major physical and economic losses. Hydraulic transient solvers can be used in the system operational diagnosis, namely for leak detection purposes, due to their capability to describe the dynamic behaviour of the systems and to provide substantial amounts of data. In this research work, the association of hydraulic transient analysis with an optimisation model, through inverse transient analysis (ITA), has been used for leak detection and its location in an experimental facility containing PVC pipes. Observed transient pressure data have been used for testing ITA. A key factor for the success of the leak detection technique used is the accurate calibration of the transient solver, namely adequate boundary conditions and the description of energy dissipation effects since PVC pipes are characterised by a viscoelastic mechanical response. Results have shown that leaks were located with an accuracy between 4-15% of the total length of the pipeline, depending on the discretisation of the system model.

Experimentation and numerical simulation of steel fibre reinforced concrete pipes

The results concerning on an experimental and a numerical study related to SFRCP are presented. Eighteen pipes with an internal diameter of 600 mm and fibre dosages of 10, 20 and 40 kg/m(3) were manufactured and tested. Some technological aspects were concluded. Likewise, a numerical parameterized model was implemented. With this model, the simulation of the resistant behaviour of SFRCP can be performed. In this sense, the results experimentally obtained were contrasted with those suggested by means MAP reaching very satisfactory correlations. Taking it into account, it could be said that the numerical model is a useful tool for the optimal design of the SFRCP fibre dosages, avoiding the need of the systematic employment of the test as an indirect design method. Consequently, the use of this model would reduce the overall cost of the pipes and would give fibres a boost as a solution for this structural typology.

Application of the essential work of fracture method in ranking the performance in service of high-density polyethylene resins employed in pressure pipes

High-density polyethylene resins have increasingly been used in the production of pipes for water- and gas-pressurized distribution systems and are expected to remain in service for several years, but they eventually fail prematurely by creep fracture. Usual standard methods used to rank resins in terms of their resistance to fracture are expensive and non-practical for quality control purposes, justifying the search for alternative methods. Essential work of fracture (EWF) method provides a relatively simple procedure to characterize the fracture behavior of ductile polymers, such as polyethylene resins. In the present work, six resins were analyzed using the EWF methodology. The results show that the plastic work dissipation factor, beta w(p), is the most reliable parameter to evaluate the performance. Attention must be given to specimen preparation that might result in excessive dispersion in the results, especially for the essential work of fracture w(e).

Failure assessments of corroded pipelines with axial defects using stress-based criteria: Numerical studies and verification analyses

Conventional procedures used to assess the integrity of corroded piping systems with axial defects generally employ simplified failure criteria based upon a plastic collapse failure mechanism incorporating the tensile properties of the pipe material. These methods establish acceptance criteria for defects based on limited experimental data for low strength structural steels which do not necessarily address specific requirements for the high grade steels currently used. For these cases, failure assessments may be overly conservative or provide significant scatter in their predictions, which lead to unnecessary repair or replacement of in-service pipelines. Motivated by these observations, this study examines the applicability of a stress-based criterion based upon plastic instability analysis to predict the failure pressure of corroded pipelines with axial defects. A central focus is to gain additional insight into effects of defect geometry and material properties on the attainment of a local limit load to support the development of stress-based burst strength criteria. The work provides an extensive body of results which lend further support to adopt failure criteria for corroded pipelines based upon ligament instability analyses. A verification study conducted on burst testing of large-diameter pipe specimens with different defect length shows the effectiveness of a stress-based criterion using local ligament instability in burst pressure predictions, even though the adopted burst criterion exhibits a potential dependence on defect geometry and possibly on material`s strain hardening capacity. Overall, the results presented here suggests that use of stress-based criteria based upon plastic instability analysis of the defect ligament is a valid engineering tool for integrity assessments of pipelines with axial corroded defects. (C) 2008 Elsevier Ltd. All rights reserved.

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic-plastic materials

In this work, the effects of indenter tip roundness oil the load-depth indentation curves were analyzed using finite element modeling. The tip roundness level was Studied based on the ratio between tip radius and maximum penetration depth (R/h(max)), which varied from 0.02 to 1. The proportional Curvature constant (C), the exponent of depth during loading (alpha), the initial unloading slope (S), the correction factor (beta), the level of piling-up or sinking-in (h(c)/h(max)), and the ratio h(max)/h(f) are shown to be strongly influenced by the ratio R/h(max). The hardness (H) was found to be independent of R/h(max) in the range studied. The Oliver and Pharr method was successful in following the variation of h(c)/h(max) with the ratio R/h(max) through the variation of S with the ratio R/h(max). However, this work confirmed the differences between the hardness values calculated using the Oliver-Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that Occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (W(p)/W(t)) was found to be independent of the ratio R/h(max), which demonstrates that the methods for the Calculation of mechanical properties based on the *indentation energy are potentially not Susceptible to errors caused by tip roundness.

Analysis of the effects of conical indentation variables on the indentation response of elastic-plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load-depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 2(6) was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/h(max), n, theta, E, and h(max). The dimensional variables E and h(max) were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/h(max) was obtained with two different h(max) values. A set of dimensionless functions was defined to analyze the effect of the input variables: Pi(1) = P(1)/Eh(2), Pi(2) = h(c)/h, Pi(3) = H/Y, Pi(4) = S/Eh(max), Pi(6) = h(max)/h(f) and Pi(7) = W(P)/W(T). These six functions were found to depend only on the dimensionless variables studied (Y/E, R/h(max), n, theta). Another dimension less function, Pi(5) = beta, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on beta was theta. However, beta showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that beta is especially Susceptible to the error in the Calculation of the initial unloading slope.

Evolution of magnetic properties and crystallographic texture in electrical steel with large plastic deformation

Deformation leads to a hardening of steel due to an increase in the density of dislocations and a reduction in their mobility, giving rise to a state of elevated residual stresses in the crystal lattice. In the microstructure, one observes an increase in the contribution of crystalline orientations which are unfavorable to the magnetization, as seen, for example, by a decrease in B(50), the magnetic flux density at a field of 50 A/cm. The present study was carried out with longitudinal strips of fully processed non-oriented (NO) electrical steel, with deformations up to 70% resulting from cold rolling in the longitudinal direction. With increasing plastic deformation, the value of B(50) gradually decreases until it reaches a minimum value, where it remains even for larger deformations. On the other hand, the coercive field H(c) continually increases. Magnetometry results and electron backscatter diffraction results are compared and discussed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3560895]

Eucalyptus sp seedling response to potassium fertilization and soil water

A considerable portion of Brazil's commercial eucalypt plantations is located in areas Subjected to periods of water deficit and grown in soils with low natural fertility, particularly poor In potassium. Potassium is influential in controlling water relations of plants. The objective of this study was to verify the influence of potassium fertilization and soil water potential (psi(w)) oil the dry matter production and oil water relations Of eucalypt seedlings grown under greenhouse conditions. the experimental units were arranged in 4x4x2 randomized blocks factorial design, as follow: four species of Eucalyptus (Eucalyptus grandis, Eucalyptus urophylla, Eucalyptus camaldulensis and hybrid Eucalyptus grandis x Eucalyptus urophylla), four dosages of K (0, 50, 100 and 200 mg dm(-3)) and two soil water potentials (-0.01 M Pa and -0.1 M Pa). Plastic containers with 15 cm diameter and 18 cm height, with Styrofoam base, containing 3.0 dm(3) of soil and two plants per container were used. Soil water potential was kept at -0.01 MPa for 40 days after seeding. Afterward, the experimental units were divided into two groups: in one group the potential was kept at 0.01 MPa, and in the other one, at -0.10 MPa. Sol I water potential was control led gravimetrically twice a day with water replacement until the desired potential was reestablished. A week before harvesting, the leaf water potential (psi), the photosynthetic rate (A), the stomatal conductance (gs) and the transpiration rate were evaluated. The last week before harvesting, the mass of the containers was recorded daily before watering to determine the consumption of water by the plants. After harvesting, total dry matter and leaf area were evaluated. the data were Submitted to analysis of variance, to Tukey's tests and regression analyses. The application of K influenced A, gs and the transpiration rate. Plants deficient in K showed lower A and higher Us and transpiration rates. There were no statistical differences in A, gs and transpiration rates ill plants with and Without water deficit. The addition of K reduced the consumption of water per unit of leaf area and, in general, plants submitted to water deficit presented a lower consumption of water.

INFLUENCE OF ALTITUDE, AGE AND DIAMETER ON YIELD AND ALPHA-BISABOLOL CONTENT OF CANDEIA TREES (Eremanthus erythropappus)

The heartwood of candeia tree is a source of essential oil rich in alpha-bisabolol, a substance widely used in the cosmetic and pharmaceutical industry. Bearing in mind the economic importance of alpha-bisabolol, this work aimed to evaluate the influence of tree age on the yield and content of alpha-bisabolol present in essential oil from candeia, considering two distinct reliefs and three diameter classes, in Aiuruoca region, south Minas Gerais state. The two distinct reliefs correspond respectively to one section of the stand growing at 1,000m of altitude (Area 1) and another section growing at 1,100m of altitude (Area 2). In each section, 15 trees were felled from among 3 different diameter classes. Discs were removed from the base of each tree to estimate their age by doing growth ring count. Soil samples were taken and Subjected to physical and chemical analysis. The logs were reduced into chips and random samples were taken for distillation to extract essential oil. The method used was steam distillation at a pressure of 2 kgf/cm(2)/2.5 h. The chemical analysis was performed in a gas chromatograph (GC) based on the alpha-bisabolol standard reference. The yield of essential oil from trees in Area I was higher than that from trees in Area 2, with the same pattern of influence for older trees. In Area 2, the alpha-bisabolol content was higher in younger trees. No differences were found between the relevant parameters in relation to diameter classes.

The Lobel-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree at least some k is an element of N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r( T, T') of trees T, T' from the above classes.

Influence of concrete strength and length/diameter on the axial capacity of CFT columns

This paper presents an experimental analysis of the confinement effects in steel-concrete composite columns regarding two parameters: concrete compressive strength and column slenderness. Sixteen concrete-filled steel tubular columns with circular cross section were tested under axial loading. The tested columns were filled by concrete with compressive strengths of 30, 60. 80, and 100 MPa, and had length/diameter ratios of 3, 5, 7, and 10. The experimental values of the columns` ultimate load were compared to the predictions of 4 code provisions: the Brazilian Code NBR 8800:2008, Eurocode 4 (EN 1994-1-1:2004), AINSI/AISC 360:2005, and CAN/CSA S16-01:2001. According to the results, the load capacity of the composite columns increased with increasing concrete strength and decreased with increasing length/diameter ratio. In general, the code provisions were highly accurate in the prediction of column capacity. Among them, the Brazilian Code was the most conservative, while Eurocode 4 presented the values closest to the experimental results. (C) 2009 Elsevier Ltd. All rights reserved.

A discussion on volume change in the plastic phase

This technical note discusses the possibility of using a more simplified scheme to estimate the plastic multiplier when some material shows volume changes, e.g. soil, balsa wood foam and other similar materials. Two procedures regarding volume changes during the plastic phase are discussed here. The first one is the classic procedure applied to non-associative plasticity, for which a Drucker-Prager-like surface is adopted to represent the plastic potential. For the second procedure, the plastic potential is not explicitly known, however, its orthogonal direction is chosen respecting a plastic volume change parameter similar to Poisson`s ratio. Copyright (C) 2007 John Wiley & Sons, Ltd.