This paper presents four explicit formulae to calculate the friction factor for all flow regimes present at Moody diagram without iterations, including the critical zone, for four different problems. The first formula is used to calculate the head losses of pipes given its discharges, lengths, diameters, absolute roughness, the kinematic viscosity of the fluid that flows in the pipes and the gravity acceleration. The second formula is used to calculate the discharges of pipes given its head losses, lengths, diameters, absolute roughness, the kinematic viscosity of the fluid that flows in the pipes and the gravity acceleration. The third formula is used to calculate the diameters of pipes given its discharges, lengths, head losses, absolute roughness, the kinematic viscosity of the fluid that flows in the pipes and the gravity acceleration. The fourth formula is used to calculate the diameters of pipes given its lengths, head losses, absolute roughness, the kinematic viscosity of the fluid that flows in the pipes, the fluid velocities in the pipes and the gravity acceleration. The calculated friction factors are used to calculate the discharges, head losses and diameters of pipes for the steady state and for the extended period state. A case study is presented where it was possible to apply the first two formulae to calculate the friction factors for the steady state in a water main with nine pipes. The results show that the two applied formulae are working well because the calculated pressure heads of some nodes of the water main were compared to the pressure heads gauged in situ on the same nodes of the water main and the results were close.
This paper presents an experimental research about the behavior of two-phase flows in inclined pipes. The inclination angle varied from 5° to 45° and the slurry solid concentration varied up to 15%. It was concluded that the head losses of the downward sloping pipe flow are always lower than the head losses of the horizontal flow and these are always lower than the head losses of the upward sloping pipe flow, regardless the concentration and inclination angle. It was possible to develop empirical equations to calculate the head losses of the horizontal flow and the upward and downward sloping pipe flows
This paper uses the maximum entropy model to calculate the discharge in open channels. Rivers and an artificial rectangular channel are considered in this paper. The maximum entropy model needs to gauge the flow velocity only in three points to calculate the discharge of any given open channel. The flow velocity needs to be gauged on the river thalweg. A genetic algorithm was used to determine the three parameters of the maximum entropy equation. The discharge calculation results obtained by the maximum entropy model aided by the genetic algorithm were compared to the discharge calculation results obtained by the traditional (using a rotor current meter) and acoustic methods (Acoustic Doppler Current Profiler or ADCP). It was concluded that the maximum entropy model is reliable because it yields results very close to the results obtained by the traditional and acoustic methods. It was also concluded that it makes the discharge measurement easier in any given open channel.
This paper presents a non-elastic matrix model to calculate hydraulic networks, based on a method created by Nahavandi and Catanzaro (Journal of Hydraulics Division, 99(HY1), pp.47-63, 1973). It is a method that calculates the discharges and pressure heads in hydraulic networks for the steady state, for the extended period and for the transient state. This method has advantages concerning the Cross method, because the latter does not allow the calculation of transient situations such as the settings of valves, the starting and stopping of boosters, the branch ruptures, etc. The applicability of the method created by Nahavandi and Catanzaro was enhanced, because the programming and input data to consider the presence of valves, reservoirs or boosters in the hydraulic network were developed. Furthermore, the mathematical formulation and programming to calculate the extended period and transient state were also developed. The matrix method is working well, because the model was applied to calculate some hydraulic networks used as examples and the values calculated by the model are similar to the ones obtained from the technical literature.
This paper presents a hybrid model that calculates the heads, the discharges in pipes, the head losses in pipes (caused by discharges and valves) and the booster heads in hydraulic networks. The steady state is calculated considering the hydraulic network without valves and boosters. The extended period simulation is calculated considering the presence of valves and/or boosters to solve over pressure and/or under pressure problems respectively. The hybrid model uses a genetic algorithm to minimize the dissipated hydraulic power sum in the whole hydraulic network for all calculation time steps of the extended period simulation (objective function) by setting optimal valve openings. It was studied how it affects the behavior of a hydraulic network. A real hydraulic network that had over pressure and under pressure problems was analyzed. It was necessary to install boosters and valves to solve the pressure problems. The results show that when valves were installed without planning its openings, the total head losses increased from 5.9% to 13.6%, while the total head losses in the same hydraulic network increased 2.7% when planning the installed valves openings. It's concluded that the dissipated power minimization was an effective way to optimize the studied hydraulic network operations by minimizing the head losses increases caused by the installed valves.
This paper uses the maximum entropy model to develop explicit formulae to calculate the friction factor for three flow regimes present in the Moody Diagram without iterations for four different problems. The developed formulae calculate the friction factors for the critical point flows, for the smooth turbulent flows and for the laminar flows. The development of the friction factor formulae is based on the maximum entropy model. This development can be regarded as a conceptual model, but not completely, because of the relationship between the Reynolds number (Re) and the entropy parameter (M) determined by curve fittings accomplished with accurate experimental data. The developed friction factors formulae can be used to calculate the discharges, head losses and diameters of pipes for the steady state and for the extended period simulation. It is concluded that the developed formulae to calculate the discharges, the head losses and the diameters are correct and have the potential to be also used in real hydraulic networks. It is also concluded that the developed formulae made easier the calculation of the friction factor for the three flow regimes.
Resumo-A segurança da informação em redes sem fioé um aspecto de projeto que tem demandado um aumento de pesquisa e desenvolvimento, de modo a diminuir as chances de invasão e quebra de chaves de segurança. Neste artigo, os autores apresentam resultados de experimentos para testes de segurança em redes sem fio, por meio do uso do software Reaver.
This paper utilizes the maximum entropy model to calculate discharges in pipes. The proposed model requires the flow velocities to be gauged in just two positions along the pipe radius to calculate the discharge of any given pipe with circular cross-section regardless its diameter size. A genetic algorithm is used to determine the two parameters of the entropy equation for pipe flow. Three water mains are assessed. The discharge values achieved by the maximum entropy model coupled to the genetic algorithm for two water mains are compared to those achieved by a calibrated AquaProbe ABB electromagnetic flow meter and remain within the device accuracy (± 2%), as reported by its manufacturer. A Cole type Pitot tube in series with a Venturi tube are used to respectively define three velocity profiles and gauge three different discharges for the third water main. The three discharge values obtained by the maximum entropy model are compared to the ones obtained by the Venturi tube and remain within the presented uncertainties (3.3%, 3.1% and 2.8%) for each discharge gauged by the Venturi tube. The discharge calculation in any given pipe is facilitated by the presented method.
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