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Darcy-Weisbach resistance coefficient determination using Newton-Raphson approach for android 4. Determinación del coeficiente de fricción de Darcy-Weisbach mediante la which table represents a linear function calculator del método de aproximación Newton-Raphson para aplicaciones Android 4. Tecnuravol. Context: The article presents the friction coefficient calculation for pressure pipes, from Newton-Raphson numerical method, under JavaScript source code for Android 4.
Methodology: The what is the meaning phylogenetically development is based on Colebrook-White model for turbulent flows. The app also establishes the friction coefficient for laminar flows from the Poiseuille equation and determines the range for the enter flow in a transition zone unstable flow.
An algorithm of successive approximations was implemented for non-linear equation solution based on the relative roughness and Reynolds number. Results: In the Newton-Raphson method, if the initial value moves away from zero or presents different inflection points, the probability of divergence of the method increases significantly. To overcome this anomaly, a friction coefficient equal to 0. The values calculated by the app were calibrated with the Excel analysis tool Goal Seek.
Conclusion: The app is available for free in Google Play Store, and is a tool to support educational processes and the professional field. La aplicación también establece el coeficiente de fricción para flujos laminares utiliando la ecuación de Poiseuille, y determina el rango de flujo de entrada en zona de transición flujo inestable. Resultados: En el método de Newton-Raphson, la probabilidad de divergencia aumenta considerabemente si el valor inicial es diferente de cero o presenta distintos puntos de inflección.
Para superar esta anomalía, se propone un coeficiente de fricción de 0. De esta manera se garantiza la convergencia de flujos turbulentos con aproximación de 0. Es una herramienta para apoyar procesos educativos y trabajos en sector productivo. In the last decade, the development of apps for mobile devices on Android platform, along with the increase of processing velocity and storage capacity, have originated user- service oriented technologies.
This is especially evident in the case of specialized user needs. Educative Software Engineering ESE classifies these computational tools into algorithms and heuristics. Algorithms pose which table represents a linear function calculator systematic processes that lead the student to a determined answer. On the other hand, heuristic tools lead to appropriation of knowledge by means of experimentation and autonomous discovering. Synergies between both algorithmic and heuristic tools produce the intelligent tutorial systems development Galvis A.
Therefore, the aim of this paper is to present the development of a mobile app in Android platform that calculate Darcy's friction factor, to be used as a tool in both learning and which table represents a linear function calculator processes. JavaScript source code for Android v. Poiseuille model was used for laminar flow cases, and Colebrook-White model for turbulent flow cases. Transition zone between the two types of developed flow regimen, where flow present an unstable behavior, was also calculated.
According to regulation for potable water and basic sanitation RAShydraulic calculation for pressured systems in Colombia must be effectuated using Darcy-Weisbach model. It is a widely known empiric equation that determines load loss due to energy dissipation in the form of friction. This friction is the result of the interaction between fluid and its conducing structure, or which table represents a linear function calculator equation 1.
There are numerous models to calculate Darcy's friction coefficient, or friction factor. Most of them are empirical models limited to the range of experimentation in which they were formulated, such as Moody equation. Another example is Swamee-Jain general equation. It presents satisfactory results for most flow conditions, except for smooth turbulent flow, in which a correction factor is necessary Andrade, However, Colebrook-White model has been widely preferred due to its precision within turbulent conditions.
Since it is a non-explicit expression, its solution requires the use of numeric methods. In this work, we used Newton-Rapson method for optimizing point integration equation 2. Laminar Flow is determined by values of Reynolds number below It is known that under this flow condition, viscous forces are significant in comparison to inertial forces, and therefore the fluid moves in an overlapping form with independent layers. In this case, the system behaves according which table represents a linear function calculator the Newton equation for viscous fluids.
Saldarriaga, In figure 1we see the typical velocity distribution of a laminar flow inside a cylindric pipe. The highest velocity is reached in the center of the tube, and the lowest flow velocities are found in the surface of the pipe, where the fluid is in direct contact with the solid walls. The result of this phenomenon is a parabolic velocity profile. Figure 1 Laminar flow scheme Source: own work.
In the condition of a laminar flow, and therefore a Reynolds Number belowfriction coefficient may be calculated from Poiseuille equation equation 3. According to Reynolds' early experiments, for values between andapproximately, the flow undergoes a transitional behavior. Because of that, this range of values of Reynolds Number is known as the Transition Zone. In this case, neither laminar or turbulent flow are well defined, and thus friction factor cannot be calculated equation 4. Turbulent flow may be defined as a vectoral chaos; in it we find continuous mixture conditions, due to vortex rupture.
Sotelo, Despite this widely observed phenomenon, recent studies have found vortex behavioral patterns in turbulent systems, which may defy the paradigms of turbulence according to current notions. In fact, tests to model disorganized and complex turbulent flow conditions into series of somehow organized movement patterns, known as "coherent structures", have been made with mixed results.
Dennis, Newton-Raphson method optimizes the Newton point integration method by defining a more robust convergence equation. However, if the function is not differentiable and presents discontinuity in the calculation interval, the Newton-Raphson method will not converge. In such cases, it will be necessary to apply another numeric method to find the root of the non-linear equation. Newton-Raphson method requires an initial assumed value f 0 seed value equation 5. Now, in the problem of calculating the friction factor, Colebrook-White equation becomes the function, as what are examples of coping mechanisms below equation 6.
Therefore, Newton-Rapson convergence equation will become equation 8. In this work, we followed four main methodological steps figure 2 : 1 to define the numeric method to solve Colebrook-White equation in the Turbulent Flow condition, 2 to stablish the flow diagram of the app's iterative process, 3 to develop the source code in JavaScript, and 4 to calibrate resulting calculations with Goal Seek function in Excel. Figure 2 methodological steps followed during the development of the app.
Source: own work. Source code was developed using JavaScript. Once the solution converges, the result appears in a separated window on the screen. The relative rugosity and Reynold Number, which are both dimensionless. In figure 3we present the flow diagram of the iterative process the which table represents a linear function calculator follows to calculate Darcy's friction factor. Figure 3 App Flow Diagram Source: own work.
Resulting calculations for Darcy's friction factor were calibrated by comparing them to solutions calculated through the Goal Seek function in Excel. In table 1we present the comparison between various calculation with different input data. Table 1 App Calibration Source: own work. The relative rugosity of a pipe is 0.
If the Reynolds Number isthe app conduces the calculation of friction coefficient using Poiseuille model for Laminar Flow. Figure 4 Laminar flow Friction coefficient app Source: own work. If the relative rugosity of the pipe is 0. Figure 5 Unstable flow Friction coefficient app Source: own work. If the relative rugosity of a pipe is 0.
Figure 6 Turbulent Flow Friction coefficient app Source: own work. The solution for turbulent flow conditions is coherent with the one obtained by the Goal Seek function, shown in the table 2. Table 2 Friction Coefficient calculation through Excel goal seek Source: own work. It also indicates when the input data corresponds to the Transition Zone. The development of mobile apps for educational purposes m-learning is a valuable tool for autonomous learning.
It allows students to experiment with varied input which table represents a linear function calculator and explore different initial conditions of the problem. Andrade, L. Analysis of the Swamee-Jain's equation for the calculation of friction factor. Revista Brasileira de Engenharia Agrícola e Ambiental. Dennis, D. Coherent structures in wall-bounded turbulence.
Anais da Academia Brasileira de Ciências Introducción a los métodos numéricos para la resolución de ecuaciones. Galvis A. Ingeniería de Software Educativo. Gasca M. Metodología para el desarrollo de aplicaciones móviles. Tecnura Gómez C. Ingeniería de software educativo con modelaje orientado por objetos: un medio para desarrollar micromundos interactivos. Lindley, C. Java Script Enlightenment. New York: What does it mean when a persons location is unavailable St.