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Wave Characteristic Method
In fluid dynamics, the wave method (WM), or wave characteristic method (WCM), is a model describing unsteady flow of fluids in conduits (pipes). Details of model The wave method is based on the physically accurate concept that transient pipe flow occurs as a result of pressure waves generated and propagated from a disturbance in the pipe system (valve closure, pump trip, etc.) This method was developed and first described by Don J. Wood in 1966. A pressure wave, which represents a rapid pressure and associated flow change, travels at sonic velocity for the liquid pipe medium, and the wave is partially transmitted and reflected at all discontinuities in the pipe system (pipe junctions, pumps, open or closed ends, surge tanks, etc.) A pressure wave can also be modified by pipe wall resistance. This description is one that closely represents the actual mechanism of transient pipe flow. Advantages The WM has the very significant advantage that computations need be made only at nodes ...
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Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ...
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Scientific Model
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject. Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling. The following was said by John von Neumann. There is also an increasing attention to scientific modelling in fields such as science education, philosophy of science, sys ...
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Pipe (fluid Conveyance)
A pipe is a tubular section or hollow cylinder, usually but not necessarily of circular cross-section, used mainly to convey substances which can flow — liquids and gases (fluids), slurries, powders and masses of small solids. It can also be used for structural applications; hollow pipe is far stiffer per unit weight than solid members. In common usage the words ''pipe'' and ''tube'' are usually interchangeable, but in industry and engineering, the terms are uniquely defined. Depending on the applicable standard to which it is manufactured, pipe is generally specified by a nominal diameter with a constant outside diameter (OD) and a schedule that defines the thickness. Tube is most often specified by the OD and wall thickness, but may be specified by any two of OD, inside diameter (ID), and wall thickness. Pipe is generally manufactured to one of several international and national industrial standards. While similar standards exist for specific industry applicati ...
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Transient (civil Engineering)
In civil engineering, a transient is used to refer to any pressure wave that is short lived (i.e. not static pressure or pressure differential due to friction/minor loss in flow). The most common occurrence of this is called water hammer. In a pipe network, when a valve or pump is suddenly shut off, the water flowing in an adjacent pipe is suddenly forced to stop. A region of high pressure builds up immediately behind said valve or pump and a region of low pressure forms in front of it. The momentum of the water is suddenly transferred into the fitting and Newton's Third Law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ... kicks in forming a high-pressure region of water as it all "piles up" in the pipe. This high pressure region then travels back along the pipe in the form of a wav ...
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Pipe Flow
In fluid mechanics, pipe flow is a type of liquid flow within a closed conduit, such as a pipe or tube. The other type of flow within a conduit is open channel flow. These two types of flow are similar in many ways, but differ in one important aspect. Pipe flow does not have a free surface which is found in open-channel flow. Pipe flow, being confined within closed conduit, does not exert direct atmospheric pressure, but does exert hydraulic pressure on the conduit. Not all flow within a closed conduit is considered pipe flow. Storm sewers are closed conduits but usually maintain a free surface and therefore are considered open-channel flow. The exception to this is when a storm sewer operates at full capacity, and then can become pipe flow. Energy in pipe flow is expressed as head and is defined by the Bernoulli equation. In order to conceptualize head along the course of flow within a pipe, diagrams often contain a hydraulic grade line (HGL). Pipe flow is subject to frictio ...
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Pressure Waves
A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any affected location or at a seismograph. P waves may be transmitted through gases, liquids, or solids. Nomenclature The name ''P wave'' can stand for either pressure wave (as it is formed from alternating compressions and rarefactions) or primary wave (as it has high velocity and is therefore the first wave to be recorded by a seismograph). The name ''S wave'' represents another seismic wave propagation mode, standing for secondary or shear wave. Seismic waves in the Earth Primary and secondary waves are body waves that travel within the Earth. The motion and behavior of both P and S waves in the Earth are monitored to probe the interior structure of the Earth. Discontinuities in velocity as a function of depth are indicative of change ...
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Method Of Characteristics
In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation. The method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data given on a suitable hypersurface. Characteristics of first-order partial differential equation For a first-order PDE (partial differential equation), the method of characteristics discovers curves (called characteristic curves or just characteristics) along which the PDE becomes an ordinary differential equation (ODE). Once the ODE is found, it can be solved along the characteristic curves and transformed into a solution for the original PDE. For the sake of simplicity, we confine our attention to the case of a function of two independent variables ...
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EPANET
EPANET (Environmental Protection Agency Network Evaluation Tool) is a public domain, water distribution system modeling software package developed by the United States Environmental Protection Agency's (EPA) Water Supply and Water Resources Division. It performs extended-period simulation of hydraulic and water-quality behavior within pressurized pipe networks and is designed to be "a research tool that improves our understanding of the movement and fate of drinking-water constituents within distribution systems". EPANET first appeared in 1993. EPANET 2 is available both as a standalone program and as an open-source toolkit (Application Programming Interface in C). Its computational engine is used by many software companies that developed more powerful, proprietary packages, often GIS-centric. The EPANET ".inp" input file format,Rossman, L. A., "EPANET 2 Users Manual", 2000 which represents network topology, water consumption, and control rules, is supported by many free and comme ...
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Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ...
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