# Wave method

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In fluid dynamics, the wave method (WM), or wave characteristic method (WCM), is a model describing unsteady flow of fluids in conduits (pipes).

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 and hydrodynamics. 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,

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.

## 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. [1] 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. [1]

In civil engineering, a transient is used to refer to any pressure wave that is short lived. 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 kicks in forming growing the 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 wave. The border of the high-pressure zone is referred to as a pressure wave, or transient.

Pipe flow, a branch of hydraulics and fluid mechanics, is a type of liquid flow within a closed conduit. 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.

The WM has the very significant advantage[ according to whom? ] that computations need be made only at nodes in the piping system. Other techniques such as the method of characteristics (MOC) require calculations at equally spaced interior points in a pipeline. This requirement can easily increase the number of calculations by a factor of 10 or more. However, virtually identical solutions are obtained by the WM and the MOC. [2]

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.

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Open-channel flow, a branch of hydraulics and fluid mechanics, is a type of liquid flow within a conduit with a free surface, known as a channel. The other type of flow within a conduit is pipe flow. These two types of flow are similar in many ways but differ in one important respect: the free surface. Open-channel flow has a free surface, whereas pipe flow does not.

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## References

1. Wood D.J., Dorsch R. and Lightner, C. (March 1966). "Wave Analysis of Unsteady Flow in Conduits". Journal of the Hydraulics Division. 92 (HY2): 83 220.CS1 maint: Multiple names: authors list (link)
2. Wood, D.J.; Lingireddy, S.; Boulos, P.F.; Karney, B.W. & McPherson, D.L. (July 2005). "Numerical Methods for Modeling Transient Flow in Distribution Systems". Journal - American Water Works Association. 97 (7): 104–115. doi:10.1002/j.1551-8833.2005.tb10936.x.

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