Explaining 'Attenuation' in Water Hammer in Pipelines

[Mikealvarado100]

Hi
Who can explain about 'Attenuation' phenomenon in pipelines when water hammer occurs? I mean how it happens.

 

[Matthew Smith]

Water hammer manifests itself as pressure fluctuations in piping systems, as rotational speed variations (overspeed, reverse rotation) in hydraulic machinery or as water level oscillations in surge tanks. The velocity profiles in rapid transients are significantly different from the "steady" profiles in slowly varying transients. Transients in pipelines may cause a drop in pressure large enough to invalidate the assumption of fluid homogeneity and continuity.

The assumption of steady viscous losses may be satisfactory for slow transients where the wall shear stress has a quasi-steady behaviour. Previous investigations of the behaviour of steady friction models for rapid transients showed large discrepancies in attenuation, shape and timing of pressure traces when computational results were compared with measurements. The magnitude of the discrepancies is governed by the flow conditions (severity of transients; laminar, transitional or turbulent flow) and liquid properties (viscosity).

Vaporous cavitation (including column separation) occurs in pipelines when the liquid pressure drops to the vapour pressure of the liquid. The amount of free and/or released gas in the liquid is assumed small. This is usually the case in most parts of the hydroelectric power plant water conveying system (pressure tunnel, penstock). The water hammer wave propagates at a constant speed as long as the pressure is above the vapour pressure. Cavitation may occur as a localized vapour cavity (large void fractions, often leading to a column separation) and/or as distributed vaporous cavitation (small void fractions). A localized (discrete) vapour cavity may form at a boundary (shut-off gate or valve, draft tube of a water turbine), at a high point along the pipe, or at an intermediate section of the pipe (intermediate cavity) if two low-pressure waves meet.

 

[Mikealvarado100]

Mattew
Thank you very much.
I know how cavitation or transient occurs. I want you to focus on 'Attenuation' phenomenon. Is it justified with Newton's third law?

And let me ask here a question about Packing too:
Regarding to what Chaudhry says in his book ('Applied Hydraulic Transients', P. 192 of 1979 edition, Chapter 7, Part 7.2. Definitions) Packing phenomenon will occurs in two steps: a) increasing as d-e and b) increasing as e-j. One of these increasing (d-e) because of 'slope in water surface, ...'. What does this increasing mean? If oil or water or another liquid flows from low level (Z0) to high level (Z1) in a pipeline (elevation of Z0<Z1), then this type of Packing will occur or not? I have not problem with second increasing in packing which occurs because of e-j packing.

Thank you.