Modeling One and Twophase Water Hammer Flows - Advances in Control and Automation of Water Systems - page 47

• Pipe is supported only at one end and allowed to undergo stress and strain both
laterally and longitudinally:

−

(3.9)

Y= 5/4 µ

For thick-walled pipelines, various theoretical equations have been proposed to
compute celerity; however, field investigations are needed to verify these equations.
For pipes that exhibit significant visco-elastic effects (for example, plastics such as
PVC and polyethylene), Covas et al. (2002) showed that these effects, including creep,
can affect wave speed in pipes and must be accounted for if highly accurate results are
desired. They proposed methods that account for such effects in both the continuity
and momentum equations [7, 8].

3.2.2 similar Work Presentations
• Arithmetic method —Assumes that flow stops instantaneously (in less than the
characteristic time, 2 L/a), cannot handle water column separation directly, and
neglects friction (Allievi, 1902; Joukowski, 1898).
• Graphical method —Neglects friction in its theoretical development but in-
cludes a means of accounting for it through a correction (Parmakian, 1963). It is
time-consuming and not suited to solving networks or pipelines with complex
profiles.
• Design charts —Provides basic design information for simple topologies at a
few specific points (valve closure, pump and pipeline with no protection, surge
tank, or air chamber protection). This method has been replaced by computer
programs (Fok, 1978; Fok, 1980; Fok et al., 1982) based on the transient energy
concept and backed by field and laboratory work (Fok, 1987).
• Wave-plan method —Represents initial transient disturbances as a series of
pulses and tracks reflections at boundaries (Wood et al., 1966).
• Method of Characteristics (MOC)— most widely used and tested approach,
with support for complex boundary conditions and friction and vaporous cavita-
tions models. (PDEs) of continuity and momentum (e.g., Navier-Stokes) into
ordinary differential equations that are solved algebraically along lines called
characteristics. An MOC solution is exact along characteristics, but friction, va-
porous cavitations and some boundary representations introduce errors in the re-
sults (Elansary, Silva, and Chaudhry, 1994; Gray, 1953; Streeter and Lai, 1962).
• Field Tests— Field tests can provide key modeling parameters such as the pres-
sure-wave speed or pump inertia. Advanced flow and pressure sensors equipped
with high-speed data loggers and “PLC” in water pipeline makes it possible to
capture fast transients, down to 5 milliseconds. Methods such as inverse tran-
sient calibration and leak detection in calculation of Unaccounted for Water
(UFW) use such data. Location for Field Tests and Lab. model was at Rasht
city in the north of Iran. Pilot subject was named “Interpenetration of two fluids
at parallel between plates and turbulent moving in pipe”. For data collection
process, Rasht city water main pipeline have been selected as Field Tests Mod-
el. Rasht city in the north of Iran was located in Guilan province (1,050,000