Applied Hydraulic Transients: Automation and Advanced Control - Advances in Control and Automation of Water Systems - page 122

θ = Mixed ness integral measure, µ = fluid dynamic viscosity(kg/m.s)

R = pipe radius (m²), γ = specific weight (N/m³)

J = junction point (m), I = moment of inertia ( m

4

)

A = Pipe cross-sectional area (m²) r= pipe radius (m)
d = pipe diameter(m), d p = is subjected to a static pressure rise
E ν = bulk modulus of elasticity, α = kinetic energy correction factor
P = surge pressure (m), ρ = density (kg/m3)
C = Velocity of surge wave (m/s), g = acceleration of gravity (m/s²)
ΔV= changes in velocity of water (m/s), K = wave number
Tp = pipe thickness (m), Ep = pipe module of elasticity (kg/m 2 )
Ew = module of elasticity of water (kg/m 2 ), C1=pipe support coefficient
T = Time (s), Y = depends on pipeline support-

Characteristics and Poisson's ratio

7.1 introduction
Analysis, design, and operational procedures all benefit from computer simulations.
The study of hydraulic transients is generally considered to have begun with the works
of Joukowsky (1898) and Allievi (1902). The historical development of this subject
makes for good reading. A number of pioneers made breakthrough contributions to the
field, including R. Angus and John Parmakian (1963) and Wood (1970), who popular-
ized and refined the graphical calculation method. Benjamin Wylie and Victor Streeter
(1993) combined the method of characteristics (MOC) with computer modeling. The
field of fluid transients is still rapidly evolving worldwide by Brunone et al ., (2000);
Koelle and Luvizotto, (1996); Filion and Karney, (2002); Hamam and McCorquo-
dale, (1982); Savic and Walters, (1995); Walski and Lutes, (1994); Wu and Simpson,
(2000). Various methods have been developed to solve transient flow in pipes. This
range has been formed from approximate equations to numerical solutions of the non-
linear Navier-Stokes equations. The similarity of the transient conditions caused by
different source devices provides the key to transient analysis in a wide range of dif-
ferent systems by understanding the initial state of the system and the ways in which
energy and mass are added or removed from it. This is best illustrated by an example
for a present research pumping system (Figure 7.1).
This chapter refers to a fluid transient as a “Dynamic” operating case, which may
also include sudden thrust due to relief valves that pop open or rapid piping accelera-
tions due to an earthquake. So it is advisable to investigate fluid-structure interpenetra-
tion (FSI). Model design need to find the relation between two or many of variables
accordance to fluid transient as a “Dynamic” operating [1-3]. In this chapter, transient
flow characteristics in pipe have been studied by using new computational techniques.
For data collection process, the main pipeline of water networks of Rasht city in the
north of Iran have been used (Research Field Tests Model). Model of main pipeline
of networks have been selected for the city of Rasht, Guilan province (with 1,050,000