A Numerical Exploration of Transient Decay Mechanisms in Water Distribution Systems - Advances in Control and Automation of Water Systems - page 2

C = wave velocity(m/s), σ = viscous stress tensor

u = velocity (m/s), c = speed of pressure wave (celerity-

m/s)

D = diameter of each pipe (m), f = Darcy-Weisbach friction factor

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 )

4

( m

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/m 3 )

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), ψ = depends on pipeline support-

characteristics and Poisson's ratio

1.1 introduction
Water hammer as fluid dynamics phenomena is an important case study for designer
engineers. Water hammer is a disaster pressure surge or wave caused by the kinetic
energy of a fluid in motion when it is forced to stop or change direction suddenly [1].
The majority of transients in water and wastewater systems are the result of changes at
system boundaries, typically at the upstream and downstream ends of the system or at
local high points. Consequently, results of present chapter can reduce the risk of sys-
tem damage or failure with proper analysis to determine the system's default dynamic
response. Design of protection equipment has helped to control transient energy. It has
specified operational procedures to avoid transients. Analysis, design, and operational
procedures all benefit from computer simulations in this chapter. The study of hy-
draulic transients is generally considered to have begun with the works of Joukowski
(1898) [2] and Allievi (1902) [3]. The historical development of this subject makes
for good reading. A number of pioneers have made breakthrough contributions to the
field, including Angus, Parmakian (1963) [4] and Wood (1970) [5], who popularized
and refined the graphical calculation method. Wylie and Streeter (1993) [6] combined
the method of characteristics with computer modeling. The field of fluid transients
is still rapidly evolving worldwide by Brunone et al. (2000) [7]; Koelle and Luvi-
zotto, (1996) [8]; Filion and Karney, (2002) [9]; Hamam and McCorquodale, (1982)
[10]; Savic and Walters, (1995) [11]; Walski and Lutes, (1994) [12]; Wu and Simpson,
(2000) [13]. Various methods have been developed to solve transient flow in pipes.
These ranges have been formed from approximate equations to numerical solutions of
the nonlinear Navier-Stokes equations. In present chapter a computational approach
is presented to analyze and record the transient flow (down to 5 milliseconds). Transient