Water Hammer and Hydrodynamics’ Instability - Advances in Control and Automation of Water Systems - page 62

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/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/m2)
Ew = module of elasticity of water (kg/m2), C1=pipe support coefficient
T=time (s), Y= depends on pipeline support-

characteristics and Poisson's ratio

4.1 introduction
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
system damage or failure with proper analysis to determine the system's default dy-
namic response, design protection equipment to control transient energy, and specify
operational procedures to avoid transients. Analysis, design, and operational proce-
dures all benefit from computer simulations in this chapter. The study of hydraulic
transients is generally considered to have begun with the works of Joukowski (1898)
and Allievi (1902). The historical development of this subject makes for good read-
ing. A number of pioneers made breakthrough contributions to the field, including R.
Angus and John Parmakian (1963) and Wood (1970), who popularized and refined the
graphical calculation method. Benjamin Wylie and Victor Streeter (1993) combined
the method of characteristics 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 McCorquodale, (1982); Savic and
Walters, (1995); Walski and Lutes, (1994); Wu and Simpson, (2000). 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. Water hammer uncontrolled energy appears as pressure spikes. Vibration
and interpenetration between the water flows and mixture components is the visible
example of water hammer and is the culprit that usually leads the way to component
failure. A pump's motor exerts a torque on a shaft that delivers energy to the pump's
impeller, forcing it to rotate and add energy to the fluid as it passes from the suction to
the discharge side of the pump volute. Pumps convey fluid to the downstream end of a
system whose profile can be either uphill or downhill, with irregularities such as local
high or low points. When the pump starts, pressure can increase rapidly. Whenever
power sags or fails, the pump slows or stops and a sudden drop in pressure propagates
downstream (a rise in pressure also propagates upstream in the suction system). The