Modeling One and Twophase Water Hammer Flows - Advances in Control and Automation of Water Systems - page 42

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/m2)

Ew = module of elasticity of water, C1=pipe support coefficient

(kg/m2)
T=time (s),

Y= depends on pipeline support-

characteristics and Poisson's ratio

q=flow rate (m³/s)
A=surge tank cross section area (m²)
y=surge tank and reservoir elevation difference (m)
a=pipe cross section area (m²)
L=pipe length (m)
hf=friction loss
W=frequency
T=period of motion
Y max . =Max fluctuation
K=volumetric coefficient
P=fluid power
t=pipe thickness (mm)
F=fluid force

3.1 introduction
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 pop-
ularized 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 [1].