Civil Engineering Reference
In-Depth Information
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/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),
Y = depends on pipeline support-
characteristics and Poisson's ratio
2.1 introduction
Pump pulsation, due to interpenetration of two fluids, such as hydrodynamics insta-
bility is a very loud banging, knocking, or hammering noise in the pipes that occurs
when the flow is suddenly turned off. Pump pulsation is a sound like human heart by
fluid pulsation in the pipe. This chapter refers to
pump pulsation as a fluid transient in
a “Dynamic” operating case, which may also include pulsation by fluid reciprocating
or peristaltic positive displacement, sudden thrust due to relief valves that pop open
or rapid piping accelerations due to an earthquake. It is advisable to investigate fluid-
structure interpenetration (FSI) that can develop for dynamic cases but the decision
to undertake such analysis is largely up to the designer; except for boilers or nuclear
installations (Figure 2.1).
figure 2.1
Common Cause of Hydraulic Transients.
Many researchers have studied water hammer and transient flow. Chaudhry and
Hussaini (1985) have solved water hammer equations by MacCormak, Lambda, and
Gabutti explicit Finite Difference (FD) schemes [1]. They found that these second-
order FD schemes result in better solutions than the first-order. Izquierdo and Iglesias
(2002) have developed a computer program to simulate hydraulic transients in a sim-
ple pipeline system by mathematical modeling [2]. They also presented the users with
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