ABSTRACT
C=surge wave velocity (m/s),g=acceleration of gravity (m/s²)
v2-v1=velocity difference (m/s), V=volume e=pipe thickness (m),Ee=module of elasticity(kg/m²)
K=module of elasticity of water(kg/m²),θ = mixed ness integral measure
C=wave velocity(m/s),σ = viscous stress tensor
u = velocity (m/s),c = speed of pressure wave (celeritym/s)
D = diameter of each pipe (m),f = Darcy-Weisbach friction factor
d=pipe diameter(m),dp =is subjected to a static pressure rise Eν=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 dynamic response, design protection equipment to control transient energy, and specify operational procedures to avoid transients. Analysis, design, and operational procedures 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 reading. 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
key to transient analysis in a wide range of different systems. The initial state of the system and the ways in which energy and mass are added or removed from it must be considered. This is best illustrated by an example for a typical pumping system. In this chapter, a scale model which can be built to reproduce transients observed in a prototype (real) system have been compared by Field Tests. Water transmission line has been equipped with high-speed data loggers and Programmable Logic Control “PLC”. Beside these metering instruments, advanced flow and pressure sensors have been installed in water pipeline (transmission line).
