Modeling One and Twophase Water Hammer Flows - Advances in Control and Automation of Water Systems - page 41

3

Modeling One and Two-
phase Water Hammer
Flows

contents

3.1 Introduction ......................................................................................................................42
3.2 Materials and Methods .....................................................................................................44
3.2.1 Two Phase Flow ....................................................................................................44
3.2.2 Similar Work Presentations ..................................................................................47
3.2.3 Laboratory Models ...............................................................................................49
3.2.3.1 Newton Second Law for Laboratory Model ..........................................49
3.3 Results and Discussion .....................................................................................................51
3.3.1 Regression modeling results has been compared with Field Tests .......................51
3.3.2 Comparison of Present research results with other expert's research ..................57
3.4 Conclusion ........................................................................................................................58
Keywords ...................................................................................................................................59
References ..................................................................................................................................59

nomenclAtures
λ = coefficient of combination,

w = weight

t = time, λ ۪ = unit of length

V = velocity

ρ1 = density of the light fluid (kg/m3),

ρ2 = density of the heavy fluid (kg/m3), C = surge wave velocity in pipe

s = length, f = friction factor

τ = shear stress, H2-H1=pressure difference (m-H2O)

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 (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)