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Some aspects of physical and numerical modeling of water hammer in pipelines

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Abstract

In this work, a computational method was used for the prediction of water transmission failure. The proposed method allowed for any arbitrary combination of devices in the water pipeline system. The method used was by a scale model and a prototype (real) system for a city main water pipeline where transient flow was caused by the failure of a transmission system.

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Abbreviations

λ :

Coefficient of combination

I :

Moment of inertia (m4)

w :

Weight (kg)

P :

Fluid power (pa)

z :

Elevation at the centroid (m)

t :

Time (s)

λ 0 :

Unit of length

p :

Pressure (N/m2)

α :

Pipe cross section area (m2)

V :

Velocity (m/s)

s :

Length (m)

f :

Friction factor

τ :

Shear stress (Pa)

H2–H1:

Pressure difference (m-H2O)

C :

Surge wave velocity (m/s)

V :

Volume (m3)

F :

Fluid force (N)

W :

Frequency

q :

Flow rate (m3/s)

D :

Diameter of each pipe (m)

μ :

Fluid dynamic viscosity (kg/m s)

R :

Pipe radius (m)

γ :

Specific weight (N/m3)

ν :

Fluid dynamic viscosity (kg/m s)

J :

Junction point (m)

y :

Surge tank and reservoir elevation difference (m)

K :

Volumetric coefficient (GN/m2)

T :

Period of motion

A :

Pipe cross-sectional area (m2)

dp :

Is subjected to a static pressure rise (m)

h p :

Head gain from a pump (m)

h L :

Combined head loss (m)

E ν :

Bulk modulus of elasticity (Pa)

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)

K :

Wave number

T p :

Pipe thickness (m)

E p :

Pipe module of elasticity (kg/m2)

E w :

Module of elasticity of water (kg/m2)

C 1 :

Pipe support coefficient

Y max  :

Max. fluctuation

Min.:

Minimum

Max.:

Maximum

Lab.:

Laboratory

References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, National Academy of Science of Azerbaijan “AMEA”, Baku, Azerbaijan

    Kaveh Hariri Asli

  2. No. 1045, Alley Azerbany 2, Farhang ring, Rasht, 41886-13133, Iran

    Kaveh Hariri Asli

  3. Azerbaijan State Oil Academy, Baku, Azerbaijan

    Faig Bakhman Ogli Naghiyev

  4. University of Guilan, Rasht, Iran

    Akbar Khodaparast Haghi

Authors
  1. Kaveh Hariri Asli
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  2. Faig Bakhman Ogli Naghiyev
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  3. Akbar Khodaparast Haghi
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Correspondence to Kaveh Hariri Asli.

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Asli, K.H., Naghiyev, F.B.O. & Haghi, A.K. Some aspects of physical and numerical modeling of water hammer in pipelines. Nonlinear Dyn 60, 677–701 (2010). https://doi.org/10.1007/s11071-009-9624-7

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