This study investigates the energy relations and dissipations in viscoelastic pipeline under fluid transients. The investigation is carried out analytically using energy analysis and Fourier transform techniques for viscoelastic waterhammer governing equations. The analytical results show that the viscoelastic term in waterhammer models is wrongly referred to in literature as being wave damping/dissipation when in actual fact it is the work done by the fluid on the pipe and vice versa. The energy dissipation is actually occurred in the pipe-wall due to the viscoelastic material strain. Moreover, the energy transfer/exchange between the fluid and pipe-wall and energy dissipation in the pipe-wall due to viscoelasticity effect is relating to the ratio of the pipe viscoelastic frequency and the fluid wave frequency.

1.
Vardy
,
A. E.
, and
Hwang
,
K.
, 1991, “
A Characteristics Model of Transient Friction in Pipes
,”
J. Hydraul. Res.
0022-1686,
29
(
5
), pp.
669
684
.
2.
Brunone
,
B.
,
Karney
,
B.
,
Mecarelli
,
M.
, and
Ferrante
,
M.
, 2000, “
Velocity Profiles and Unsteady Pipe Friction in Transient Flow
,”
J. Water Resour. Plann. Manage.
0733-9496,
126
(
4
), pp.
236
244
.
3.
Ghidaoui
,
M. S.
,
Mansour
,
G. S.
, and
Zhao
,
M.
, 2002, “
Applicability of Quasi-Steady and Axisymmetric Turbulence Models in Waterhammer Models
,”
J. Hydraul. Eng.
0733-9429,
128
(
10
), pp.
917
924
.
4.
Franke
,
P. G.
, and
Seyler
,
F.
, 1983, “
Computation of Unsteady Pipe Flow With Respect to Viscoelastic Material Properties
,”
J. Hydraul. Res.
0022-1686,
21
(
5
), pp.
345
353
.
5.
Ghilardi
,
P.
, and
Paoletti
,
A.
, 1986, “
Additional Viscoelastic Pipes as Pressure Surges Suppressors
,”
Proceedings of the 5th International Conference on Pressure Surges, BHRA
, Cranfield, UK, pp.
113
121
.
6.
Güney
,
M. S.
, 1983, “
Waterhammer in Viscoelastic Pipes Where Cross-Section Parameters Are Time-Dependent
,”
Fourth International Conference on Pressure Surges, BHRA
, England, UK, Sep. 21–23.
7.
Pezzinga
,
G.
, and
Scandura
,
P.
, 1995, “
Unsteady Flow in Installation With Polymeric Additional Pipe
,”
J. Hydraul. Eng.
0733-9429,
121
(
11
), pp.
802
811
.
8.
Covas
,
D.
,
Stoianov
,
I.
,
Mano
,
J.
,
Ramos
,
H.
,
Graham
,
N.
, and
Maksimovic
,
C.
, 2004, “
The Dynamic Effect of Pipe-Wall Viscoelasticity in Hydraulic Transients, Part 1—Experimental Analysis and Creep Characterization
,”
J. Hydraul. Res.
0022-1686,
42
(
5
), pp.
516
530
.
9.
Covas
,
D.
,
Stoianov
,
I.
,
Mano
,
J.
,
Ramos
,
H.
,
Graham
,
N.
, and
Maksimovic
,
C.
, 2005, “
The Dynamic Effect of Pipe-Wall Viscoelasticity in Hydraulic Transients, Part 2—Model Development, Calibration and Verification
,”
J. Hydraul. Res.
0022-1686,
43
(
1
), pp.
56
70
.
10.
Liou
,
J. C.
, 1998, “
Pipeline Leak Detection by Impulse Response Extraction
,”
ASME J. Fluids Eng.
0098-2202,
120
(
4
), pp.
833
838
.
11.
Wang
,
X. J.
,
Lambert
,
M. F.
,
Simpson
,
A. R.
,
Liggett
,
J. A.
, and
Vítkovský
,
J. P.
, 2002, “
Leak Detection in Pipeline Systems Using the Damping of Fluid Transients
,”
J. Hydraul. Eng.
0733-9429,
128
(
7
), pp.
697
711
.
12.
Ferrante
,
M.
, and
Brunone
,
B.
, 2003a, “
Pipe System Diagnosis and Leak Detection by Unsteady-State Tests—1: Harmonic Analysis
,”
Adv. Water Resour.
0309-1708,
26
, pp.
95
105
.
13.
Ferrante
,
M.
, and
Brunone
,
B.
, 2003b, “
Pipe System Diagnosis and Leak Detection by Unsteady-State Tests—2: Wavelet Analysis
,”
Adv. Water Resour.
0309-1708,
26
, pp.
107
116
;
Ferrante
,
M.
, and
Brunone
,
B.
, 2003b, “
Pipe System Diagnosis and Leak Detection by Unsteady-State Tests—2: Wavelet Analysis
,”
Mathematics
,
7th ed.
,
Wiley
,
New York
.
14.
Lee
,
P. J.
,
Lambert
,
M. F.
,
Simpson
,
A. R.
,
Vítkovský
,
J. P.
, and
Liggett
,
J.
, 2006, “
Experimental Verification of the Frequency Response Method for Pipeline Leak Detection
,”
J. Hydraul. Res.
0022-1686,
44
(
5
), pp.
693
707
.
15.
Lee
,
P. J.
,
Vítkovský
,
J. P.
,
Lambert
,
M. F.
,
Simpson
,
A. R.
, and
Liggett
,
J.
, 2007, “
Leak Location In Pipelines Using the Impulse Response Function
,”
J. Hydraul. Res.
0022-1686,
45
(
5
), pp.
643
652
.
16.
Sattar
,
A. M.
, and
Chaudhry
,
M. H.
, 2008, “
Leak Detection in Pipelines by Frequency Response Method
,”
J. Hydraul. Res.
0022-1686,
46
, pp.
138
151
.
17.
Aklonis
,
J. J.
, and
MacKnight
,
W. J.
, 1983,
Introduction to Polymer Viscoelasticity
,
2nd ed.
,
Wiley
,
New York
.
18.
Ghidaoui
,
M. S.
,
Zhao
,
M.
,
McInnis
,
D. A.
, and
Axworthy
,
D. H.
, 2005, “
A Review of Waterhammer Theory and Practice
,”
ASME Appl. Mech. Rev.
,
58
(
1
), pp.
49
76
.
19.
Zielke
,
W.
, 1968, “
Frequency-Dependent Friction in Transient Pipe Flow
,”
ASME J. Basic Eng.
0021-9223,
90
(
1
), pp.
109
115
.
20.
Vardy
,
A. E.
, and
Brown
,
J. M. B.
, 1995, “
Transient, Turbulent Smooth Pipe Flow
,”
J. Hydraul. Res.
0022-1686,
33
(
4
), pp.
435
456
.
21.
Karney
,
B. W.
, 1990, “
Energy Relations in Transient Closed-Conduit Flow
,”
J. Hydraul. Eng.
0733-9429,
116
(
10
), pp.
1180
1196
.
22.
Kreyszig
,
E.
, 1993,
Advanced Engineering Mathematics
,
7th ed.
,
Wiley
,
New York
.
You do not currently have access to this content.