A Review of Water Hammer Theory and Practice

[+] Author and Article Information
Mohamed S. Ghidaoui, Ming Zhao

Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong, China

Duncan A. McInnis

Surface Water Group, Komex International Ltd., 4500 16th Avenue, Suite 100, N. W. Calgary, Alberta T3B 0M6, Canada

David H. Axworthy

163 N. Marengo Avenue, #316, Pasadena, CA 91101email: bm300@lafn.org

Appl. Mech. Rev 58(1), 49-76 (Mar 08, 2005) (28 pages) doi:10.1115/1.1828050 History: Online March 08, 2005
Copyright © 2005 by ASME
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Vanderburg,  V. H., 1986, “Knowing Technology as if People Mattered,” Man-Env. Syst. 16, pp. 69–75.
Kuhn, T., 1962, The Structure of Scientific Revolutions, University of Chicago Press, Chicago, IL.
Menabrea,  L. F., 1885, “Note sur les effects de choc de l’eau dans les conduites,” C. R. Hebd. Seances Acad. Sci. 47, July–Dec., pp. 221–224.
Michaud,  J., 1878, “Coups de bélier dans les conduites. Étude des moyens employés pour en atteneur les effects,” Bull. Soc. Vaudoise Ing. Arch. 4(3,4), pp. 56–64, 65–77.
Weston,  E. B., 1885, “Description of Some Experiments Made on the Providence, RI Water Works to Ascertain the Force of Water Ram in Pipes,” Trans. Am. Soc. Civ. Eng. 14, p. 238.
Carpenter, R. C., 1893, “Experiments on Waterhammer,” Trans. ASME, 15 .
Frizell,  J. P., 1898, “Pressures Resulting from Changes of Velocity of Water in Pipes,” Trans. Am. Soc. Civ. Eng. 39, pp. 1–18.
Joukowski,  N. E., 1898, “Memoirs of the Imperial Academy Society of St. Petersburg,” 9 (5) (Russian translated by O Simin 1904), Proc. Amer. Water Works Assoc. 24, pp. 341–424.
Allievi, L., 1903, “Teoria generale del moto perturbato dell’acqu ani tubi in pressione,” Ann. Soc. Ing. Arch. Ithaliana (French translation by Allievi (1904, Revue de mécanique).
Allievi, L., 1913, “Teoria del colpo d’ariete,” Atti Collegio Ing. Arch. (English translation by Halmos EE 1929), “The Theory of Waterhammer,” Trans. ASME.
Courant, R. and Friedrichs, K. O., 1976, Supersonic Flow and Shock Waves, Springer-Verlag, New York.
Jaeger, C., 1933, Theorie Generale du Coup de Belier, Dunod, Paris.
Jaeger, C., 1956, Engineering Fluid Mechanics translated from German by P.O. Wolf, Blackie, London.
Wood,  F. M., 1937, “The Application of Heavisides Operational Calculus to the Solution of Problems in Waterhammer,” Trans. ASME 59, pp. 707–713.
Rich, G., 1944, “Waterhammer Analysis by the Laplace-Mellin Transformations,” Trans. ASME, pp. 1944–45.
Rich, G., 1951, Hydraulic Transients, 1st Edition, McGraw-Hill, New York, 1951 (Dover Reprint).
Parmakian, J., 1955, Water-Hammer Analysis. Prentice-Hall Englewood Cliffs, N.J., 1955 (Dover Reprint, 1963).
Streeter,  V. L., and Lai,  C., 1963, “Waterhammer Analysis Including Fluid Friction,” Trans. Am. Soc. Civ. Eng. 128, pp. 1491–1524.
Streeter, V. L. and Wylie, E. B., 1967, Hydraulic Transients, McGraw-Hill, New York.
Chaudhry, M. H., 1987, Applied Hydraulic Transients, Van Nostrand Reinhold, New York.
Watters, G. Z., 1984, Analysis and Control of Unsteady Flow in Pipelines, Butterworth, Stoneham, Ma.
Wylie, E. B. and Streeter, V. .L 1984, Fluid Transients, FEB Press, Ann Arbor.
Wylie, E. B., Streeter, V. L., and Suo, Lisheng, 1993, Fluid Transient in Systems, Prentice-Hall, Englewood Cliffs,
Mitra,  A. K., and Rouleau  W. T., 1985, “Radial and Axial Variations in Transient Pressure Waves Transmitted Through Liquid Transmission Lines,” ASME J. Fluids Eng. 107, pp. 105–111.
Vardy,  A. E., and Hwang,  K. L., 1991, “A Characteristic Model of Transient Friction in Pipes,” J. Hydraul. Res. 29(5), pp. 669–685.
Ghidaoui, M. S. 2001, “Fundamental Theory of Waterhammer,” Special Issue of the Urban Water J. (Special Issue on Transients, Guest Editor: B. W. Karney), 1 (2), pp. 71–83.
Walker,  J. S., 1975, “Perturbation Solutions for Steady One-Dimensional Waterhammer Waves,” ASME J. Fluids Eng. 6, pp. 260–262.
Hinze, J. O., 1975, Turbulence, McGraw-Hill Classic Textbook Reissue Series, New York.
Bergant, A. and Simpson, A. R., 1994, “Estimating Unsteady Friction in Transient Cavitating Pipe Flow,” Proc. 2nd Int. Conf. on Water Pipeline Systems, Edinburgh, UK, May 24–26, BHRA Group Conf. Series Publ. No. 110, pp. 3–15.
Axworthy,  D. H., Ghidaoui,  M. S., and McInnis,  D. A., 2000, “Extended Thermodynamics Derivation of Energy Dissipation in Unsteady Pipe Flow,” J. Hydraul. Eng. 126(4), pp. 276–287.
Brunone,  B., Karney,  B. W., Mecarelli,  M., and Ferrante,  M., 2000, “Velocity Profiles and Unsteady Pipe Friction in Transient Flow,” J. Water Resour. Plan. Manage. 126(4), pp. 236–244.
Ghidaoui,  M. S., and Mansour,  S., 2002, “Efficient Treatment of the Vardy-Brown Unsteady Shear in Pipe Transients,” J. Hydraul. Eng. 128(1), pp. 102–112.
Korteweg,  D. J., 1878, “Über die fortpflanzungsgeschwindigkeit des schalles in elastischen rohren,” Ann. Phys. Chemie 5(12), pp. 525–542.
Lighthill, J., 1996, Waves in Fluids, Cambridge University Press, UK.
Tijsseling,  A. S., 1995, “Fluid-Structure Interaction in Liquid-Filled Pipe Systems: A Review,” J. Fluids Struct. 10, pp. 109–146.
Streeter, V. L. and Wylie, E. B., 1985, Fluid Mechanics (8th Edition), McGraw Hill New York.
Silva-Araya,  W. F., and Chaudhry,  M. H., 1997, “Computation of Energy Dissipation in Transient Flow,” J. Hydraul. Eng. 123(2), pp. 108–115.
Pezzinga,  G., 1999, “Quasi-2D Model for Unsteady Flow in Pipe Networks,” J. Hydraul. Eng. 125(7), pp. 676–685.
Daily,  J. W., Hankey,  W. L., Olive,  R. W., and Jordaan,  J. M., 1956, “Resistance Coefficients for Accelerated and Decelerated Flows Through Smooth Tubes and Orifices,” Trans. ASME 78(July), pp. 1071–1077.
Shuy,  E. B., 1996, “Wall Shear Stress in Accelerating and Decelerating Turbulent Pipe Flows,” J. Hydraul. Res. 34(2), pp. 173–183.
Vardy,  A. E., and Brown,  J. M. B., 1997, “Discussion on Wall Shear Stress in Accelerating and Decelerating Pipe Flow,” J. Hydraul. Res. 35(1), pp. 137–139.
Ghidaoui,  M. S., and Kolyshkin,  A. A., 2001, “Stability Analysis of Velocity Profiles in Water-Hammer Flows,” J. Hydraul. Eng. 127(6), pp. 499–512.
Carstens,  M. R., and Roller,  J. E., 1959, “Boundary-Shear Stress in Unsteady Turbulent Pipe Flow,” J. Hydraul. Div., Am. Soc. Civ. Eng. 85(HY2), pp. 67–81.
Pezzinga,  G., 2000, “Evaluation of Unsteady Flow Resistances by Quasi-2d or 1d Models,” J. Hydraul. Eng. 126(10), pp. 778–785.
Eichinger, P. and Lein, G., 1992, The Influence of Friction on Unsteady Pipe Flow, Unsteady Flow and Fluid Transients, Bettess and Watts (eds), Balkema, Rotterdam, The Netherlands, 41–50.
Ghidaoui,  M. S., Mansour,  S. G. S., and Zhao,  M., 2002, “Applicability of Quasi Steady and Axisymmetric Turbulence Models in Water Hammer,” J. Hydraul. Eng. 128(10), pp. 917–924.
Vardy, A. E. and Brown, J, M., 1996, “On Turbulent, Unsteady, Smooth-Pipe Friction, Pressure Surges and Fluid Transient,” BHR Group, London, pp. 289–311.
Brunone, B. and Golia, U. M., 1991, “Some Considerations on Velocity Profiles in Unsteady Pipe Flows,” Proc. Int. Conf. on Enthropy and Energy Dissipation in Water Resources, Maratea, Italy, pp. 481–487.
Greco, M., 1990, “Some Recent Findings On Column Separation During Water Hammer,” Excerpta, G.N.I., Padua, Italy, Libreria Progetto, ed., 5 , 261–272.
Brunone, B., Golia, U. M., and Greco, M., 1991, “Some Remarks on the Momentum Equation for Fast Transients,” Proc. Int. Conf. on Hydr. Transients With Water Column Separation, IAHR, Valencia, Spain, 201–209.
Brunone, B., Golia, U. M., and Greco, M., 1991, “Modelling of Fast Transients by Numerical Methods,” Proc. Int. Conf. on Hydr. Transients With Water Column Separation, IAHR, Valencia, Spain, 273–280.
Bergant,  A., Simpson,  A. R., and Vitkovsky,  J., 2001, “Developments in Unsteady Pipe Flow Friction Modelling,” J. Hydraul. Res. 39(3), pp. 249–257.
Brunone,  B., Golia,  U. M., and Greco,  M., 1995, “Effects of Two-Dimensionality on Pipe Transients Modeling,” J. Hydraul. Eng. 121(12), pp. 906–912.
Wylie,  E. B., 1997, “Frictional Effects in Unsteady Turbulent Pipe Flows,” Appl. Mech. Rev. 50(11), Part 2, pp. S241–S244.
Vitkovsky, J. P., Lambert, M. F., Simpson, A. R., and Bergant, A., 2000, “Advances in Unsteady Friction Modelling in Transient Pipe Flow,” 8th Int. Conf. on Pressure Surges, The Hague, The Netherlands.
Zielke,  W., 1968, “Frequency-Dependent Friction in Transient Pipe Flow,” ASME J. Basic Eng. 90(1), pp. 109–115.
Trikha,  A. K., 1975, “An Efficient Method for Simulating Frequency-Dependent Friction in Transient Liquid Flow,” ASME J. Fluids Eng. 97(1), pp. 97–105.
Suzuki,  K., Taketomi,  T., and Sato,  S., 1991, “Improving Zielke’s Method of Simulating Frequency-Dependent Friction in Laminar Liquid Pipe Flow,” ASME J. Fluids Eng. 113(4), pp. 569–573.
Vardy,  A. E., Hwang,  K. L., and Brown,  J. M. B., 1993, “A Weighting Model of Transient Turbulent Pipe Friction,” J. Hydraul. Res. 31, pp. 533–548.
Vardy,  A. E., and Brown,  J. M. B., 1995, “Transient, Turbulent, Smooth Pipe Friction,” J. Hydraul. Res. 33, pp. 435–456.
Almeida, A. B. and Koelle, E., 1992, Fluid Transients in Pipe Networks, Computational Mechanics Publications, Elsevier, New York.
Lister, M., 1960, The Numerical Solution of Hyperbolic Partial Differential Equations by the Method of Characteristics, A Ralston and HS Wilf (eds), Numerical Methods for Digital Computers, Wiley New York, 165–179.
Wiggert,  D. C., and Sundquist,  M. J., 1977, “Fixed-Grid Characteristics for Pipeline Transients,” J. Hydraul. Div., Am. Soc. Civ. Eng. 103(HY12), pp. 1403–1415.
Goldberg,  D. E., and Wylie,  E. B., 1983, “Characteristics Method Using Time-Line Interpolations,” J. Hydraul. Eng. 109(5), pp. 670–683.
Lai,  C., 1989, “Comprehensive Method of Characteristics Models for Flow Simulation,” J. Hydraul. Eng. 114(9), pp. 1074–1095.
Yang,  J. C., and Hsu,  E. L., 1990, “Time-Line Interpolation for Solution of the Dispersion Equation,” J. Hydraul. Res. 28(4), pp. 503–523.
Yang,  J. C., and Hsu,  E. L., 1991, “On the Use of the Reach-Back Characteristics Method of Calculation of Dispersion,” Int. J. Numer. Methods Fluids 12, pp. 225–235.
Bentley,  L. R., 1991, Discussion of “On the Use of the Reach-Back Characteristics Method for Calculation of Dispersion,” by J. C. Yang, and EL Hsu, Int. J. Numer. Methods Fluids 13(5), pp. 1205–1206.
Sibertheros,  I. A., Holley,  E. R., and Branski,  J. M., 1991, “Spline Interpolations for Water Hammer Analysis,” J. Hydraul. Eng. 117(10), pp. 1332–1349.
Karney,  B. W., and Ghidaoui,  M. S., 1997, “Flexible Discretization Algorithm for Fixed Grid MOC in Pipeline Systems,” J. Hydraul. Eng. 123(11), pp. 1004–1011.
Wood,  D. J., Dorsch,  R. G., and Lightnor,  C., 1966, “Wave-Plan Analysis of Unsteady Flow in Closed Conduits,” J. Hydraul. Div., Am. Soc. Civ. Eng. 92(HY12), pp. 83–110.
Wylie, E. B. and Streeter, V. L., 1970, “Network System Transient Calculations by Implicit Method,” 45th Annual Meeting of the Society of Petroleum Engineers of AIME, Houston, Texas October 4–7, paper No. 2963.
Holly,  F. M., and Preissmann,  A., 1977, “Accurate Calculation of Transport in Two Dimensions,” J. Hydraul. Div., Am. Soc. Civ. Eng. 103(HY11), pp. 1259–1277.
Chaudhry,  M. H., and Hussaini,  M. Y., 1985, “Second-Order Accurate Explicitly Finite-Difference Schemes for Water Hammer Analysis,” ASME J. Fluids Eng. 107, pp. 523–529.
Toro, E. F., 1997, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Berlin.
Toro, E. F., 2001, Shock-Capturing Methods for Free-Surface Shallow Flows, Wiley Ltd, Chichester, England.
Guinot,  V., 2002, “Riemann Solvers for Water Hammer Simulations by Godunov Method,” Int. J. Numer. Methods Eng. 49, pp. 851–870.
Hwang,  Y. H., and Chung,  N. M., 2002, “A Fast Godunov Method for the Water-Hammer Problem,” Int. J. Numer. Methods Fluids 40, pp. 799–819.
O’Brian,  G. G., Hyman,  M. A., and Kaplan,  S., 1951, “A Study of the Numerical Solution of Partial Differential Equations,” J. Math. Phys. 29(4), pp. 223–251.
Damuller,  D. C., Bhallamudi,  S. M., and Chaudhry,  M. H., 1989, “Modelling Unsteady Flow in Curved Channel,” J. Hydraul. Eng. 115(11), pp. 1471–1495.
Samuels,  G. P., and Skeel,  P. C., 1990, “Stability Limits for Preissmann’s Scheme,” J. Hydraul. Div., Am. Soc. Civ. Eng. 116(HY8), pp. 997–1011.
Karney,  B. W., and Ghidaoui,  M. S., 1992, “Discussion on Spline Interpolations for Water Hammer Analysis,” J. Hydraul. Eng. 118(11), pp. 1597–1600.
Sivaloganathan,  K., 1978, “Flood Routing by Characteristic Methods,” J. Hydraul. Div., Am. Soc. Civ. Eng. 107(HY7), pp. 1075–1091.
Wylie, E. B., 1980, “Inaccuracies in the Characteristics Method,” Proc. Spec. Conf. on Comp. and Physical Modelling in Hydr. Eng. ASCE, Chicago, 165–176.
Ghidaoui,  M. S., and Karney,  B. W., 1994, “Equivalent Differential Equations in Fixed-Grid Characteristics Method,” J. Hydraul. Eng. 120(10), pp. 1159–1176.
Ghidaoui,  M. S., Karney,  B. W., and McInnis,  D. A., 1998, “Energy Estimates for Discretization Errors in Waterhammer Problems,” J. Hydraul. Eng. 123(11), pp. 384–393.
Das,  D., and Arakeri,  J. H., 1998, “Transition of Unsteady Velocity Profiles with Reverse Flow,” J. Fluid Mech. 374, pp. 251–283.
Brunone, B., Karney, B. W., and Ferrante, M., 1999, “Velocity Profiles Unsteady Friction Losses and Transient Modelling,” Proc. 26th Annu. Water Resour. Plng. and Mgmt. Conf. ASCE, Reston, VA (on CD-ROM).
Lodahl,  C. R., Sumer,  B. M., and Fredsoe,  J., 1998, “Turbulent Combined Oscillatory Flow and Current in Pipe,” J. Fluid Mech. 373, pp. 313–348.
Ghidaoui,  M. S., and Kolyshkin,  A. A., 2002, “A Quasi-Steady Approach to the Instability of Time-Dependent Flows in Pipes,” J. Fluid Mech. 465, pp. 301–330.
Pezzinga,  G., and Scandura,  P., 1995, “Unsteady Flow in Installations with Polymeric Additional Pipe,” J. Hydraul. Eng. 121(11), pp. 802–811.
Greenblatt,  D., and Moss,  E. A., 1999, “Pipe-Flow Relaminarization by Temporal Acceleration,” Phys. Fluids 11(11), pp. 3478–3481.
He,  S., and Jackson,  J. D2000, “A Study of Turbulence Under Conditions of Transient Flow in a Pipe,” J. Fluid Mech. 408, pp. 1–38.
Tu,  S. W., and Ramaprian,  B. R., 1983, “Fully Developed Periodic Turbulent Pipe Flow–Part 1: Main Experimental Results and Comparison with Predictions,” J. Fluid Mech. 137, pp. 31–58.
Brereton,  G. L., Reynolds,  W. C., and Jayaraman,  R., 1990, “Response of a Turbulent Boundary Layer to Sinusoidal Free-Stream Unsteadiness,” J. Fluid Mech. 221, pp. 131–159.
Akhavan,  R., Kamm,  R. D., and Shapiro,  A. H., 1991, “Investigation of Transition to Turbulence in Bounded Oscillatory Stokes Flows–Part 1: Experiments,” J. Fluid Mech. 225, pp. 395–422.
Akhavan,  R., Kamm,  R. D., and Shapiro,  A. H., 1991, “Investigation of Transition to Turbulence in Bounded Oscillatory Stokes Flows–Part 2: Numerical Simulations,” J. Fluid Mech. 225, pp. 423–444.
Silva-Araya,  W. F., and Chaudhry,  M. H., 2001, “Unsteady Friction in Rough Pipes,” J. Hydraul. Eng. 127(7), pp. 607–618.
Ohmi,  M., Kyomen,  S., and Usui,  T., 1985, “Numerical Analysis of Transient Turbulent Flow in a Liquid Line,” Bull. JSME 28(239), pp. 799–806.
Wood,  D. J., and Funk,  J. E., 1970, “A Boundary-Layer Theory for Transient Viscous Losses in Turbulent Flow,” ASME J. Basic Eng. 102, pp. 865–873.
Bratland, O., 1986, “Frequency-Dependent Friction and Radial Kinetic Energy Variation in Transient Pipe Flow,” Proc. 5th Int. Conf. on Pressure Surges, BHRA, Hannover, Germany, 95–101.
Rodi, W., 1993, Turbulence Models and Their Application in Hydraulics: A State-of-the-Art Review, 3rd Edition, Int. Association for Hydraulic Research, Delft, Balkema.
Kita,  Y., Adachi,  Y., and Hirose,  K., 1980, “Periodically Oscillating Turbulent Flow in a Pipe,” Bull. JSME 23(179), pp. 654–664.
Eggels, J. G. M., 1994, “Direct and Large Eddy Simulation of Turbulent Flow in a Cylindrical Pipe Geometry,” PhD Dissertation, Delft University of Technology.
Zhao,  M., and Ghidaoui,  M. S., 2003, “An Efficient Solution for Quasi-Two-Dimensional Water Hammer Problems,” J. Hydraul. Eng., 129(12), pp. 1007–1013.
Karney,  B. W., and McInnis,  D., 1990, “Transient Analysis of Water Distribution Systems,” J. AWWA 82(7), pp. 62–70.
Wylie,  E. B., 1983, “The Microcomputer and Pipeline Transients,” J. Hydraul. Div., Am. Soc. Civ. Eng. 109(HY12), pp. 539–42.
Karney, B. W., 1984, “Analysis of Fluid Transients in Large Distribution Networks,” Ph.D. thesis, University of British Columbia, Vancouver, Canada.
Fox, J. A., 1977, Hydraulic Analysis and Unsteady Flow in Pipe Networks, MacMillan Press, London.
Koelle, E., 1982, “Transient Analysis of Pressure Conduit Hydraulic Systems,” Proc the Int. Institute on Hydraulic Transients and Cavitation, Sao Paulo, Brazil, B1.1–B1.38.
McInnis, D. A., 1992, “Comprehensive Hydraulic Analysis of Complex Pipe Systems,” Ph.D. thesis, University of Toronto, Toronto, Canada.
McInnis,  D. A., Karney,  B. W., and Axworthy,  D. H., 1997, “Efficient Valve Representation in Fixed-Grid Characteristics Method,” J. Hydraul. Eng. 123(8), pp. 709–718.
Beck, J. L. and Katafygiotis, L. S., 1992, “Updating Dynamic Models and Their Associated Uncertainties for Structural Systems,” Pro. the 9th Engineering Mechanics Conference, L. D. Lutes and J. M. Niedzwecki, eds., ASCE, Reston, VA, pp. 681–684.
Sykes,  J. F., 1985, “Sensitivity Analysis for Steady State Ground Water Flow Using Adjoint Operators,” Water Resour. Res. 21(3), pp. 359–371.
Sun,  N. Z., and Yeh,  W. G., 1990, “Coupled Inverse Problems in Groundwater Modeling–2: Identifiability and Experimental Design,” Water Resour. Res. 26(10), pp. 2527–2540.
Sun, N. Z., 1994, Inverse Problems in Groundwater Modeling, Kluwer Academic Publishers.
Jarny,  Y., Ozisik,  M. N., and Bardon,  J. P., 1991, “A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction,” Int. J. Heat Mass Transfer 34(11), pp. 2911–2919.
Cacuci,  D. G., and Hall,  M. C. G., 1984, “Efficient Estimation of Feedback Effects with Application to Climate Models,” J. Atmos. Sci. 13(2), pp. 2063–2068.
Hall,  M. C. G. , 1986, “Application of Adjoint Sensitivity Theory to an Atmospheric General Circulation Model,” J. Atmos. Sci. 43(22), pp. 2644–2651.
Marchuk, G. I., 1995, Adjoint Equations and Analysis of Complex Systems, Kluwer, London.
Liggett,  J. A., and Chen,  L. C., 1994, “Inverse Transient Analysis in Pipe Networks,” J. Hydraul. Eng. 120(8), pp. 934–995.
Karney, B. W. and Tang, K., 2003, personal communication.
Brunone,  B., 1999, “Transient Test-Based Technique for Leak Detection in Outfall Pipes,” J. Water Resour. Plan. Manage. 125(5), pp. 302–306.
Brunone,  B., and Ferrante,  M., 2001, “Detecting Leaks in Pressurised Pipes by Means of Transient,” J. Hydraul. Res. 39(5), pp. 539–547.
Mpesha,  W., Gassman,  S. L., and Chaudhry,  M. H., 2001, “Leak Detection in Pipes by Frequency Response Method,” J. Hydraul. Eng. 127(2), pp. 137–147.
Mpesha,  W., Chaudhry,  M. H., and Gassman  SL 2002, “Leak Detection in Pipes by Frequency Response Method Using a Step Excitation,” J. Hydraul. Res. 40(1), pp. 55–62.
Ferrante,  M., and Brunone,  B., 2002, “Pipe System Diagnosis and Leak Detection by Unsteady-State Tests–1: Harmonic Analysis,” Adv. Water Resour. 26, pp. 95–105.
Wang,  Xiao-Jian, Lambert,  M. F., Simpson,  A. R., and Liggett,  J. A., 2002, “Leak Detection in Pipelines Using the Damping of Fluid Transients,” J. Hydraul. Eng. 128(7), pp. 697–711.
Ferrante,  M., and Brunone,  B., 2002, “Pipe System Diagnosis and Leak Detection by Unsteady-State Tests–2: Wavelent Analysis,” Adv. Water Resour. 26, pp. 107–116.
Payment,  P., 1999, “Poor Efficacy of Residual Chlorine Disinfectant in Drinking Water to Inactivate Waterborne Pathogens in Distribution system,” Can. J. Microbiol. 45(8), pp. 709–715.
Funk, J. E., van Vuuren, S. J., Wood, D. J., and LeChevallier, M., 1999, “Pathogen Intrusion into Water Distribution Systems Due to Transients,” Proc. 3rd ASME/JSME Joint Fluids Engineering Conf., July 18–23, San Francisco, California.
Germanopoulos, G. and Jowitt, P. W., 1989, “Leakge Reduction by Excessive Pressure Minimization in a Water Supply Network,” Proc. Inst. of Civ. Eng. (UK), 195–214.
McInnis, D. A., 2003, “A Relative-Risk Assessment Framework for Evaluating Pathogen Intrusion During Transient Events in Water Pipelines,” Urban Water J. (Special Issue on Transients, Guest Editor: B. W. Karney), 1 (2), pp. 113–127.


Grahic Jump Location
Control volume diagram used for momentum equation derivation
Grahic Jump Location
Velocity profiles for steady-state and after wave passages
Grahic Jump Location
Pressure head traces obtained from models and experiment
Grahic Jump Location
Weighting function for different Reynolds numbers
Grahic Jump Location
Method of characteristics grid
Grahic Jump Location
Generalized node with one external flow
Grahic Jump Location
Control volume diagram used for continuity equation derivation




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