Skip to main content
SpringerLink
Log in

Transient Open-Channel Flows

  • Chapter
Applied Hydraulic Transients

  • 5053 Accesses

Abstract

In the previous chapters, we considered transient flows in the closed conduits. In this chapter, we discuss transient flows in open channels. A flow having a free surface is considered open-channel flow even though the channel may be closed at the top, e.g., a tunnel flowing partially full. A number of common terms are defined, and the examples of transient flows are presented. The dynamic and continuity equations describing these flows are derived, and a number of methods for their solution are discussed. Details of explicit finite-difference and implicit finite-difference method are then presented. This is followed by a discussion of a number of special topics on open-channel transients. The chapter concludes with a case study.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    a At a net head of 164.6 m.

References

  • Abbott, M. B., 1966, An Introduction to the Method of Characteristics, American Elsevier, New York.

    Google Scholar 

  • Abbott, M. B. and Verwey, A., 1970, “Four-Point Method of Characteristics,” Jour. Hydr. Div., Amer. Soc. of Civil Engrs., vol. 96, Dec., pp. 2549-2564.

    Google Scholar 

  • Amein, M. and Fang, C. S., 1970, “Implicit Flood Routing in Natural Channels,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 96, Dec., pp. 2481-2500.

    Google Scholar 

  • Anderson, D. A., Tannehill, J. C. and Pletcher, R. H., 1984, Computational Fluid Mechanics and Heat Transfer, McGraw-Bill, New York, NY.

    MATH  Google Scholar 

  • Babcock, C. I., 1975, “Impulse Wave and Hydraulic Bore Inception and Propagation as Resulting from Landslides,” a research problem presented to Georgia Inst. of Tech., Atlanta, Georgia, in partial fulfillment of the requirements for the degree of M.Sc. in civil engineering, Oct..

    Google Scholar 

  • Balloffet, A., Cole, E. and Balloffet, A. F., 1974, “Dam Collapse Wave in a River,” Jour. Hyd. Div., Amer. Soc. of Civil Engrs., vol. 100, No. HY5, May, pp. 645-665.

    Google Scholar 

  • Baltzer, R. A. and Lai, C., 1968, “Computer Simulation of Unsteady Flows in Waterways,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 94, July, pp. 1083-1117.

    Google Scholar 

  • Benet, F. and Cunge, J. A., 1971, “Analysis of Experiments on Secondary Undulations Caused by Surge Waves in Trapezoidal Channels,” Jour. of Hydraulic Research, Inter. Assoc. for Hyd. Research, vol. 9, no. I, pp. 11-33.

    Google Scholar 

  • Calame, J., 1932, “Calcul de l’onde translation dans les canaux d’usines,” Editions la Concorde, Lausanne, Switzerland.

    Google Scholar 

  • Chaudhry, M. H., 1976, “Mathematical Modelling of Transient Stale Flows in Open Channels,” Proc. International Symposium on Unsteady Flow in Open Channels, Newcastle-upon-Tyne, published by British Hydromechanics Research Assoc., Cranfield, Bedford, England, pp. C1-1 C1-18.

    Google Scholar 

  • Chaudhry, M. H. and Kao, K. H., 1976, “G. M. Shrum Generating Station: Tailrace Surges and Operating Guidelines During High Tailwater Levels,” Report, British Columbia Hydro and Power Authority, Vancouver, B.C., November.

    Google Scholar 

  • Chaudhry, M. H., Mercer, A. G. and Cass, D. E., 1983, “Modeling of Slide-Generated Waves in a Reservoir,” Jour. Hydraulic Engineering, Amer. Soc. of Civil Engrs., vol. 109, Nov., pp. 1505-1520.

    Google Scholar 

  • Chaudhry, M. H. and Hussaini, M. Y., 1985, “Second-Order Accurate Explicit Finite Difference Schemes for Waterhammer Analysis,” Jour. of Fluids Engineering, Amer. Soc. Mech. Engrs., Dec., pp. 523-529.

    Google Scholar 

  • Chaudhry, M. H. 2008, “Open-Channel Flow,” 2nd ed., Springer, New York, NY.

    Google Scholar 

  • Chen, C. L., 1980, “Laboratory Verification of a Dam-Break Flood Model,” Jour. Hyd. Div., Amer. Soc. of Civil Engrs., April, pp. 535-556.

    Google Scholar 

  • Chiang, W. L., Divoky, D., Parnicky, P. and Wier, W., 1981, “Numerical Model of LandslideGenerated Waves,” Prepared for U.S. Bureau of Reclamation by Tetra Tech., Inc., California, Nov..

    Google Scholar 

  • Chow, V. T., 1959, Open-Channel Hydraulics, McGraw-Hili Book Co., New York, NY.

    Google Scholar 

  • Cooley, R. L. and Moin, S. A., 1976, “Finite Element Solution of Saint-Venant Equations,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 102, June, pp. 759-775.

    Google Scholar 

  • Courant, R., Friedrichs, K. and Lewy, H., 1928, “Uberdie paniellen Differenzengleichungen der Mathematischen Physik,” Math. Ann., vol. 110, pp. 32-74 (in German).

    Article  MathSciNet  Google Scholar 

  • Cunge, J. A. and Wegner, M., 1964, “Integration Numerique des equations d’ecoulement de Barre de Saint Venant par un schema Implicite de differences finies,” La Houille Blanche, No. I, pp. 33-39.

    Google Scholar 

  • Cunge, J. A., 1966, “Comparison of Physical and Mathematical Model Test Results on Translation Waves in the Oraison-Manosque Power Canal,” La Houille Blanche, no. I, Grenoble, France, pp. 55-69, (in French).

    Google Scholar 

  • Cunge, J. A., 1969, “On the Subject of a Flood Propagation Computation Method (Muskingum Method),” Jour. of Hydraulic Research, vol. 7, no. 2, pp. 205-230.

    Article  Google Scholar 

  • Cunge, J. A., 1970, “Calcul de Propagation des Ondes de Rupture de Barrage,” La Houille Blanche, no. I, pp. 25-33.

    Google Scholar 

  • Cunge, J. A., Holley, F. M. and Verwey, A., 1980, Practical Aspects of Computational River Hydraulics, Pitman, London, UK.

    Google Scholar 

  • Das, M. M. and Wiegel, R. L., 1972, “Waves Generated by Horizontal Motion of a Wall,” Jour., Waterways, Harbors and Coastal Engineering Div., Amer. Soc. of Civ. Engrs., vol. 98, no. WWI, Feb., pp. 49-65.

    Google Scholar 

  • Davidson, D. D. and McCartney, B. L., 1975, “Water Waves Generated by Landslides in Reservoirs,” Jour., Hyd. Div., Amer. Soc. of Civ. Engrs., vol. 101, Dec., pp. 1489-1501.

    Google Scholar 

  • De Saint-Venant, B., 1871, “Theorie du movement non-permanent des eaux avec application aux crues des vivieres et a I’introduction des marees dans leur lit,” Acad. Sci. Comptes Rendus, Paris, vol. 73, pp. 148-154,237-240 (translated into English by U.S. Corps of Engineers, No. 49-g, Waterways Experiment Station, Vicksburg, Miss., 1949).

    Google Scholar 

  • Dressler, R. F., 1952, “Hydraulic Resistance Effect upon the Dam Break Functions,” Jour. of Research, U.S. Bureau of Standards, vol. 49, No.3, Sept., pp. 217-225.

    Google Scholar 

  • Dressler, R. F., 1954, “Comparison of Theories and Experiments for the Hydraulic Dam-Break Wave,” Intern. Assoc. of Scientific Hydrology, no. 38, vol. 3, pp. 319-328.

    Google Scholar 

  • Drioli, C., 1937, “Esperienze sul moto pertubato nei canali induslriali,” L’ Energie Elellrica, no. IV- V, vol. XIV, Milan, Italy, April-May.

    Google Scholar 

  • Dronkers, J. J., 1964, Tidal Computations in Rivers and Coastal Waters, North Holland Publishing Co., Amsterdam, the Netherlands.

    Google Scholar 

  • Favre, H., 1935, Ondes de translation dans les canaux de’couverts, Dunod.

    Google Scholar 

  • Fennema, R. J. and Chaudhry, M. H., 1986, “Explicit Numerical Schemes for Unsteady FreeSurface Flows with Shocks,” Water Resources Research, vol. 22(13).

    Google Scholar 

  • Fennema, R. J. and Chaudhry, M. H., 1986, “Simulation of One-Dimensional Dam-Break Flows” Jour. of Hydraulic Research., Intern. Assoc. for Hydraulic Research, vol. 25(1), pp. 41-51.

    Google Scholar 

  • Forstad, F., 1968, “Waves Generated by Landslides in Norwaygias Fjords and Lakes,” Publication No. 79, Norwegian Geotechnical Institute, Oslo, pp. 13-32.

    Google Scholar 

  • Fread, D. L. and Harbaugh, T. E., 1973, “Transient Simulation of Breached Earth Dams,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., Jan., pp. 139-154.

    Google Scholar 

  • Fread, D. L., 1974,“Numerical Properties of Implicit Four-Point Finite-Difference Equations of Unsteady Flow,” Tech. Memo NWS HYDRO-18, NOAA, U.S. National Weather Service.

    Google Scholar 

  • Fread, D. L., 1977, “The Development and Testing of a Dam-Break Flood Forecasting Model,” Proc., Dam Break Flood Routing Model Workshop, U.S. Dept. of Commerce, National Tech. Service, Oct., pp. 164-197.

    Google Scholar 

  • Henderson, F. M., 1966, Open Channel Flow, MacMillan, New York, NY.

    Google Scholar 

  • Jaeger, C., 1956, Engineering Fluid Mechanics, Blackie & Son Limited, London, UK, pp. 381-392.

    Google Scholar 

  • Jameson, A., Schmidt, W. and Turkel, E., 1981, “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes,” AIAA 14th Fluid and Plasma Dynamics Conf., Palo Alto, Calif., AIAA-81-1259.

    Google Scholar 

  • Johnson, R. D., 1922, “The Correlation of Momentum and Energy Changes in Steady Flow with Varying Velocity and the Application of the Former to Problems of Unsteady Flow or Surges in Open Channels,” Engineers and Engineering, The Engineers Club of Philadelphia, p.233.

    Google Scholar 

  • Kachadoorian, R., 1965, “Effects of the Earthquake of March 27 1964, at Whittier, Alaska,” Professional Paper, No. 542-B, U.S. Geological Survey.

    Google Scholar 

  • Kamphuis, J. W., 1970, “Mathematical Tidal Study of St. Lawrence River.” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 96, No. HY3, March, pp. 643-664.

    Google Scholar 

  • Kamphuis, J. W. and Bowering, R. J., 1970, “Impulse Waves Generated by Landslides,” Proc., Twelfth Coastal Engineering Conference, Amer. Soc. of Civ. Engrs., Washington, DC., Sept., pp. 575-588.

    Google Scholar 

  • Kao, K. H., 1977, “Numbering of a Y-Branch System to Obtain a Banded Matrix for Implicit Finite-Difference Scheme,” B.C. Hydro interoffice memorandum, Hydraulic Section, November.

    Google Scholar 

  • Katopodes, N. D. and Strelkoff, T., 1978, “Computing Two-Dimensional Dam-Break Flood Waves,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., Sept., pp. 1269-1287.

    Google Scholar 

  • Katopodes, N. D. and Strelkoff, T., 1979, “Two-Dimensional Shallow Water-Wave Models,” Jour. Engineering Mechanics Div., Amer. Soc. of Civil Engrs., vol. 105, No. EM2, Proc. Paper 14532, pp. 317-334.

    Google Scholar 

  • Katopodes, N. D. and Schamber, D. R., 1983, “Applicability of Dam-Break Flood Wave Models,” Jour. Hydraulic Engineering, Amer. Soc. of Civil Engrs., vol. 109, May, pp. 702-721.

    Google Scholar 

  • Katopodes, N. D., 1984, “A Dissipative Galerkin Scheme for Open-Channel Flow,” Jour. Hydraulic Engineering, Amer. Soc. of Civil Engrs., vol. 110, HY4, Proc. Paper 18743, April.

    Google Scholar 

  • Katopodes, N. D., 1984, “Two-Dimensional Surges and Shocks in Open Channels,” Jour. Hydraulic Engineering, Amer. Soc. of Civil Engrs., vol. 110, June, pp. 794-812.

    Google Scholar 

  • Kiersch, G. A., 1964, “Vaiont Reservoir Disaster,” Civ. Engineering, Amer. Soc. of Civ. Engrs., vol. 34, no. 3, March, pp. 32-47.

    Google Scholar 

  • Koutitas, C. G., 1977, “Finite Element Approach to Waves due to Landslides.” Jour., Hyd. Div., Amer. Soc. of Civ. Engrs., vol. 103, Sept., pp. 1021-1029.

    Google Scholar 

  • Law, L. and Brebner, A., 1968, “On Water Waves Generated by Landslides,” Third Australasian Conference on Hydraulics and Fluid Mechanics, Sidney, Australia, Nov., pp. 155159.

    Google Scholar 

  • Lax, P. D., 1954, “Weak Solutions of Nonlinear Hyperbolic Partial Differential Equations and Their Numerical Computation,” Communications on Pure and Applied Mathematics, vol. 7, pp. 159-163.

    Article  MATH  MathSciNet  Google Scholar 

  • Lax, P. D. and Wendroff, B., 1960,“Systems of Conservation Laws,” Communications on Pure and Applied Mathematics, vol. 13, pp. 217-237.

    Article  MATH  MathSciNet  Google Scholar 

  • Leendertse, J. J., 1967, “Aspects of a Computational Model for Long Period Water-Wave Propagation,” Memo RM-5294-PR, Rand Corporation, May.

    Google Scholar 

  • Liggett, J. A. and Woolhiser, D. A., 1967, “Difference Solutions of the Shallow-Water Equation,” Jour. Engineering Mech. Div., Amer. Soc. of Civil Engrs., vol. 93, April, pp. 39-71.

    Google Scholar 

  • MacCormack, R. W., 1969, “The Effect of Viscosity in Hypervelocity Impact Cratering,”Paper No. 69-354, Amer. Inst. Aero. Astro., Cincinnati, OH, April 30/May 2.

    Google Scholar 

  • Mahmood, K. and Yevjevich, V. (ed.), 1975, Unsteady Flow in Open Channels, Water Resources Publications, Fort Collins, CO.

    Google Scholar 

  • Martin, C. S. and Zovne, J. J., 1971, “Finite-Difference Simulation of Bore Propagation,” Jour., Hyd. Div., Amer. Soc. ofCiv. Engrs., vol. 97, No. HY7, July, pp. 993-1010.

    Google Scholar 

  • Martin, C. S. and DeFazio, F. G., 1969, “Open Channel Surge Simulation by Digital Computers,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 95, Nov., pp. 2049-2070.

    Google Scholar 

  • McCracken, D. D. and Dorn, W. S., 1967, Numerical Methods and FORTRAN Programming, John Wiley & Sons, New York, NY.

    Google Scholar 

  • McCullock, D. S., 1966, “Slide-Induced Waves, Seiching and Ground Fracturing Caused by the Earthquakes of March 27 1964, at Kenai Lake, Alaska,” Professional Paper 543-A, U.S. Geological Survey.

    Google Scholar 

  • Mercer, A. G., Chaudhry, M. H. and Cass, D. E., 1979, “Modeling of Slide-Generated Waves,” Proc, Fourth Hydrotechnical Conference, vol. 2, Canadian Society for Civil Engineering, May, pp. 730-745.

    Google Scholar 

  • Meyer-Peter, E. and Favre, H., 1932, “Ueber die Eigenschaften von Schwallen und die Berechnung von UnteIWasserstollen,” Schweizerische Bauzaitung, Nos. 4-5, vol. 100, Zurich, Switzerland, July, pp. 43-50, 61-66.

    Google Scholar 

  • Miller, D. J., 1960 “Giant Waves in Lituya Bay, Alaska,” Professional Paper 354-L, U.S. Geological Survey.

    Google Scholar 

  • Noda, E., 1970, “Water Waves Generated by Landslides,” Jour., Waterways, Harbors and Coastal Engineering Div., Amer., Soc. of Civ. Engrs., vol. 96, no. WW4, Nov., pp. 835-855.

    Google Scholar 

  • Patridge, P. W. and Brebbia, C. A., 1976, “Quadratic Finite Elements in Shallow Water Problems,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 102, Sept., pp. 1299-1313.

    Google Scholar 

  • Ponce, V. M. and Yevjevich, V., 1978, “Muskingum-Cunge Method with Variable Parameters,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 104, Dec., pp. 1663-1667.

    Google Scholar 

  • Preissmann, A. and Cunge, J. A., 1961, “Calcul des intumescences sur machines electroniques,” Proc. IX Meeting, International Assoc. for Hydraulic Research, Dubrovnik.

    Google Scholar 

  • Price, R. K., 1974, “Comparison of Four Numerical Methods for Flood Routing,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 100, July, pp. 879-899.

    Google Scholar 

  • Prins, J. E., 1958, “Characteristics of Waves Generated by a Local Disturbance,” Trans., Amer. Geophysical Union, vol. 39, no. 5, Oct., pp. 865-874.

    Google Scholar 

  • Proceedings 1977, Dam-Break Flood Routing Model Workshop, U.S. National Technical Information Service, Oct..

    Google Scholar 

  • Pugh, C. A., 1982, “Hydraulic Model Studies of Landslide-Generated Water Waves-Morrow Point Reservoir,” Report No. REC-ERC-82-9, Bureau of Reclamation, Denver, Colo., April.

    Google Scholar 

  • Rajar, R., 1978, “Mathematical Simulation of Dam-Break Flow,” Jour. Hyd. Div., Amer. Soc. of Civil Engrs., July, pp. 1011-1026.

    Google Scholar 

  • Rajar, R., 1983, “Two-Dimensional Dam-Break Flow in Steep Curved Channels,” XX Congress, Intern. Assoc. for Hydraulic Research, Moscow, Sept., pp. 199-200.

    Google Scholar 

  • Raney, D. C. and Butler, H. L., 1975, “A Numerical Model for Predicting the Effects of Landslide- Generated Water Waves,” Research Report H-75-1, U.S. Army Engineer WateIWays Experiment Station, Vicksburg, Miss., Feb..

    Google Scholar 

  • Richtmyer, R. D. and Morton, K. W., 1967, Difference Methods for Initial- Value Problems, 2nd ed., Interscience Publishers, New York, NY.

    MATH  Google Scholar 

  • Ritter, A., 1982, “Die Fortpflanzung der Wasserwellen,” Zeitschrifi des Vereines Deutscher Ingenieure, vol. 36, No. 33, Aug., pp. 947-954.

    Google Scholar 

  • Rouse, H. (ed.), 1961, Engineering Hydraulics, John Wiley & Sons, New York, NY.

    Google Scholar 

  • Sakkas, J. G. and Strelkoff, T., 1973, “Dam-Break Flood in a Prismatic Dry Channel,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., Dec., pp. 2195-2216.

    Google Scholar 

  • Schamber, D. R. and Katopodes, N. D., 1984, “One-Dimensional Models for Parially Breached Dams,” Jour. Hydraulic Engineering, Amer. Soc. of Civil Engrs., vol. 110, August, pp. 1086-1102.

    Google Scholar 

  • Schulte, A. M. and Chaudhry, M. H., 1987, “Gradually-Varied Flows in Open-Channel Networks,” Jour. Hydraulic Research, vol. 25(3), pp. 357-371.

    Article  Google Scholar 

  • Song, C. S. S., Cardle, J. A. and Leung, K. S., 1983, “Transient Mixed-Flow Models for SlOrm Sewers,” Jour. Hydraulic Engineering, Amer. Soc. of Civil Engrs., vol. 109, Nov., pp. 1487-1504.

    Google Scholar 

  • Stoker, J. J., 1948, “The Formation of Breakers and Bores,” Communications on Pure and Applied Mathematics, vol. I, pp. 1-87.

    Article  MathSciNet  Google Scholar 

  • Stoker, J. J., 1957, Water Waves, Interscience, New York, NY.

    MATH  Google Scholar 

  • Strelkoff, T., 1969, “One-Dimensional Equations of Open Channel Flow,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 95, May, pp. 861-876.

    Google Scholar 

  • Strelkoff, T., 1970, “Numerical Solution of Saint-Venant Equations,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 96, January, pp. 223-252.

    Google Scholar 

  • Terzidis, G. and Strelkoff, T., 1970, “Computation of Open Channel Surges and Shocks,” Jour., Hyd. Div., Amer. Soc. of Civil Engrs., vol. 96, Dec., pp. 2581-2610.

    Google Scholar 

  • Vasiliev, O. F. et al. 1965, “Numerical Methods for the Calculation of Shock Wave Propagation in Open Channels,” Proc. 11th Congress, International Assoc. for Hyd. Research, Leningrad, vol. III, l3 pp.

    Google Scholar 

  • Warming, R. F. and Hyett, B. J., 1974, “The Modified Equation Approach to the Stability and Accuracy Analysis of Finite-Difference Methods,” Jour. of Computational Physics, vol. 14, pp. 159-179.

    Article  MATH  MathSciNet  Google Scholar 

  • Whitham, G. B., 1955, “The Effects of Hydraulic Resistance in the Dam-Break Problem,” Proc., Royal Society, No. 1170, Jan..

    Google Scholar 

  • Wiegel, R. L., 1955, “Laboratory Studies of Gravity Waves Generated by the Movement of a Submerged Body,”Trans. Amer. Geophysical Union, vol. 36, no. 5, Oct., pp. 759-774.

    Google Scholar 

  • Wiggert, D. C., 1970, “Prediction of Surge Flows in the Batiaz Tunnel,” Research Report, Laboratory for Hydraulics and Soil Mechanics, Federal Institute of Technology, Zurich, Switzerland, no. 127, June.

    Google Scholar 

  • Wiggert, D. C., 1972, “Transient Flow in Free-Surface, Pressurized Systems,” Jour., Hyd. Div., Amer. Soc. of Civ. Engrs., Jan., pp. 11-27.

    Google Scholar 

  • Yen, B. C., 1973, “Open-Channel Flow Equations Revisited,” Jour., Engineering Mech. Div., Amer. Soc. of Civ. Engrs., vol. 99, Oct., pp. 979-1009.

    Google Scholar 

  • “Wave Action Generated by Slides into Mica Reservoir, Hydraulic Model Studies,” Report, Western Canada Hydraulic Laboratories, Port Coquitlam, B.C., Canada, Nov. 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Engineering and Computing, University of South Carolina, Columbia, SC, USA

    M. Hanif Chaudhry

Authors
  1. M. Hanif Chaudhry
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Author

About this chapter

Cite this chapter

Chaudhry, M.H. (2014). Transient Open-Channel Flows. In: Applied Hydraulic Transients. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8538-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-8538-4_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-8537-7

  • Online ISBN: 978-1-4614-8538-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation