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Simplified Equations of the Unsteady Flow in Open Channel

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Numerical Modeling in Open Channel Hydraulics

Part of the book series: Water Science and Technology Library ((WSTL,volume 83))

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Abstract

The system of Saint Venant equations derived in Chapter 1 in the form of Eqs. (1.77) and (1.78) or Eqs. (1.79) and (1.80) is called the dynamic wave model or the complete dynamic model. This model of unsteady open channel flow gives reliable results if the underlying assumptions are satisfied. On the other hand, the Saint Venant model requires rather complex methods of solution and relatively large number of data characterizing both the channel and the flow conditions. For this reasons hydrologists tried to simplify the system of Saint Venant equations to obtain models, which require less input information.

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References

  • Abbott MB (1979) Computational hydraulics-Elements of the theory of free surface flow. Pitman, London

    Google Scholar 

  • Cappelaere B (1997) Accurate diffusive wave routing. J. Hydr. Engng. ASCE 123 (3):174–181

    Article  Google Scholar 

  • Chow VT (1964) Handbook of applied hydrology. McGraw-Hill, New York

    Google Scholar 

  • Chow VT (1959) Open channel hydraulics. Mc Graw-Hill, New York

    Google Scholar 

  • Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw-Hill, New York

    Google Scholar 

  • Cunge JA (1969) On the subject of a flood propagation computation method (Muskingum method). J. Hydr. Res. 7 (2):205—229

    Article  Google Scholar 

  • Cunge J, Holly FM, Verwey A (1980) Practical aspects of computational river hydraulics. Pitman Publishing, London

    Google Scholar 

  • Dooge JCI (1959) A general theory of the unit hydrograph. J. Geophys. Res. 64 (1):205—230

    Google Scholar 

  • Eagleson PS (1970) Dynamic hydrology. McGraw-Hill, New York

    Google Scholar 

  • Fletcher CAJ (1991) Computational techniques for fluid dynamics, vol. I. Springer-Verlag, Berlin

    Google Scholar 

  • Gasiorowski D, Szymkiewicz R (2007) Mass and momentum conservation in the simplified flood routing models. J. Hydrol. 346:51–58

    Article  Google Scholar 

  • Gresho PM, Sani RL (2000) Incompressible flow and the finite–element method, vol. 1: advection-diffusion. Wiley, Chichester, England

    Google Scholar 

  • Hayami S (1951). On the propagation of flood waves. Kyoto Univ. Disaster Prevent. Res. Inst. Bull. 1:1–16

    Google Scholar 

  • Henderson FM (1966) Open channel flow. Macmillan Company, New York

    Google Scholar 

  • Korn GA, Korn TM (1968) Mathematical handbook for scientists and engineers, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Lighthill MJ, Whitham GB (1955) On kinematic waves, I: flood movement in long rivers. Proc. R. Soc. London, Ser. A 229:281–316

    Article  MATH  MathSciNet  Google Scholar 

  • McQuarrie DA (2003) Mathematical methods for scientists and engineers. University Science Books, Sausalito, CA

    MATH  Google Scholar 

  • Miller WA, Cunge JA (1975) Simplified equations of unsteady flow. In: Mahmood K, Yevjewich V (eds) Unsteady flow in open channels. Water Resources Publishing, Fort Collins, CO

    Google Scholar 

  • Nash JE (1957) The form of Instantaneous Unit Hydrograph. IASH Publication no. 45, 3–4:114–121

    Google Scholar 

  • O’Donnell T (1960) Instantaneous unit hydrograph derivation by harmonic analysis. IASH Publication no. 51:546–557

    Google Scholar 

  • Ponce VM (1990) Generalized diffusion wave with inertial effects. Water Resour. Res. 26 (5):1099–1101

    Article  Google Scholar 

  • Ponce VM, Li RM, Simmons DB (1978) Applicability of kinematic and diffusion models. J. Hydr. Div. ASCE 104 (3):353–360

    Google Scholar 

  • Rodriguez-Iturbe I, Valdes JB (1979) The geomorpholigic structure of hydrologic response. Water Resour. Res. 15 (6):1409–1420

    Article  Google Scholar 

  • Singh VP (1996) Kinematic wave modeling in water resources: surface water hydrology. Wiley, New York

    Google Scholar 

  • Strupczewski WG, Napiórkowski JJ, Dooge JCI (1989) The distributed Muskingum model. J. Hydrol. 111:235–257

    Article  Google Scholar 

  • Szymkiewicz R (2002) An alternative IUH for the hydrologic lumped models. J. Hydrol. 259:246—253

    Article  Google Scholar 

  • Tang X, Knight DW, Samuels PG (1999) Variable parameters Muskingum–Cunge method for flood routing in a compound channel. J. Hydr. Res. 37 (5):591—614

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233, Gdańsk, Poland

    Romuald Szymkiewicz

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  1. Romuald Szymkiewicz
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Correspondence to Romuald Szymkiewicz .

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Szymkiewicz, R. (2010). Simplified Equations of the Unsteady Flow in Open Channel. In: Numerical Modeling in Open Channel Hydraulics. Water Science and Technology Library, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3674-2_9

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