Summary
This paper, second in a series of three, develops a mathematical model, using the volume balance approach, to simulate vertical and horizontal recession of border irrigation. An equation is proposed for computing Manning's roughness factor N in both laminar and transitional flow regimes in recession phases. The model has four parameters which can be determined experimentally. Experimental data from ten vegetated as well as nonvegetated borders were used to verify the model. Average difference (AD) between calculated and observed vertical recession times was less than 4.4 min, and between calculated and observed horizontal recession times less than 4.6 min for the ten experimental data sets. Average relative error (ARE) in computed horizontal recession was less than 13% for these data sets. The model was found to be especially accurate for Reynold's number between 1,800 and 2,500.
Similar content being viewed by others
References
Atchison KT (1973) Retardance coefficients and other data for a vegetated irrigation border. M. S. Thesis, University of Arizona, Tucson, AZ, USA
Bowman CC (1960) Manning's equation for shallow flow. U.S.P.A., Proc ARS-SCS Workshop on Hydraulic of Surface Irrigation, ARS41-43, pp 21–23
Chen CL (1976) Flow resistance in broad shallow grassed channels. J Hydraulics Div ASCE (HY3), p 308
Chow VT (1959) Open-channel Hydraulics. McGraw-Hill Book Co, New York, pp 7–16
Cowan WL (1950) Estimating hydraulic roughness coefficient. Trans Am Geophys Union 31:603
Engman ET (1986) Roughness coefficients for routing surface runoff. J Irrig Drain Eng, ASCE 112:39
Gourlay MR (1970) Discussion of “Flow retardation in vegetated channels”, by Kouwen N, Unny TE, and Hill HM. Irrig Drain Division, ASCE 96 (IR3), Paper 7498:351–357
Kostyakov AN (1932) On the dynamics of the coefficient of water percolation in soils and on the necessity of studying it from a dynamic point of view for purpose of amelioration. Trans Sixth Committee International Soc Soil Sci, Part A, Russian, pp 17–21
Kruse EG, Huntley CW, Robinson AR (1965) Flow resistance in simulated irrigation border and furrows. Conservation Research Report No 3, ARS, USDA
Michael AM, Pandya AC (1971) Hydraulic Resistance relationships in irrigation borders. J Agric Eng Res 16:72
Myers LE (1959) Flow regimes in surface irrigation. Agricultural Engineers 40, pp 11, 676–677, 682–683
Palmer VJ (1946) Retardance coefficients for low flow in channels lined with vegetation. Trans Am Geophys Union 27:187
Ram RS, Lal R (1971) Recession flow in border irrigation. J Agric Eng Ind Soc Agric Eng 8:62
Roth RL (1971) Roughness during border irrigation. M.S. Thesis, University of Arizona, Tucson, AZ, USA
Shermen B, Singh VP (1978) A kinematic model for surface irrigation. Water Resour Res 14:357
Shermen B, Singh VP (1982) A kinematic model for surface irrigation: an extension. Water Resour Res 18:659
Shockley DG, Woodward HJ, Phelan JT (1964) Quasi-rational method of border irrigation design. Trans ASAE 7:420
Strelkoff T (1977) Algebraic computations of flow in border irrigation. J Irrig Drain ASCE 103 (IR3):357
Strelkoff T, Clemens AJ (1981) Dimensionless stream advance in sloping borders. J Irrig Drain ASCE 107 (IR3): 361
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Singh, V.P., Yu, F.X. A mathematical model for border irrigation II. Vertical and horizontal recession phases. Irrig Sci 8, 175–190 (1987). https://doi.org/10.1007/BF00259380
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00259380