Mathematical Model of Water Advance in Border Irrigation

Bassett, D. L.

doi:10.13031/2013.38056

Cited by 19 publications

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“…A certain balance is required between flow depth and surface topography to avoid large spatial gradients of flow depth, particularly in the vicinity of the advancing front. Such conditions might violate the assumptions that led to the derivation of vertically integrated expressions of the shallow water equations (Bassett, 1972), resulting in large mass balance errors.…”

Section: Discussionmentioning

confidence: 99%

Modeling Microtopography in Basin Irrigation

Playán

Faci

Serreta

1996

J. Irrig. Drain Eng.

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Section: Discussionmentioning

confidence: 99%

Modeling Microtopography in Basin Irrigation

Playán

Faci

Serreta

1996

J. Irrig. Drain Eng.

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“…Infiltration characteristics were considered constant over time and distance. Bassett (1972) presented his mathematical model of advance in border irrigation (sloped fields) using the equations of motion obtained from the Saint-Venant equations. The equations were solved by the method of characteristics proposed by Streeter and Wylie (1967).…”

Section: Review Of Literaturementioning

confidence: 99%

A VOLUME BALANCE SOLUTION FOR WATER FLOW OVER FLAT SOIL SURFACES¹

Guardo

1995

J American Water Resour Assoc

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This paper presents the development of a mathematical model to compute the advance of water flowing over flat soil surfaces. The solution is of interest to the design and management of irrigation systems, and the model can also be applied to overland flow problems. The hydraulics of water flow during the advance phase is simulated by the Lewis‐Milne integral equation. The general solution to this equation is obtained by using the Laplace transform theory. A particular solution was developed, based on series expansions, that uses the modified Kostiakov equation to predict infiltration. The solution is given by a double infinite series that has terms of alternate sign. Results from this model show satisfactory agreement when compared with field data collected by the author.

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“…Numerical solutions of these equations were presented by Bassett (1972), Sakkas and Strelkoff (1974) and Katapodes and Strelkoff(1977). By dropping the two first terms of the momentum equation (Eq.…”

Section: General Equations For Border Irrigationmentioning

confidence: 99%

An improved Lewis-Milne equation for the advance phase of border irrigation

1990

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The Lewis-Milne (LM) equation has been widely applied for design of border irrigation systems. This equation is based on the concept of mass conservation while the momentum balance is replaced by the assumption of a constant surface water depth, Although this constant water depth depends on the inflow rate, slope and roughness of the infiltrating surface, no explicit relation has been derived for its estimation. Assuming negligible border slope, the present study theoretically treats the constant depth in the LM equation by utilizing the simple dam-break wave solution along with boundary layer theory. The wave front is analyzed separately from the rest of the advancing water by considering both friction and infiltration effects on the momentum balance. The resulting equations in their general form are too complicated for closed-form solutions. Solutions are therefore given for specialized cases and the mean depth of flow is presented as a function of the initial water depth at the inlet, the surface roughness and the rate of infiltration. The solution is calibrated and tested using experimental data.For efficient design and operation of surface irrigation systems it is essential to know the dynamics of water movement over the infiltrating soil surface. Theoretically, the problem can be simulated by the mass continuity and momentum balance hydrodynamic equations. However, simpler approaches are also feasible, which utilize the mass continuity equation, and replace the momentum balance equation with an empirAbbreviations. a(t)=advance length, c=mean depth in LM equation, cy =friction factor, Ch=Chezy's friction coefficient, g = acceleration due to gravity, h(x, t)= water depth, h o = water depth at the upstream end, i(z)=rate of infiltration f(x, t)= discharge, qo = constant inflow discharge, Sy = energy loss gradient or frictional slope, So=bed slope, t=time, u(x, t)=mean velocity along the water depth, x=distance, Y(z)=cumulative infiltration, r/(t)= distance separating two flow regions, ~ = infiltration opportunity time.ical relation. One such simplified approach is the wellknown work of Lewis and Milne (1938). By assuming constant rate of inflow and mean constant depth of surface water, Lewis and Milne (LM) developed an integral equation for solution of irrigation advance phase. Analytical solutions of the LM equation for various infiltration functions were provided by Philip and Farrell (1964) and Parlange (1973).Most studies dealing with the LM equation treat the mean surface water depth as constant despite the fact that from field and experimental observations, it has been documented that this depth depends on inflow discharge, slope, surface roughness and infiltration. An attempt to relate the mean depth to certain physical quantities was made by Singh and Prasad (1983). This paper is an improvement and verification of their work.The physical processes of surface flow over an infiltrating surface constitute a very complicated and not yet fully understood system. The system is generally time-dependent, thr...

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Mathematical Model of Water Advance in Border Irrigation

Cited by 19 publications

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Modeling Microtopography in Basin Irrigation

Modeling Microtopography in Basin Irrigation

A VOLUME BALANCE SOLUTION FOR WATER FLOW OVER FLAT SOIL SURFACES¹

An improved Lewis-Milne equation for the advance phase of border irrigation

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Mathematical Model of Water Advance in Border Irrigation

Cited by 19 publications

References 0 publications

Modeling Microtopography in Basin Irrigation

Modeling Microtopography in Basin Irrigation

A VOLUME BALANCE SOLUTION FOR WATER FLOW OVER FLAT SOIL SURFACES1

An improved Lewis-Milne equation for the advance phase of border irrigation

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A VOLUME BALANCE SOLUTION FOR WATER FLOW OVER FLAT SOIL SURFACES¹