A Simplified Mathematical Equation to Study the Relationship between Water Driving Forces and Water Losses Amount in Irrigation Canals in the Field

Y. A. M. Abd–Allah *

Soil, Water and Environment Research Inst. Agric. Res. Center, Giza, Egypt.

*Author to whom correspondence should be addressed.


This investigation aimed to study the effect of water driving forces in irrigation canals in the case of using one or two irrigation canals in the field and its impact on water losses amount by deriving a mathematical equation. The results across the two seasons showed that mean water driving forces (WDF) in the case of using one irrigation canal in field (0.26m3/16.63minute) was greater than two irrigation canals (0.24m3/36.13minute) and the water losses amount (WLA)resulted from using one irrigation canal (17.78 m3) was less than the two irrigation canals (36.25 m3) by saving 18.47m3 of irrigation water. Consequently, there is an inverse relationship between water driving forces in irrigation canals in the field and water losses amount. Grain yield in the case of using one irrigation canal in the field was 1.414 mg ha-1, while in the two irrigation canals recorded 1.365 mg ha-1by increasing 49.17 kg ha-1. Accordingly, a quantity of irrigation water can be saved during surface irrigation in order to achieve water abundance can be used to irrigate new lands. The quadratic model was the best statistical model to describe the relationship between Water Driving Force (WDF) and Water Movement Time (WMT) irrigation canal in field. Using the fitted quadratic model, it is clear that the Critical Water Movement Time (CWMT) which reflects the lowest WDF value was 25.55 min.

Keywords: Irrigation, canals, driving forces, quadratic model

How to Cite

Abd–Allah , Y. A. M. (2023). A Simplified Mathematical Equation to Study the Relationship between Water Driving Forces and Water Losses Amount in Irrigation Canals in the Field. International Journal of Plant & Soil Science, 35(22), 91–101. https://doi.org/10.9734/ijpss/2023/v35i224116


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FAO, Food and Agriculture Organization of the United Nations. Wheat sector review, Egypt; 2015.

FAO, Food and Agriculture Organization, Country Gender Assessment of the Agriculture and Rural Sector: Egypt– Brief. Country Gender Assessment series– Near East and North Africa. Cairo; 2022.

Chen HT, Wang WC, Chen XN, Qiu L. Multi-objective reservoir operation using particle swarm optimization with adaptive random inertia weights. Water Sci. Eng. 2020;13(2):136-144.

Noorisameleh Z, Khaledi S, Shakiba A, Firouzabadi PZ, Gough WA, Mirza MMQ. Comparative evaluation of impacts of climate change and droughts on river flow vulnerability in Iran. Water Sci. Eng. 2020;13(4):265-274.

Kanakoudis V, Muhammetoglu H. Urban water pipe networks management towards nonrevenue water reduction: Two case studies from Greece and Turkey. CLEAN-Soil, Air, Water. 2014;42(7):880-892.

Barkhordari S, Shahdany SMH. A systematic approach for estimating water losses in irrigation canals. Water Sci. Eng. 2022;15(2):161-169.

Sen R Fahmida, Akter MI. Determination of conveyance loss through earthen channel by cutthroat flume. Int. J. Hydraul. Eng. 2018;7(1):11-14.

Yao L, Feng S, Mao X, Huo Z, Kang S, Barry DA. Coupled effects of canal lining and multi-layered soil structure on canal seepage and soil water dynamics. J. Hydrology. 20124;30(431):91–102.

Ashton CH, Hope VS. Environmental valuation and the economic level of leakage. Urban Water. 2001;3:261–270.

Reilly TE, Goodman AS. Quantitative analysis of saltwater-freshwater relationships in groundwater systems—A historical perspective. J. Hydrology. 1985;80(1-2):125-160.‏

Reilly TE. Systems in Freshwater-Saltwater Environments. Regional Ground-Water Quality. 1993;443.‏

Williams RJB, Cooke GW. Some effects of farmyard manure and grass residues on soil structure. Soil Sci. 1961;92:30-37.

Hartge KH. Settling of soils as an aspect of structural stability (German) J. Pl. Nurt. Soil Sci. 1969;122:250-259.

De leenher L, De Boodt M. Soil Physics. Inter. Training Center for post graduate Soil Scientists, Gent. 1965;126-135.

Israelson OW, Hansen VE. Irrigation principles and practices. 3rd Ed. John Willey and Sons. New York; 1962.

Vomocil JA. Particle-Size Analysis In Methods of Soil Analysis. C.F. Klute, A.(Ed.) Part 1. Agron.9, 15, 299, Am. Soc. Agron. Madison, Wisconsin. U.S.A.; 1986.

Richards RL. Diagnosis and Improvement of Saline and Alkali Soils. Agriculture Handbook No. 60, US Guvt. Printing office, Washington; 1954.

Neter J, Wasserman W, Kunter MH. Applied Linear Statistical Models.3rd ed., IRWIN, Homewood, Boston, USA; 1990.