Issue 
La Houille Blanche
Number 2, Mars 1965



Page(s)  159  164  
DOI  https://doi.org/10.1051/lhb/1965016  
Published online  24 March 2010 
Calcul des débits dans les réseaux d'irrigation
The calculation of irrigation network flows
^{1}
Ingénieur civil du Génie rural à la SO.GR.E.A.H.
^{2}
Attaché de recherches au C.N.R.S.
As a result of the increasingly frequent use made of computers for both agronomical investigations and compilation of tender documents and designs, it has become necessary to find a calculation method making the most of the scope afforded by modern computers and thus avoiding the difficulties normally encountered with conventional calculation methods. By relying on a rigourous analysis of the agronomical data considered in the calculation, the authors have successfully extended the standard method originally developed by Clement. Clement's method With modern 'on demand' sprinkler irrigation methods, a careful study is necessary when rates of flow calculations must be assumed for dimensioning collective networks. Clement's now classical study, which was based on a number of simplifying assumptions, yielded the following useful formula for ordinary calculation and plotting purposes : where d = d0 (np + u √npq) where d = rate of pipe flow ; d0 = rate of offtake flow ; n = number of offtakes ; u = a coefficient depending on demand satisfaction probability ; p = offtake operation frequency ; q = 1  p. This formula is based on the assumption that all the offtakes are operating at exactly the same frequency and with the same rates of flow. For a given demand satisfaction probability, it gives a flow summation which is rigourous if individual demands are independent and very numerous. As conditions in practice differ from these assumptions to varying degrees, however, designers have to ressort to various expedients or make certain additional assumptions when applying Clement's method. This is why it has been necessary to find a new method whereby diversified data can be allowed for, especially as regards agronomical conditions. The new method The object is to define the agronomical characteristics of each 'irrigation unit', this being the area supplied from one offtake (In a set of m offtakes, each one is identified by a subscript i, the values of which range from 1 to m) The purpose of the preliminary investigations is to establish the offtake rate of flow, dp operating frequency Pi, and probable use for irrigation αi for each offtake. These data respectively allow for the operating time required to supply the necessary quantities of water to the plants and to meet crop rotation requirements, which may  or may not  call for irrigation once every year. This finally yields the parameters P'i = αiPi and q'i == 1  Pi'. with αi = 1 for offtakes never out of operation. With the basic data for the method presented in this way, a mathematical study yields a direct calculation method for the rate of flow d, but this calculation is both tedious and delicate toperform. Fortunately, however, an approximation similar to that adopted by Clement, can be made, which gives the following new expression for the rate of flow : d = m Σ i = 1 p' idi + u √ m Σ i = 1 p'iq'idi2 This formula lends itself very well to computer calculation. To sum up, therefore, this method of calculation allows for both true individual offtake discharge and operating frequency, for each offtake. It also •givesthe irrigation probability for each "irrigation unit', and therefore also probable irrigation concentration. Thus, by starting out from the individual data for each "unit' and using a suitable mathematical formula, this method provides a means of rigourously dimensioning sprinkler irrigation systems designed for "on demand' operation with the aid of a computer.
© Société Hydrotechnique de France, 1965