Validity of the Theory of Probability in On-Demand Irrigation Networks

Abstract

The experimental procedure largely verified the validity of the theory of probability in on-demand irrigation networks. The irrigation water demand, during periods of high requirement, in the region’s network of the irrigation pumping station Σ9, in the three years from 1988 to 1990, followed the five distributions: Erlang, gamma, lognormal, normal, and Weibull, in four of the total six data sets. The Erlang, gamma, lognormal, and Weibull distributions fit well to four data sets of the years from 1988 to 1990, whereas the normal distribution fits well also to four data sets but only of the two year period 1988–1989. The new demand formula approximates better the irrigation water demand in the peak consumption period. In a network with conduit of very small slope and use of self-propelled sprinklers with operating characteristics adapted to the hydraulic conditions of the network, the population of outlets may be uniform in the provision without a flow limiter, when there is discipline among the users. The same crop in the same plain area with specific local climate, small general slope, and high territorial homogeneity can significantly alter the demand for irrigation water in time, which favors the randomization of demand over time.