Application of Beta Distribution Function in Determination of Water Distribution Pattern under NELSON-F80AP Model Impact Sprinkler

Speed and direction of wind affect water distribution pattern of sprinkler irrigation system. Based on an acceptable water distribution uniformity range, distribution pattern of any single sprinkler under different wind conditions is needed to determine the best sprinklers arrangement. In this study, water distribution of NELSON-F80AP sprinkler was assumed to be a function of the Beta probability distribution and influences of wind speed and direction on the distribution pattern were studied. Similar to common sprinkler irrigation systems, a single sprinkler (NELSON-F80AP model) with wetting radius of 22.86 m and application angle of 360^ο was set at about 1 m height from land surface. According to the operating pressure in the irrigation system, 40 psi pressure was applied during the experiments. Firstly, Beta distribution function parameters were calculated on the basis of the measured water distribution pattern under controlled (no wind) condition. Then, the change of distribution pattern due to different conditions of wind and its relevant suitable probability function parameters for each condition were determined. The water distribution pattern uniformity was fair and a good fitness between the calculated and observed data was obtained in the wind speed range of 0-3 m/s. The relative error was less than 3.53% in this case. In the speed range of 3-6 m/s, the distribution pattern uniformity was poor and the relative error was raised up to 4.65%. For the wind speeds greater than 6 m/s, relative error between the calculated and measured pattern was about 8.48%, because of wind drift and evaporation losses and also the effect of wind on the uniformity of water distribution pattern.