Application of Beta Distribution Function in Determination of Water Distribution Pattern under Spray Sprinkler of Center Pivot Irrigation System

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Abstract

Speed and direction of wind greatly influence the water distribution pattern in a sprinkler irrigation system. Based on an acceptable water distribution uniformity range, distribution pattern of any single sprinkler, under different wind conditions, is needed for determinae the most suitable sprinkler arrangement. In this study water distribution of a spray sprinkler was assumed to be a function of the Beta probability distribution. Then influences of wind speed and direction on the distribution pattern was studied. Similar to Sprinkler situation on the center pivot irrigation system, a spray sprinkler PROS-04 with wetting radius of 9 m and application angle of 180° was set in 3m height from land surface. In match with the application pressure adopted in center pivot system, a 29 psi pressure was aplied during the carried out experiments. In total 17 experiments were recorded in different conditions of wind speed within a range of 0-6 m/s. Initially the Beta distibution function parameters were evaluated on the basis of measured water distribution pattern under controlled (no wind) condition. Then the change of distribution pattern to different wind conditions as well as the relevant suitable probability function parameters for each condition were determined. The water distribution pattern uniformity was observed as fair. A good proximity between the calculated and observated data was also resulted in the wind speed range of 0-3 m/s, the relative error being less than 4% in this case. In wind speeds of 3-6 m/s the distribution pattern uniformity was poor with the relative error being raised up to 7%. In wind speed greater than 6 m/s the relative error between the calculated and measured pattern was about 10%, because of wind drift and evaporation losses and also due to the diverse effect of wind on water uniformity distribution pattern.

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