MATHEMATICAL MODEL FOR MICRO-IRRIGATION DESING FOR CENTER PIVOT CORNERS

Abstract

A mathematical model was developed to analyzing hydraulic characteristics in a micro-irrigation system design micro-irrigation system for center pivot corners. Different shape division (square, rectangular and approximately triangular shape) for center pivot corner, pipe diameters and lengths of lateral and telescopic manifold pipe with uniform slopes were studied. The model divided the center pivot corner into subunits micro-irrigation system (parts) and estimated lateral and emitter discharges and pressure head distribution along a lateral and manifold starting from the downstream as well as uniformity calculation. The friction head loss between successive emitters, laterals and manifold were also estimated using the Darcy-Weisbach formula. The model for designing manifold was run successfully for supplying water to one or two-side laterals. Field studies were undertaken to test the validity of the mathematical model for (EU), (UC), (QVAR) and (HVAR). Emission flow and pressure distributions were measured and compared quite well with those predicted from the model. The results indicated that, for approximately triangular shape part 1 for center pivot radius 450 m, outside lateral diameter 16 mm, lateral spacing 1.0 m and emitter spacing 0.5 m, average emitter discharge per lateral for 76 lateral were ranged from 3.618 to 3.766 l/h,. Lateral dynamic head increased from 0.81 to 1.26 bar for 76 lateral, (UC), increased by 7.42% and (UC) increased with decreasing lateral friction losses, Inlet lateral discharge for 76 laterals were ranged from 7.1 to 240.6 l/h for minimum (2 m) and maximum (63 m) lateral lengths, respectively. The model has been verified under different three center pivot radiuses (270, 359 and 450 m), which have same lateral diameter (16 mm), emitter spacing 1.0 m, lateral spacing 2.5 m and same in-line emitter discharge equation q=4.02H0.5 as an example for grape cultivation. Also, three different outside lateral diameters 16, 18 and 20 mm which, has same emitter spacing 0.5 m, lateral spacing 1.0 m and the same emitter type with constant center pivot radius (450 m) were verified for strawberry cultivation. In comparison between model output results of center pivot corner with R=450 m for lateral diameters 18 and 20 mm, it is clear that the number of parts dose not changed (13 parts) and total manifold discharge was equal to 313.46 (m3/h) for both lateral diameters. While, number of parts was (19 parts).for lateral diameters 16 mm. QVAR at lateral diameter 18 and 20 mm were ranged from 0.7 to 6.51% and 0.47 to 4.35% respectively. Also, HVAR were ranged from 1.14 to12.59% and 0.94 to 8.52% respectively. However, lateral diameter 20 mm was more effective in improving (QVAR) and (HVAR). In case of R=450 m for lateral diameters 16 mm, manifold diameters 50, 63, 75 and 90 mm versus lengths were 641, 185, 97 and 92 m respectively, while, manifold length were 505, 182, 91 and 158 m for lateral diameters 18 mm.