Procedure for predicting and designing moving sprinkler application patterns

Summary Water application pattern, WAP, is one of the most important factors that determine the instantaneous and the cumulative application rates of moving irrigation machines. The mathematical background of a procedure to predict and design the WAP of moving irrigation machines is introduced. It includes a mathematical analysis of the effect of pressure head, height and spacing between emitters on the WAP, and a nomograph that presents this analysis graphically and illustrates the design procedure of the application pattern of irrigation machines.Abbreviations P()a water application rate at a normalized radial distance from the emitter [m/s] - ka number of linear segments needed to represent the pattern - s/Ra normalized radial distance from the emitter - Ra wetted radius [m] - sa radial distance from the emitter [m] - n_j n_i/ha normalized water application rate at point - j, ha maximum water application rate [m/s] n_j water application rate at point j [m/s] - _j=m_j/Ra normalized radial distance of point j from emitter - m_ja radial distance of point - ja from emitter [m], CWAP - (x)a Cumulative Water Application Pattern: amount of water per unit area applied at a distance - xa from the travel path of the emitter [m³/m²] - xa distance from the travel path of the emitter [m] - T_xa time of application at a distance - xa from the travel path of the emitter [s] - va velocity of propagation of the machine [m/s] - k₁a the outmost linear segment that its radial distance from the emitter - m_k1a is smaller than the distance of the travel path from the emitter - x, T_ja time at which the - j^tha linear segment (ring) stops influencing the point located at a distance - xa from the emitter - ₁, ₂, ₃a dimensionless numbers derived by dimensional analysis - ua water jet velocity [m/s] - ga gravity acceleration [m/s²] - da nozzle diameter [m], v kinematic viscosity [m²/s] - Ha emitters height [m] - , a regression analysis coefficients - Paa Pattern fit coefficient for water application - F(r)a normalized desired water application pattern [1/m] - f(r)a normalized actual water application pattern [1/m] - La common distance on which - F(r) and f(r)a are defined [m], SP spacing interval between emitters [m] - DSa dimensionless spacing interval between emitters - DSa variation of dimensionless spacing interval - Paa variation of Pa coefficient - Pa pressure head [kPa]