Development of a mathematical model to predict head losses from disc filters in drip irrigation systems using dimensional analysis

A model was developed using dimensional analysis to predict head losses in disc filters. Three different filter designs, each with four different inlet and outlet pipe diameters, were used to measure head losses at different flow rates in the laboratory. The parameters influencing head losses were considered to be the inside diameters of the inlet and outlet pipes, the inside diameter of the filter body, the inflow and outflow area where the inlet and the outlet pipes intersect with the body of the filter, the, effective length of filter disc group, the outside and inside diameter of the filter disc, the water velocity in the inlet pipe and the kinematic viscosity of water. A dimensional analysis was carried out using Buckingham's pi-theorem. To develop the model, experimental head loss data from 12 filters were considered. The model accounted for 90.18% of the variation in the pressure coefficient. A comparison between the predicted and the measured head losses was in close agreement with a correlation coefficient of 99.5%. The results showed that the model may be used to determine head losses in disc filters with an acceptable accuracy if the variables are within the following ranges; inside diameters of inlet and outlet pipe 52.5-102.3 mm; inside diameter of filter body 155-210 mm; effective length of disc group 231-545 mm, inside diameter of filter disc 105-128 mm; outside diameter of filter disc 129-164 mm; inflow area where the inlet pipe intersects with the body of the filter 2240-16430 mm 2; outflow area where the outlet pipe intersects with the body of the filter 2160-9480 mm 2; flow rate 4.50-73.43 m 3h -1; and Reynolds number 19,005-361,310. © 2008 IAgrE

Development of a software to determine the emitter characteristics and the optimum length of new designed drip irrigation laterals

An appropriate design of a drip irrigation system in order to increase the uniformity of water distribution with a high efficiency is of importance. The first step for the design is the determination of suitable length of laterals. In order to do this, the emitter characteristics and the friction losses of new designed laterals on which the emitters are placed must be known by laboratory experiments. On the other hand, mathematical models developed can also be used for the determination of friction losses in drip irrigation laterals. In this study, a software in Visual Basic 6.0 programming language was developed and it helps analyzing the data from a new designed emitter in order to find out the main characteristics and friction losses and to obtain the optimum lateral length of the lateral in the shortest time with an acceptable accuracy in. The software included several options for the selection of in-line or on-line emitter type, pressure compensating or non-pressure compensating emitters. The software calculates the optimum lateral length based on the measurement and model equations and utilizes the step by step procedure. Optimum lateral length criterias in the software such as C u and q var for non-pressure compensating emitter and lateral end pressure for compensating emitter were used. The comparison of optimum lateral lengths indicated a very good agreement between the experimentally obtained results and the results from the use of mathematical models for different criteria and different slope conditions. The differences in optimum lateral lengths between the experimental and calculated values obtained from the mathematical models ranged between -0.4 and 0.7%. © Association for Scientific Research

Development of a mathematical model to predict clean water head losses in hydrocyclone filters in drip irrigation systems using dimensional analysis

WOS: 000276939400008A model was developed using dimensional analysis, to predict head losses in hydrocyclone filters. Different hydrocyclone filters with different specifications were used to measure head losses at different flow rates in the laboratory. The parameters influencing head losses were considered to be the inside diameters of the inlet and outlet pipes, cylindrical section diameter of the filter, apex diameter of the conical part, cylindrical section length of the filter, conical section length of the filter body, length of the outlet (vortex finder) pipe, water velocity in inlet pipe, acceleration of gravity, kinematic viscosity of water. A dimensional analysis was carried out, using Buckingham's pi-theorem. To develop a model, experimental head loss data from 21 filters were considered in the study. The model accounted for 96.7% of the variation in the pressure coefficient. The predicted and the measured head losses were in close agreement with a correlation coefficient of 98.1%. The results showed that the model may be used to determine head losses in hydrocyclone filters with an acceptable accuracy if the variables are within the following ranges: inside diameter of inlet and outlet pipe 0.053-0.154 m; cylindrical section diameter of the filter 0.195-0.46 m; apex diameter of the conical part 0.04-0.06 m; cylindrical section length of the filter 0.16-0.41 m; conical section length of the filter body 0.37-0.955 m; length of the vortex finder pipe 0.155-0.627 m; flow rate 3.7-98.48 m(3) h(-1); and Reynolds number 18 860-421 065. The performance of the model was compared with models developed for industrial hydrocyclones and the necessary comparisons were established by using statistical test procedures. The model in this study provides better predictions as compared to some other models available in the literature. (C) 2010 IAgrE. Published by Elsevier Ltd. All rights reserved

Development of Prediction Models for Friction Losses in Drip Irrigation Laterals equipped with Integrated In-line and On-line Emitters using Dimensional Analysis

This paper presents models developed to predict friction head losses in drip irrigation laterals. Some domestic and imported drip irrigation laterals equipped with integrated in-line and on-line emitters placed at different spacings ranging from 0·2 and 1 m were considered in this study. The parameters affecting the variation in friction head losses in laterals were defined as dimensionless terms using Buckingham's ? theorem. Two mathematical models were developed in this study. In order to develop a model for integrated in-line emitters, experimental friction head losses data from 16 different drip irrigation pipes with above-mentioned spacings were used and the model developed accounted for 98·53% of the variation in the data. Another model developed was for predicting the friction head losses in laterals with on-line emitters. For the development of a model, experimental friction head losses data from six different drip irrigation pipes equipped with on-line emitters with above-mentioned spacings were used. The model developed for on-line emitters was able to explain the 98·76% of the variation in the data collected in the laboratory. The developed models in this study for in-line and on-line emitters were compared against the models available in the literature in terms of total friction head losses and lateral lengths. It was found that the total friction head loss differences between the developed model and the model existing in the literature were small and varied between -1·7% and +1·7% for in-line emitters while the same comparison for on-line emitters indicated a range between -0·9 and +1·9%. The results showed that the developed mathematical models may be used to determine the friction head losses in drip laterals with integrated in-line and on-line emitters placed on laterals at different spacings ranging from 0·2 to 1 m. © 2007 IAgrE