A Mathematical Model for Hydraulic Characterization of Microtube Emitters Using Dimensional Analysis

Document Type : Original Research

Authors
G. Katsurayama 1
L. Sobenko 2
A. P. de Camargo 3
T. A. Botrel 2
J. A. Frizzone 2
S. N. Duarte 2
1 Federal Institute of Education, Science, and Technology of Santa Catarina, Araquari, Santa Catarina, Brazil.
2 Biosystems Engineering Department, College of Agriculture “Luiz de Queiroz”, University of São Paulo, Piracicaba, São Paulo, Brazi.
3 University of Campinas, Agricultural Engineering College, Campinas, São Paulo, Brazil.
Abstract
A microtube emitter is a simple, low-cost emitter in which the length can be adjusted according to the distribution of pressures along an irrigation lateral line to deliver uniform discharge. To accurately design micro-irrigation systems using microtubes, it is necessary to use an equation that correlates hydraulic parameters, microtube characteristics, and fluid properties. Therefore, the objectives of this research were: (a) To develop an equation for design purposes using dimensional analysis by Buckingham’s Pi theorem to represent the hydraulic processes in a microtube emitter operating in the laminar flow regime and (b) To compare the accuracy of the developed model against models that are currently used for microtube sizing. The data required to develop and validate the model was obtained experimentally in the laboratory by evaluating three types of microtubes with nominal diameters of 0.7, 0.8 and 1.0 mm. A model using pressure head, microtube length, flow rate, internal diameter, gravitational acceleration, and water properties was proposed and validated. The model for estimating hydraulic parameters in microtube emitters also presented better performance than other models available in the literature. Finally, an application example was presented and an irrigation lateral line using microtubes as emitters was designed using the proposed model.

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Almeida, C.D.G.C., Botrel, T.A. and Smith, R.J. 2009. Characterization of the microtube emitters used in a novel micro-sprinkler. Irrig. Sci., 27: 209–214.
Almeida, C.D.G.C. and Botrel, T.A., 2010. Microtubes diameter determination in trickle irrigation [Abstract in English]. Rev. Bras. Ciênc. Agrár., 5: 413–417.
Alves, D.G., Pinto, M.F., Salvador, C.A., Almeida, A.C.S., Almeida, C.D.G.C. and Botrel, T.A. 2012. Modeling for the design of micro-irrigation system using branched microtubes [Abstract in English]. Rev. Bras. Eng. Agríc. Ambiental, 16(2): 125-132.
American Society for Agricultural Engineering - ASAE EP405.1 APR1988 (R2014). 2014. Design and installation of microirrigation systems. ASABE, St. Joseph, MI, 5p.
Buckingham, E., 1914. On physically similar systems: Illustrations of the use of dimensional equations. Phys. Rev., 4: 345–376.
Chatterjee, S. and Simonoff, J. 2013. Handbook of regression analysis. Wiley: Hoboken.
Duran-Ros, M., Arbat, G., Barragán, J., Ramírez de Cartagena, F. and Puig-Bargués, J. 2010. Assessment of head loss equations developed with dimensional analysis for micro irrigation filters using effluents. Biosyst. Eng., 106: 521–526.
Flores, J.H.N., Rettore Neto, O., Faria, L.C. and Timm, L.C. 2017. Estimation of the kinetic head coefficient (k) based on the geometric characteristics of emitter pipes. Eng. Agríc., 37(6): 1091–1102.
Fox, R.W., McDonald, A.T. and Pritchard, P.J. 2011. Introduction to fluid mechanics. 8.ed. IE-Wiley: Hoboken.
Frizzone, J.A., Freitas, P.S.L. de, Rezende, R. and Faria, M.A. de. 2012. Microirrigação: Gotejamento e microaspersão. Maringá: Eduem.
Gupta, S.K., Mehta, R.C. and Dwivedi, V.K. 2013. Modeling of relative energy loss of free hydraulic jump in horizontal prismatic channel. Procedia Eng., 51: 529–537.
Helal, E., Sobeih, M. and El-din, M.E. 2018. Effect of floating bridges on open channels’ flow and bed morphology. J. Irrig. Drain. Eng., 144(9): 04018026.
Holzapfel, E.A., Abarca, W.A., Paz, V.P.S., Arumi, J.L., Rodriguez, A., Orrego, X. and Lopez, M.A. 2007. Seleccíon técnico-economica de emissores. Rev. Bras. Eng. Agríc Ambiental, 11(6): 547–556.
Juana, L., Rodrigues-Sinobas, L. and Losada, A. 2002. Determining minor head losses in drip irrigation laterals. I: Methodology. J. Irrig. Drain. Eng., 128(6): 376–384.
Katsurayama, G.T., Saretta, E., Camargo, A.P., Botrel, T.A. and Salvador, C.A. 2017. Methodology for designing lateral lines with microtubes operated under variable inlet pressure. Rev. Bras. Eng. Agríc. Ambiental, 21: 594–599.
Kell, G.S. 1975. Density, thermal expansivity, and compressibility of liquid water from 0° to 150°C. J. Chem. Eng. Data, 20: 97–105.
Keller, J. and Bliesner, R.D. 1990. Sprinkler and Trickle Irrigation. Chapman and Hall,
New York.
Keshtgar, A., Bhuiyan, M.A. and Jayasuriya, N. 2013. Design of drip irrigation system using microtubes for full emission uniformity. Irrig. Drain., 62: 613–623.
Kumar, M., Reddy, K.S., Adake, R.V. and Rao, C.V.K.N. 2015. Solar powered micro-irrigation system for small holders of dryland agriculture in India. Agric. Water Manage., 158: 112–119.
Lemons, D.S., 2017. A student’s guide to dimensional analysis. New York: Cambridge University Press.
Munson, B.R., Yong, D.F., Okiishi, T.H. and Huebsch, W.W. 2009. Fundamentals of fluid mechanics. 7.ed. IE-Wiley: Hoboken.
Perboni, A., Frizzone J.A., Camargo, A.P. and Pinto, M.F. 2015. Modelling head loss along emitting pipes using dimensional analysis. J. Braz. Assoc. Agric. Eng., 35: 442–457.
Pinto, M.F., Camargo, A.P., Rettore Neto, O. and Frizzone, J.A. 2014. Hydraulic characterization of porous pipes made of recycled automobile tires used in subsurface irrigation [Abstract in English]. Rev. Bras. Eng. Agríc. Ambiental, 18: 1095–1101.
Provenzano, G.P., Alagna, V., Autovino, D. and Juarez, J.M. 2016. Analysis of geometrical relationships and friction losses in small-diameter lay-flat polyethylene pipes. J. Irrig. Drain. Eng., 142: 1–9.
Sobenko, L.R., Frizzone, J.A., Camargo, A.P., Saretta, E. and Rocha, H.S. 2019. Characterization of venturi injector using dimensional analysis. Rev. Bras. Eng. Agríc. Ambiental, 23(7): 484–491.
Souza, R.O.R.M. and Botrel, T.A. 2004. Modeling for the design of microtubes in trickle irrigation [Abstract in English]. Rev. Bras. Eng. Agríc. Ambiental, 8(1): 16–22.
Souza, R.O.R.M., Miranda, E.P., Nascimento Neto, J.R., Ferreira, T.T.S. and Mesquita, F.P. 2009. Gravity Drip Irrigation in Agricultural Communities of Ceará [Abstract in English]. Rev. Ciênc. Agron., 40(1): 34–40.
Vekariya, P.B., Subbaiah, R. and Mashru, H.H. 2010. Hydraulics of microtube emitters: A dimensional analysis approach. Irrig. Sci., 29: 341–350.
Vermeiren, L. and Jobling, G.A. 1980. Localized irrigation: Design, installation, operation, evaluation. Rome: FAO.
Vilaça, F.N., Camargo, A.P., Frizzone, J.A., Mateos, L. and Koech, R. 2017. Minor losses in start connectors of microirrigation laterals. Irrig. Sci., 35: 227–240.
Wu, W., Chen, W.E.I., Liu, H, Yin, S. and Niu, Y. 2014. A new model for head loss assessment of screen filters developed with dimensional analysis in drip irrigation systems. Irrig. Drain., 63: 523–531.
Yurdem H., Demir, V. and Degirmencioglu, A. 2008. Development of a mathematical model to predict head losses from disc filters in drip irrigation systems using dimensional analysis. Biosyst. Eng., 100: 14–23.
Yurdem H., Demir, V. and Degirmencioglu, A. 2010. Development of a mathematical model to predict clean water head losses in hydrocyclone filters in drip irrigation systems using dimensional analysis. Biosyst. Eng., 105: 495–506.
Yurdem, H., Demir, V. and Mancuhan, A. 2015. Development of a simplified model for predicting the optimum lengths of drip irrigation laterals with coextruded cylindrical in-line emitters. Biosyst. Eng., 137: 22–35.
Zayed, M., El Molla, A. and Sallah, M. 2018. An experimental investigation of head loss through a triangular “V- shaped” screen. J. Adv. Res., 10: 69–76.
Zitterell, D.B., Frizzone, J.A. and Rettore Neto, O. 2013. Dimensional analysis approach to estimate local head losses in microirrigation connectors. Irrig. Sci., 32: 169–179.
Journal of Agricultural Science and Technology
Volume 22, Issue 4
May and June 2020
Pages 1123-1135