Based on literature review, statistics of waste management at ports in South Africa is hard to come by. The research critically assessed the current waste management practices at Transnet National Ports Authority. Transnet National Ports Authority, Port of Richards Bay (TNPA RCB) was used as a case study to examine the different types and quantities of waste produced, analysing the current waste management model as well as determining TNPA RCB compliance to pertinent waste legislation. A 10 day waste audit was conducted to obtain quantitative data and to identify the different types of waste generated. The baseline data resulting from the waste audit conducted for the first time since the establishment of the TNPA RCB, found 402 kg of general waste generated, 74 kg of this total is segregated for recycling and the remaining 328 kg is landfilled. The overall conclusion gained during compliance audit was that the TNPA RCB was partly compliant with pertinent waste legislation and obligations. Furthermore, questionnaires about waste were sent to staff members working in offices to get an overview of how they deal with current waste management. A number of barriers to sustainable waste management were identified, including: lack of knowledge and awareness; constraints on facilities and human resources; culture that resists change and contamination. To overcome these, there needs to be education, as well as co-operation between top management, staff and waste service providers to help implement new strategies. The primary conclusions from this dissertation are that there are opportunities to divert waste streams from landfill and to attain a sustainable waste management system at TNPA RCB. / Environmental Sciences / M. Sc. (Environmental Management)

L'objectif de ce travail est d'obtenir, par homogénéisation périodique, des modèles macroscopiques de transfert hydrique dans les milieux poreux partiellement saturés à partir des équations de transfert de l'eau liquide et de vapeur d'eau écrites à une échelle microscopique. La dimensionnalisation des équations fait apparaître naturellement des nombres sans dimension caractérisant les problèmes de transfert hydriques dans les milieux partiellement saturés. Nous nous sommes intéressés à trois différents régimes de transfert (diffusion de vapeur prédominante, couplage diffusion/convection, convection de l'eau liquide prédominante). Pour chaque modèle homogénéisé, nous avons obtenu une expression différente du tenseur de diffusion hydrique homogénéisé. Nous avons ensuite calculé les tenseurs de diffusion hydrique homogénéisés obtenus dans les deux régions hygroscopique et super-hygroscopique, sur des géométries plus ou moins complexes décrivant la microstructure en 2D et 3D. Des comparaisons avec des valeurs expérimentales ont été ensuite effectuées. Pour finir, une résolution numérique de l'équation de transfert hydrique macroscopique homogénéisée a été effectuée en se basant sur les données expérimentales d'un béton BHP. / We propose in this work to construct, by periodic homogenization, macroscopic models of moisture transfer in unsaturated porous media. To do this, the liquid water and water vapor transport equations are averaged from the microscopic scale. The dimensional analysis of transport equations naturally lets appear dimensionless numbers characterizing the moisture transfer in unsaturated porous media. Three different transfer regimes are addressed (predominant water vapor diffusion, coupling diffusion / convection, predominant liquid water convection). For each transfer regime, the associated homogenized moisture diffusion tensor has a different expression. Then, the homogenized moisture diffusion tensors are calculated in both hygroscopic and super-hygroscopic regions on several geometries with varying complexity, describing 2D and 3D microstructures. Comparisons with experimental values are also addressed. Finally, based on experimental data of a BHP concrete, a numerical resolution of the homogenized macroscopic moisture transfer equation is performed.

Made available in DSpace on 2017-07-10T19:24:40Z (GMT). No. of bitstreams: 1 Juliana Fenner Ruas Lucas.pdf: 7353201 bytes, checksum: 171282273d86ea92304991a62a946fc6 (MD5) Previous issue date: 2010-07-13 / The soil water content is related to the soil matrix ability to retain the water, characterized by the water matric potential. Moisture and matric potential are factors functionally interrelated and represented by the soil-water retention curve. This relationship allows inferring moisture from the matric potential measurement and vice versa, as well as deducing several soil and water in soil properties. The traditional method for determining the retention curve employs the Richards pressure plate apparatus. For practical reasons, the search for alternatives to the Richards apparatus that are financially more accessible and faster is needed. In this regard, this study aimed at evaluating the use of two devices: the triaxial compression chamber and the filter paper. Therefore, soil was initially collected and physical-chemically characterized. Undisturbed soil samples were prepared and tested in the Richards chamber, using pressures of 0, 10, 30, 60, 100, 300, 500, 1,000 and 1,500 kPa. In the triaxial compression chamber test, soil samples were submited to pressures of 0, 10, 30, 60, 100, 300, 500 and 1,000 kPa, and for each pressure, it was measured the volume of drained water and calculated the sample moisture at that pressure. In the filter paper test, it was measured the water matric potential in samples for which moisture levels were established using an appropriated calibration curve. The three tests were repeated five times, resulting in points of pressure versus moisture that were adjusted by the RETC program, using to the model of van Genuchten. It was performed a comparative analysis of the triaxial chamber and the filter paper estimated soil moisture values with the adjusted retention curve obtained by the Richards apparatus. This comparison allowed to verify the applicability of the filter paper method for determining the water retention curve in agricultural soils and the inadequacy of triaxial compression chamber for this purpose. / O teor de água no solo está relacionado com a capacidade da matriz do solo em reter a água, caracterizada pelo potencial matricial da água. Umidade e potencial matricial são fatores funcionalmente inter-relacionados e representados pela curva de retenção da água no solo. Esta relação possibilita inferir a umidade a partir da medida do potencial matricial e vice-versa, assim como estimar outras propriedades do solo e da água no solo. O método tradicional para a determinação da curva de retenção emprega a câmara de pressão de Richards. Por questões práticas, a busca por métodos alternativos ao de Richards, financeiramente mais acessíveis e menos morosos, faz-se interessante. Diante disso, desenvolveu-se o presente trabalho com o objetivo de avaliar o uso de dois dispositivos: a câmara de compressão triaxial e o papel filtro. Para tanto, realizou-se inicialmente coleta e caracterização físico-química do solo, preparo de amostras indeformadas e ensaio na câmara de Richards, utilizando pressões de 0, 10, 30, 60, 100, 300, 500, 1000 e 1500 kPa. No ensaio com a câmara de compressão triaxial, submeteu-se amostras de solo às pressões de 0, 10, 30, 60, 100, 300, 500 e 1000 kPa e, para cada pressão, foi mensurado o volume de água drenado, o que permitiu calcular a umidade da amostra àquela pressão. Com o papel filtro, mediu-se o potencial matricial da água em amostras cujas umidades foram previamente estabelecidas, utilizando-se curva de calibração adequada. Os três ensaios foram executados em quintuplicata e resultaram em pontos de pressão versus umidade que foram ajustados pelo programa RETC, usando o modelo de van Genuchten. Realizou-se uma análise comparativa de valores de umidade volumétrica estimados pelo modelo ajustado nos ensaios com a câmara triaxial e o papel filtro com a curva de retenção ajustada obtida pela câmara de Richards. Através dessa comparação, verificou-se a aplicabilidade do método do papel filtro para a determinação da curva de retenção de água em solos agrícolas e inadequação da câmara de compressão triaxial para esta finalidade.

Made available in DSpace on 2017-05-12T14:48:03Z (GMT). No. of bitstreams: 1 Juliana Fenner Ruas Lucas.pdf: 7353201 bytes, checksum: 171282273d86ea92304991a62a946fc6 (MD5) Previous issue date: 2010-07-13 / The soil water content is related to the soil matrix ability to retain the water, characterized by the water matric potential. Moisture and matric potential are factors functionally interrelated and represented by the soil-water retention curve. This relationship allows inferring moisture from the matric potential measurement and vice versa, as well as deducing several soil and water in soil properties. The traditional method for determining the retention curve employs the Richards pressure plate apparatus. For practical reasons, the search for alternatives to the Richards apparatus that are financially more accessible and faster is needed. In this regard, this study aimed at evaluating the use of two devices: the triaxial compression chamber and the filter paper. Therefore, soil was initially collected and physical-chemically characterized. Undisturbed soil samples were prepared and tested in the Richards chamber, using pressures of 0, 10, 30, 60, 100, 300, 500, 1,000 and 1,500 kPa. In the triaxial compression chamber test, soil samples were submited to pressures of 0, 10, 30, 60, 100, 300, 500 and 1,000 kPa, and for each pressure, it was measured the volume of drained water and calculated the sample moisture at that pressure. In the filter paper test, it was measured the water matric potential in samples for which moisture levels were established using an appropriated calibration curve. The three tests were repeated five times, resulting in points of pressure versus moisture that were adjusted by the RETC program, using to the model of van Genuchten. It was performed a comparative analysis of the triaxial chamber and the filter paper estimated soil moisture values with the adjusted retention curve obtained by the Richards apparatus. This comparison allowed to verify the applicability of the filter paper method for determining the water retention curve in agricultural soils and the inadequacy of triaxial compression chamber for this purpose. / O teor de água no solo está relacionado com a capacidade da matriz do solo em reter a água, caracterizada pelo potencial matricial da água. Umidade e potencial matricial são fatores funcionalmente inter-relacionados e representados pela curva de retenção da água no solo. Esta relação possibilita inferir a umidade a partir da medida do potencial matricial e vice-versa, assim como estimar outras propriedades do solo e da água no solo. O método tradicional para a determinação da curva de retenção emprega a câmara de pressão de Richards. Por questões práticas, a busca por métodos alternativos ao de Richards, financeiramente mais acessíveis e menos morosos, faz-se interessante. Diante disso, desenvolveu-se o presente trabalho com o objetivo de avaliar o uso de dois dispositivos: a câmara de compressão triaxial e o papel filtro. Para tanto, realizou-se inicialmente coleta e caracterização físico-química do solo, preparo de amostras indeformadas e ensaio na câmara de Richards, utilizando pressões de 0, 10, 30, 60, 100, 300, 500, 1000 e 1500 kPa. No ensaio com a câmara de compressão triaxial, submeteu-se amostras de solo às pressões de 0, 10, 30, 60, 100, 300, 500 e 1000 kPa e, para cada pressão, foi mensurado o volume de água drenado, o que permitiu calcular a umidade da amostra àquela pressão. Com o papel filtro, mediu-se o potencial matricial da água em amostras cujas umidades foram previamente estabelecidas, utilizando-se curva de calibração adequada. Os três ensaios foram executados em quintuplicata e resultaram em pontos de pressão versus umidade que foram ajustados pelo programa RETC, usando o modelo de van Genuchten. Realizou-se uma análise comparativa de valores de umidade volumétrica estimados pelo modelo ajustado nos ensaios com a câmara triaxial e o papel filtro com a curva de retenção ajustada obtida pela câmara de Richards. Através dessa comparação, verificou-se a aplicabilidade do método do papel filtro para a determinação da curva de retenção de água em solos agrícolas e inadequação da câmara de compressão triaxial para esta finalidade.

Nous présentons une classe de nouveaux modèles pour décrire les écoulements d’eau dans des aquifères peu profonds non confinés. Cette classe de modèles offre une alternative au modèle Richards 3d plus classique mais moins maniable. Leur dérivation est guidée par deux ambitions : le nouveau modèle doit d’une part être peu coûteux en temps de calcul et doit d’autre part donner des résultats pertinents à toute échelle de temps. Deux types d’écoulements dominants apparaissent dans ce contexte lorsque le rapport de l’épaisseur sur la longueur de l’aquifère est petit : le premier écoulement apparaît en temps court et est décrit par un problème vertical Richards 1d ; le second correspond aux grandes échelles de temps, la charge hydraulique est alors considérée comme indépendante de la variable verticale. Ces deux types d’écoulements sont donc modélisés de manière appropriée par le couplage d’une équation 1d pour la partie insaturée de l’aquifère et d’une équation 2d pour la partie saturée. Ces équations sont couplées au niveau d’une interface de profondeur h (t,x) en dessous de laquelle l’hypothèse de Dupuit est vérifiée. Le couplage est assuré de telle sorte que la masse globale du système soit conservée. Notons que la profondeur h (t,x) peut être une inconnue du problème ou être fixée artificiellement. Nous prouvons (dans le cas d’aquifères minces) en utilisant des développements asymptotiques que le problème Richards 3d se comporte de la même manière que les modèles de cette classe à toutes les échelles de temps considérées (courte, moyenne et grande). Nous décrivons un schéma numérique pour approcher le modèle couplé non linéaire. Une approximation par éléments finis est combinée à une méthode d’Euler implicite en temps. Ensuite, nous utilisons une reformulation de l’équation discrète en introduisant un opérateur de Dirichlet-to-Neumann pour gérer le couplage non linéaire en temps. Une méthode de point fixe est appliquée pour résoudre l’équation discrète reformulée. Le modèle couplé est testé numériquement dans différentes situations et pour différents types d’aquifère. Pour chacune des simulations, les résultats numériques obtenus sont en accord avec ceux obtenus à partir du problème de Richards original. Nous concluons notre travail par l’analyse mathématique d’un modèle couplant le modèle Richards 3d à celui de Dupuit. Il diffère du premier parce que nous ne supposons plus un écoulement purement vertical dans la frange capillaire supérieure. Ce modèle consiste donc en un système couplé non linéaire d’équation Richards 3d avec une équation parabolique non linéaire décrivant l’évolution de l’interface h (t,x) entre les zones saturées et non saturées de l’aquifère. Les principales difficultés à résoudre sont celles inhérentes à l’équation 3D-Richards, la prise en compte de la frontière libre h (t,x) et la présence de termes dégénérés apparaissant dans les termes diffusifs et dans les dérivées temporelles. / We present a class of new efficient models for water flow in shallow unconfined aquifers, giving an alternative to the classical but less tractable 3D-Richards model. Its derivation is guided by two ambitions : any new model should be low cost in computational time and should still give relevant results at every time scale.We thus keep track of two types of flow occurring in such a context and which are dominant when the ratio thickness over longitudinal length is small : the first one is dominant in a small time scale and is described by a vertical 1D-Richards problem ; the second one corresponds to a large time scale, when the evolution of the hydraulic head turns to become independent of the vertical variable. These two types of flow are appropriately modelled by, respectively, a one-dimensional and a two-dimensional system of PDEs boundary value problems. They are coupled along an artificial level below which the Dupuit hypothesis holds true (i.e. the vertical flow is instantaneous below the function h(t,x)) in away ensuring that the global model is mass conservative. Tuning the artificial level, which even can depend on an unknown of the problem, we browse the new class of models. We prove using asymptotic expansions that the 3DRichards problem and eachmodel of the class behaves the same at every considered time scale (short, intermediate and large) in thin aquifers. We describe a numerical scheme to approximate the non-linear coupled model. The standard Galerkin’s finite element approximation in space and Backward Euler method in time are used for discretization. Then we reformulate the discrete equation by introducing the Dirichlet to Neumann operator to handle the nonlinear coupling in time. The fixed point iterative method is applied to solve the reformulated discrete equation. We have examined the coupled model in different boundary conditions and different aquifers. In the every situations, the numerical results of the coupled models fit well with the original Richards problem. We conclude our work by the mathematical analysis of a model coupling 3D-Richards flow and Dupuit horizontal flow. It differs from the first one because we no longer assume a purely vertical flow in the upper capillary fringe. This model thus consists in a nonlinear coupled system of 3D-Richards equation with a nonlinear parabolic equation describing the evolution of the interface h(t,x) between the saturated and unsaturated zones of the aquifer. The main difficulties to be solved are those inherent to the 3D-Richards equation, the consideration of the free boundary h(t,x) and the presence of degenerate terms appearing in the diffusive terms and in the time derivatives.

The report identifies a case study in which there was competition for land between conservation and low income settlement users. The nature of these potentially conflicting interests were identified and an evaluation of how these were played out followed. The fact that the interest of the low income settlement users carried the background of apartheid based discriminations, made the situation a sensitive one. Moreover, it was a unique case whereby the needs of a community's rural lifestyle were to be met in an urban environment. The planning process had political overtones which directed the decision-making process and consequential planning. The study informs development and planning, that in post-apartheid planning, there is the need to incorporate social reconstruction within urban and rural reconstruction. In planning and development processes, planning should play a fundamental role of providing input to guide the process. The input provided by planning should be cross-sectional in the context of conflicting interests, in order for the final plan to represent a compromise, serving the better interests of all the interested parties. / Thesis (M.T.R.P.)-University of Natal, Durban, 1996.

Thesis (M.A.)--University of New Brunswick, 2000. / Includes bibliographical references.

Submitted by (ana.araujo@ufrpe.br) on 2016-08-01T17:35:24Z No. of bitstreams: 1 Kleber Napoleao Nunes de Oliveira Barros.pdf: 2964667 bytes, checksum: a3c757cb7ed16fc9c38b7834b6e0fa29 (MD5) / Made available in DSpace on 2016-08-01T17:35:24Z (GMT). No. of bitstreams: 1 Kleber Napoleao Nunes de Oliveira Barros.pdf: 2964667 bytes, checksum: a3c757cb7ed16fc9c38b7834b6e0fa29 (MD5) Previous issue date: 2010-02-22 / It is presented in this work the growth model nonlinear Chapman-Richards with distribution of errors following the new class of symmetric models processed and Bayesian inference for the parameters. The objective was to apply this structure, via Metropolis-Hastings algorithm, in order to select the equation that best predicted heights of clones of Eucalyptus urophilla experiment established at the Agronomic Institute of Pernambuco (IPA) in the city of Araripina . The Gypsum Pole of Araripe is an industrial zone, located on the upper interior of Pernambuco, which consumes large amount of wood from native vegetation (caatinga) for calcination of gypsum. In this scenario, there is great need for a solution, economically and environmentally feasible that allows minimizing the pressure on native vegetation. The generus Eucalyptus presents itself as an alternative for rapid development and versatility. The height has proven to be an important factor in prognosis of productivity and selection of clones best adapted. One of the main growth curves, is the Chapman-Richards model with normal distribution for errors. However, some alternatives have been proposed in order to reduce the influence of atypical observations generated by this model. The data were taken from a plantation, with 72 months. Were performed inferences and diagnostics for processed and unprocessed model with many distributions symmetric. After selecting the best equation, was shown some convergence of graphics and other parameters that show the fit to the data model transformed symmetric Student’s t with 5 degrees of freedom in the parameters using Bayesian inference. / É abordado neste trabalho o modelo de crescimento não linear de Chapman-Richards com distribuição dos erros seguindo a nova classe de modelos simétricos transformados e inferência Bayesiana para os parâmetros. O objetivo foi aplicar essa estrutura, via algoritmo de Metropolis-Hastings, afim de selecionar a equação que melhor estimasse as alturas de clones de Eucalyptus urophilla provenientes de experimento implantado no Instituto Agronômico de Pernambuco (IPA), na cidade de Araripina. O Polo Gesseiro do Araripe é uma zona industrial, situada no alto sertão pernambucano, que consume grande quantidade de lenha proveniente da vegetação nativa (caatinga) para calcinação da gipsita. Nesse cenário, há grande necessidade de uma solução, econômica e ambientalmente, viável que possibilite uma minimização da pressão sobre a flora nativa. O gênero Eucalyptus se apresenta como alternativa, pelo seu rápido desenvolvimento e versatilidade. A altura tem se revelado fator importante na prognose de produtividade e seleção de clones melhores adaptados. Uma das principais curvas de crescimento, é o modelo de Chapman- Richards com distribuição normal para os erros. No entanto, algumas alternativas tem sido propostas afim de reduzir a influência de observações atípicas geradas por este modelo. Os dados foram retirados de uma plantação, com 72 meses. Foram realizadas as inferências e diagnósticos para modelo transformado e não transformado com diversas distribuições simétricas. Após a seleção da melhor equação, foram mostrados alguns gráficos da convergência dos parâmetros e outros que comprovam o ajuste aos dados do modelo simétrico transformado t de Student com 5 graus de liberdade utilizando inferência Bayesiana nos parâmetros.

Submitted by (ana.araujo@ufrpe.br) on 2016-08-03T15:09:46Z No. of bitstreams: 1 Luiz Medeiros de Araujo Lima Filho.pdf: 529199 bytes, checksum: 06cae9ad9a02975b786cf55a000dbc5b (MD5) / Made available in DSpace on 2016-08-03T15:09:46Z (GMT). No. of bitstreams: 1 Luiz Medeiros de Araujo Lima Filho.pdf: 529199 bytes, checksum: 06cae9ad9a02975b786cf55a000dbc5b (MD5) Previous issue date: 2009-02-13 / Historically, the wood of the eucalyptus is used for the most varied applications, such as; firewood, charcoal, cellulose, railway sleepers, posts for electrification, bark to tan leather, essential oils, civil construction, etc. The Gypsum Pole of Araripe in Pernambuco is a great firewood consumer for the gypsum production. Due to great need to find economical and environmental alternatives for the area, the sustainable production of eucalyptus that is a fast growth tree with great versatility has an important role. In the planning of the sustainable forest management there is a variable of extreme importance: the growth. To model the growth is fundamental in the prognosis of the productivity, site quality and dynamics of populations. Usually, the growth curves are fitted through nonlinear models developed empirically to relate, for instance, height and age. The Chapman-Richards model is a nonlinear model frequently used to model forest growth. In studies of this type, in general, it is assumed that the errors follow approximately the normal distribution. However, to model the growth assuming that the errors have a normal distribution is quite sensitive to atypical values that can happen, and generate bad estimates of the parameters. To correct that problem a new class of transformed symmetrical models was developed considering for the errors symmetrical continuous distributions with heavier tails than the normal distribution and allowing a possible nonlinear structure for the mean. With the expectation of obtaining better estimates of eucalyptus growth, it was applied to the Chapman-Richards model the following distributions of the errors: normal, t of Student, Cauchy, exponential potency, logistics I and logistics II. The t distribution of Student with 2 degrees of freedom was the most efficient to estimate height and circumference growth of eucalyptus in the Gypsum Pole of Pernambuco. / Historicamente, a madeira do Eucalyptus é usada para os mais variados fins, tais como; lenha, carvão vegetal, celulose, dormentes ferroviários, postes para eletrificação, casca para curtir couro, óleos essenciais, construção civil, etc. O Pólo Gesseiro do Araripe em Pernambuco é um grande consumidor de madeira para produção de gesso. Devido à grande necessidade de se buscar uma alternativa econômica e ambiental para a região é de interesse obter uma produção sustentável para o Eucalyptus, uma vez que esta é uma árvore de rápido crescimento e grande versatilidade. No planejamento do manejo florestal sustentado uma variável é de extrema importância: o crescimento. Sua modelagem é fundamental na prognose da produtividade, qualidade do local e dinâmica de populações. Geralmente, as curvas de crescimento são estudadas por meio de modelos não-lineares desenvolvidos empiricamente para relacionar, por exemplo, altura e idade. Um modelo não-linear bastante utilizado na prática para modelar curvas de crescimento é o modelo de Chapman-Richards. Em estudos deste tipo, em geral, assume-se que os erros seguem distribuição normal. Contudo, a modelagem sob a suposição de erros com distribuição normal é bastante sensível a valores atípicos que por ventura possam ocorrer, podendo distorcer as estimativas dos parâmetros. Para corrigir esse problema Cordeiro et al. (2009) desenvolveram uma nova classe de modelos simétricos transformados considerando para os erros distribuições contínuas simétricas com caudas mais pesadas do que a distribuição normal e permitindo uma possível estrutura não-linear para a média. Dessa forma, com a expectativa de obter melhores estimativas de crescimento de Eucalyptus, aplicaram-se ao modelo de Chapman-Richards as seguintes distribuições dos erros: normal, t de Student, Cauchy, exponencial potência, logística I e logística II que apresentou a distribuição t de Student com 2 graus de liberdade com melhores estimativas de crescimento em altura e circunferência de Eucalyptus no Pólo Gesseiro de Pernambuco.

O bulbo molhado formado na irrigação por gotejamento pode ser modelado a partir informações das propriedades físico-hídricas do solo. Mas apesar do grande progresso na modelagem, a aplicação de modelos na irrigação e drenagem ainda não foi implementada em nenhum nível de maneira substancial. Assim, o objetivo do presente trabalho foi desenvolver um modelo numérico utilizando a técnica dos volumes finitos para estimar a forma e as dimensões do volume de solo molhado sob irrigação por gotejamento, e verificar a validade do modelo através da comparação com dados recolhidos em condições experimentais. O ensaio foi conduzido na área experimental do Departamento de Engenharia de Biossistemas da Escola Superior de Agricultura Luiz de Queiroz-ESALQ/USP. As sondas de TDR foram confeccionadas segundo procedimentos descritos por Souza et al. (2006). O perfil do bulbo molhado formado no solo abaixo de um emissor do tipo gotejador foi determinado para 3 tipos de material: areia, solo arenoso e solo argiloso e para 3 vazões nominais do emissor: 2, 4 e 6 L/h. Cada uma das combinações entre tipo de solo e vazão foi repetida três vezes em caixas (1000 L) diferentes, totalizando 27 medições. Um modelo numérico foi desenvolvido para simular a distribuição da água no perfil do solo abaixo de uma fonte pontual. A solução da equação diferencial para o movimento da água em solo não saturado foi realizada pela discretização do espaço-tempo utilizando a técnica dos volumes finitos. Um algoritmo em linguagem Visual Basic foi escrito para implementar o conjunto de equações e simular a evolução do bulbo molhado no tempo. Foi simulada a formação do bulbo molhado nas mesmas condições do experimento, e gráficos de isolinhas de umidade foram traçados no software Surfer. O modelo numérico proposto foi capaz de simular a formação do bulbo molhado em diferentes condições de tipo de solo e vazão do emissor. / The soil water patterns in drip irrigation can be modeled from physical and hydraulic properties of soil. But despite the great progress in modeling, the models have not been implemented at any level in irrigation and drainage. The objective of this study was to develop a numerical model using finite volume technique to estimate the shape and dimensions of the wetted soil volume under drip irrigation and verify the validity of the model by comparing data collected under experimental conditions. The trial was conducted at the experimental site of the Department of Biosystems Engineering, Escola Superior de Agricultura Luiz de Queiroz- ESALQ/USP. The TDR probes were manufactured according Souza et al. (2006). The soil water patterns under a drip emitter type was determined for three types of material: sand, sandy soil and clay soil and three nominal flows of the emitters: 2, 4 and 6 L/h. Each of the combinations of soil type and flow rate was repeated three times in boxes (1000 L), totaling 27 measurements. A numerical model was developed to simulate the distribution of water in the soil profile below a point source. The solution of the differential equation for the movement of water in unsaturated soil was carried out by the discretization of space-time using the technique of finite volume. An algorithm in Visual Basic language was written to implement the set of equations and simulate the evolution of wetted soil volume in time. Contour plots of soil water content were drawn in Surfer software. The proposed numerical model was able to simulate wetted soil volume under different conditions of soil type and flow of the emitter.