The inhibiting effect of a sharp edge on liquid spreading is well observed during drop interaction with textured surfaces. On groove-textured solid surfaces comprising unidirectional parallel grooves, the edge effect of posts results in the squeezing of drop liquid in the direction perpendicular to the grooves and the stretching of drop liquid along the grooves leading to anisotropy in drop flow, popularly known as wetting anisotropy which has been employed in several engineering applications. A recent study observed that the energy loss incurring at the edges of posts via contact angle hysteresis is primarily responsible for the anisotropic spreading of impacting drops on groove-textured surfaces. The present study aims to elucidate the role of edges on the spreading and receding dynamics of water drops. The experiments of drop impact are carried out on semi-infinite rectangular post comprising a pair of parallel 90-deg edges separated by a distance (post width) comparable to the diameter of impacting drop. The equilibrium shape of drops on the semi-infinite rectangular post is analyzed using open source computational tool Surface Evolver to optimize the ratio of initial droplet diameter to post width. Quantitative measurements of drop impact dynamics on semi-infinite rectangular posts are deduced by analysing high speed videos of impact process captured under three different camera views during experiments. Based on the role of post edges on impacting drops, different regimes of the impacting drops are characterized in terms of drop Weber number and the ratio of diameter of impacting drop to post width. Characteristic features of impact dynamics in each of the regimes are identified and discussed. It is seen that edges play a pivotal role on all stages of impact dynamics regardless of Weber number. Impacts in the regime of completely pinned drops on narrow posts are further analyzed to reveal characteristics of post-spreading oscillations.

Biofuels in civil aviation is actively studied in recent years to identify potential alternative jet fuels to meet stringent environmental regulations imposed to tackle degraded air quality caused by fossil fuel combustion. In this context, the aviation industry prefers to develop ‘drop-in’ fuels which may not require substantial modifications in existing jet engine technologies. The thesis aims at evaluating the atomization characteristics of camelina- and jatropha-derived drop-in biofuels discharging from simplex swirl atomizer used in aircraft gas turbine engines. The test fuels are characterized in detail and all fuels meet current ASTM D7566 specifications. The experiments are conducted by discharging fuel spray into quiescent atmospheric air in a fuel spray booth to obtain spray characteristics such as fuel discharge behaviour, spray cone angle, breakup behaviour of swirling fuel sheet and spray drop size distribution. The characteristics of sheet breakup are deduced from the captured images of biofuel sprays and the measurements of spray droplet size distribution are obtained using Spraytec (laser-diffraction instrument). A systematic comparison is made between the biofuel sprays and the 100% Jet A-1 (conventional aviation kerosene) sprays to evaluate the drop-in feature of the biofuels. All the measured spray characteristics of the biofuel sprays follow the Jet A-1 both in qualitative and quantitative terms which ensure the drop-in nature of the tested biofuels. The minor differences observed in the comparison of the quantitative spray measurements are attributed to the variation in the fuel properties. This claim is supported using the predictions obtained from the liquid film breakup model and the empirical correlation reported in the literature for the determination of sheet breakup characteristics and mean drop size for sprays discharging from simplex swirl atomizers.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2006. / Cooling tower spray nozzle performance characteristics such as the water distribution onto the fill material, air side pressure drop, pump head, drop size distribution and heat transfer in the spray zone were investigated experimentally and theoretically. The aim was to evaluate and simulate the performance characteristics of new and existing types of cooling tower spray nozzles with emphasis on the spray zone. Two medium and two low pressure type spray nozzles were tested and the results analysed. Single nozzle water distribution data obtained from tests was used to predict the water distribution obtained from four evenly spaced nozzles by superposition. The results were compared to data obtained from corresponding four nozzle tests. Computer codes and CFD models were developed to predict the drop trajectories, water distribution, total heat transfer and pressure drop for single nozzles and four nozzle grids. This was compared to correlated data found in literature. The performance characteristics expected from an ideal nozzle was discussed and compared to actual nozzle performance characteristics.

It seems as if there is a continued problem with mathematical performances nationally. The rate, at which FET (Further Education and Training) phase learner s discontinue Mathematics as a result of poor mathematical performances, is of great concern. This research study determined how academic self-confidence could have an influence on learners’ abilities to perform in Mathematics. The literature review confirmed that there could be a link between academic self-confidence and mathematical performance. Consequently, the researcher wanted to establish if the same could be found at a school where the emphasis is very much on mathematical achievement. The school is based in Northern Johannesburg (D10) in Gauteng, South Africa. By applying an explanatory mixed method approach (quantitative, followed by qualitative methods), the researcher identified a clear link between this school’s learners’ abilities to perform in Mathematics and their academic self-confidence. Amongst others, positive links were also identified between the learner s’ comprehension of Mathematics, their problem- solving skills as well as educator assistance, which in turn influence their academic self - confidence and consequently al so their performance s. A cycle of mathematical influences was identified that demonstrated that the influence i s not only working one way, but that a cycle forms; academic self-confidence influences the learner’s ability to perform in mathematics and mathematical performance s al so influence academic self - confidence, causing a continuous cycle of influence. / MEd (Learner Support), North-West University, Vaal Triangle Campus, 2013

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

5 Abstrakt Objectives of the Paper Description of typical communication patterns amongst employees and different types of clients in Low-threshold Centre Drop In o.p.s. displayed on individual case studies; analysis of sub- sequently recorded communication using the methods and concepts of Transactional Analysis. Recommendations for more effective communication between staff and the clients. Integration of the paper as an annex to the Operational Manual of Low-threshold Centre Drop In o.p.s. as an educational document, examining specificities of communication, its pitfalls and difficulties, including promises and possibilities in the organization. Sample File Ten individual case reports, described in a form of multiple case studies, that represent the kinds of clients with whom staff of Low-threshold Centre Drop In o.p.s. often come into contact. The specific content of each case was shaped by compiling many real-life situations, showing particular clients' position. Data Processing Methods Content and form of communication was analyzed using the methods of Transactional Analy- sis, monitoring specific communication patterns, presented in a form of multiple case studies. Individual case reports were situationally analyzed using Transactional Analysis concepts and data were inserted into spreadsheet. Each...

O demorado tratamento térmico, comum no preparo de fotocatalisadores e sua imobilização em substratos, foi contornado nesta tese, em que se investigaram duas estratégias de modificação de eletrodos de ouro com TiO2 P25. A primeira consiste em promover a formação de uma nanocamada pela simples exposição do metal por 1 min à suspensão aquosa de TiO2 (10 g L-1 em HCl 0,1 mol L-1); na segunda, deposita-se uma pequena alíquota (5 ou 8 µL) da suspensão diretamente no substrato (drop coating) para secá-lo em seguida por irradiação com lâmpada incandescente (60 W a 20 cm), obtendo-se bons resultados de uma a três camadas depositadas. Comprovou-se grande aumento da estabilidade da suspensão aquosa e duplicação da atividade fotocatalítica do nanofilme de TiO2 em decorrência da repulverização de P25 comercial em almofariz, melhoria inalcançável por sonicação da suspensão. O tamanho de partícula médio obtido por DLS para o TiO2 disperso em meio de HCl 0,1 mol L-1 atingiu 103±3 nm, enquanto que o filme depositado na superfície do ouro (observado por MEV e caracterizado por EDS) não ultrapassou 100 nm de espessura, sendo dominado por partículas de diâmetro de 20 (anatase) a 30 nm (rutilo), observadas por MET. A estabilidade da suspensão é susceptível ao ânion do ácido utilizado, sendo que resultados igualmente satisfatórios foram obtidos com HCl e HclO4 0,1 mol L-1, enquanto que para a mesma concentração de H2SO4 o TiO2 sofreu sedimentação rápida e o eletrodo preparado com a suspensão apresentou fotoatividade 10x menor. Filmes de espessuras bastante distintas (100 nm e 2 m) depositados a partir de suspensão 10 g L-1 por contato e drop coating com gota de 5,0 µL, respectivamente, foram comparados em relação à sua capacidade de transporte de elétrons e resposta eletroquímica ao Fe(CN)6 3 1,0 mmol L-1, sendo que a carga líquida formal de oxidação do EDTA 1,0 mmol L-1 é apenas 50 % maior para o filme 20x mais espesso, além de gerar distorções consideráveis nas ondas voltamétricas do sistema-sonda reversível em relação ao filme nanométrico e à superfície polida. Com eletrodos modificados pelo protocolo otimizado de drop coating (8,0 µL de TiO2 2 g L-1), testou-se o efeito da presença de diferentes eletrólitos de suporte (ácidos 0,1 mol L-1) em processos anódicos de fotooxidação em geral. A curva de decaimento da fotocorrente iph com o tempo pode ser descrita por uma equação de decaimento exponencial duplo iph = i0 + A1 exp(k1t) + A2 exp( k21t), permitindo distinguir as contribuições da fotocorrente de oxidação da água (i0) e de termos referentes a dois tipos de sítio superficiais, sendo um de cinética rápida e outro de cinética lenta. A seguinte ordem foi determinada para a fotocorrente total inicial (iph0 total) dos eletrólitos: HNO3 > HClO4 > HCl > H1SO4 > H3PO4 e as explicações propostas para tal se embasam na adsortividade dos ânions no TiO2 e na reatividade dos respectivos traps formados. O mesmo modelo de ajuste matemático foi utilizado para avaliar a fotoatividade do eletrodo modificado pela sua irradiação sucessiva e repetida em HNO3 0,1 mol L-1 (sem EDTA), sendo observada redução significativa principalmente nos parâmetros relativos aos sítios de reação e, assim, sugere-se um impedimento dos mesmos através, p. ex., da formação de peróxidos superficiais. Na presença também de EDTA, a carga líquida total despendida na sua fotooxidação se mantém relativamente constante nas sucessivas irradiações. Por fim, os experimentos de fotooxidação do EDTA sob varredura de potencial revelaram uma região de relação linear entre a fotocorrente e o potencial aplicado ao eletrodo modificado com TiO2 que se estende até a região de saturação de fotocorrente ser atingida, comportamento compatível com filmes nanoparticulados porosos não-dopados. A inclinação da região linear aumenta em função da [EDTA], como se os valores de condutância (di/dE) se elevassem dependendo da reação interfacial. Ajuste de modelo matemático hiperbólico correlacionando a (foto)resistência do filme em função da fotocorrente de saturação R = R0 + kIsph1, fornece resistência ôhmica do filme R0 de 5,0 kΩ e uma constante atrelada ao fotopotencial de 237 mA Ω. Já a curva monotônica de fotocorrente de saturação (Isph) com a [EDTA] apresenta comportamento linear até cerca de 0,7 mmol L-1, sugerindo-se que nessa região o controle por transporte de massa é a etapa limitante do processo global. Acima dessa concentração o coeficiente angular diminui gradualmente à medida que a reação de cinética de captura das lacunas passa a ser o determinante até um limite máximo (aparentemente 5,0 mmol L-1 de EDTA, nas condições do experimento) onde a disponibilidade de lacunas fotogeradas passa a governar. / The lengthy thermal treatment is a common step during the preparation and immobilization of photocatalysers on substrates, which by the way, was overcome in this thesis by the investigation of two strategies of modification of gold electrodes with P25 TiO2. The first one consists in promoting the formation of a nanolayer by the simple exposure of the metal surface to an aqueous suspension of TiO2 (10 g L-1 on 0.1 mol L-1 HCl) during 1 min; the second involves the deposition of a small drop (5 or 8 L) of the suspension on the gold substrate (drop coating) and its drying by irradiation with an incandescent lamp (60 W at 20 cm far), with worthy results also for two or three deposited layers. The stability of this aqueous suspension was appreciably improved by the repulverization of commercial P25 in a grinding mortar. As a consequence the photocatalytic activity conferred to the electrode by the formation of the TiO2 nanofilm doubled. Such improvements cannot be attained by bath sonication of the suspension. The average particle size determined by DLS for the TiO2 dispersed in 0.1 mol L-1 HCl was 103±3 nm, while the film deposited on the surface of gold consisted of particles of 20 nmn (anatase) and 30 nm (rutile) characterized by TEM and barely achieved a thickness of 100 nm (characterized by SEM and EDS). The stability of the modifying suspension is susceptible to the type of anion of the electrolyte. Good results were found with 0.1 mol L-1 HCl and HClO4, but not with 0.1 mol L-1 H2SO4. This last medium causes fast sedimentation of TiO2 and generates electrodes with one tenth of the photoactivity achieved with the other acids. The effect of film thickness on the photoactivity was evaluated for films with 100 nm and 2.0 µm prepared from a 10 g L-1 TiO2 suspension by the contact and drop coating (5 µL) strategies, respectively. The electron transport across both films and the electrochemical response for the 1.0 mmol L-1 Fe(CN) 63- probe was compared. The formal net charge for the 1.0 mmol L-1 EDTA oxidation was only 50 % higher for the 20x thicker film that also considerably distorts the voltammetric waves of the aforementioned reversible probe. The effect of different supporting electrolytes (0.1 mol L-1 acids) on the anodic photooxidation processes in general was tested with electrodes modified by an optimized drop coating protocol (8.0 µL of 2 µg L-1 TiO2). The curve describing the photocurrent decay in function of time might be ascribed to an equation of double exponential decay iph = i0 + A1 exp(k1t) + A2 exp (k2t), which allows the distinction of the contribution of water oxidation (i0) from terms of two types of surface sites: a kinetically fast site and a slow one. The total initial photocurrent (iph0 total) of the following electrolytes decays in the order: HNO3 > HClO4 > HCl > H2SO4 > H3PO4; explanations comprise the adsorbability of each respective anion on TiO2 and the reactivity of the corresponding traps formed. Similar curve fitting applied to the data of photoactivity of the gold electrode during successive irradiations of its surface in 0.1 mol L-1 HNO3 (absence of EDTA) revealed that sites reactivities underwent considerable reduction. It is suggested that during repetitive experiments the sites are impaired by the formation of surface peroxides. However, in the presence of 1.0 mmol L-1 of EDTA, the formal net charge of oxidation of the organic species remains almost unaltered. Ultimately, the experiments concerning the photooxidation of EDTA under linear potential scan revealed a region of linear relation between the photocurrent and the potential applied to the electrode modified with a TiO2 film (nanometric or micrometric), which holds until the saturation photocurrent is attained. This behavior is typical for porous non-doped nanoparticulate electrodes. The slope of the linear region increase somewhat with the EDTA concentration, as though the conductance values (di/dE) were raised depending on the interfacial reaction rate. The fitting of a hyperbolic model R = R0 + kIsph-1 for the correlation of the (photo)resistence (R) of the film with the photocurrent of saturation (Isph) allows the estimation of an ohmic resistance of 5.0 kΩ, and a photopotential related constant of 237 mA Ω. The curve of correlation between Isph and the [EDTA] is linear fit until 0.7 mmol L-1, suggesting that in this initial region the mass transport to the interface is the limiting step of the global process. Above that concentration, the slope of the curve is gradually reduced as the kinetic of capture of the holes becomes the determining step and from 5.0 mmol L-1 on an asymptotic Isph is reached (under the conditions of the experiments), where the holes photogeneration might start governing.

O objetivo desse estudo foi verificar a relação da aptidão aeróbia e de fatores neuromusculares com o desempenho em SR em tenistas com diferentes níveis de jogo. Um grupo de dez tenistas profissionais (GP) e um grupo de dez tenistas amadores (GA) foram submetidos a quatro sessões experimentais, a saber: 1) medidas antropométricas, familiarização com o teste de drop jump (DJ) e com o teste de contração voluntária isométrica máxima (CVIM) para membros inferiores, e um teste progressivo até a exaustão; 2) um teste de DJ e um teste de carga constante para avaliar a cinética on e off do consumo de oxigênio (VO2); 3) um teste de CVIM para membros inferiores, outro teste de carga constante para avaliar a cinética on e off do VO2 e familiarização com o teste de SR; 4) um teste composto por dez SR. O GP apresentou valores significativamente menores para o tempo do melhor sprint (SRmelhor) e para a média dos tempos de todos os sprints (SRmédio) em relação ao GA (p < 0,05). O percentual de aumento do tempo ao longo dos sprints (SR%aumento) do GP não foi significativamente menor em comparação ao GA (p = 0,102), porém a chance dessa variável ser menor para o GP foi considerada \"provável\". Para o GP, a única correlação significativa observada foi entre o SRmédio e o tempo de contato obtido no teste de DJ (r = 0,641, p < 0,05). Em relação ao GA, foram observadas correlações significativas da velocidade pico obtida no teste progressivo até a exaustão com o SRmelhor (r = -0,680, p < 0,05) e SRmédio (r = -0,744, p < 0,05), assim como da amplitude da fase lenta da cinética off do VO2 com o SRmelhor (r = -0,756, p < 0,05) e SRmédio (r = -0,794, p < 0,05). Portanto, esses dados sugerem que tenistas profissionais possuem um melhor desempenho em SR em comparação aos tenistas amadores. Entretanto, não está clara a importância de fatores da aptidão aeróbia e neuromusculares no desempenho dessa atividade / The objective of this study was to verify the relationship of aerobic fitness and neuromuscular factors with RS performance in tennis players with different playing level. A group of ten professional (PG) and ten amateur (AG) tennis players were submitted to four experimental sessions, to know: 1) anthropometric measurements, familiarization with the drop jump (DJ) test and the maximal voluntary isometric contraction (MVIC) test for the lower limbs, and a progressive test until exhaustion; 2) a DJ test and a constant load test for on and off oxygen consumption (VO2) kinetics measurement; 3) a MVIC test for the lower limbs, another constant load test for on and off VO2 kinetics measurement, and familiarization with the RS test; 4) a test of ten RS. The PG presented significant lower values for the best sprint time (RSbest) and mean time of all sprints (RSmean) in relation to the AG (p < 0.05). The percentage increase in time over all sprints (RSincrease) of the PG was not significantly lower in comparison to the AG (p = 0.102), however the chance of this variable to be lower for the PG was considered \"probable\". For the PG the only significant correlation observed was between RSmean and the contact time obtained in the DJ test (r = 0.641, p < 0.05). In relation to the AG, significant correlations were observed for the peak speed obtained on the progressive test until exhaustion with the RSbest (r = -0.680, p < 0.05) and RSmean (r = -0.744, p < 0.05), likewise for the amplitude of the slow phase in oxygen uptake off-kinetics with the RSbest (r = -0.756, p < 0.05) and RSmean (r = -0.794, p < 0.05). Thus, these data suggest that professional tennis players have a better performance in RS compared to amateur tennis players. However, it is not clear the importance of aerobic fitness and neuromuscular factors in the performance of this activity

Na presente pesquisa estudamos o comportamento do sujeito pronominal no português uruguaio (PU) falado na região de fronteira entre Brasil e Uruguai (Santana do Livramento-Rivera). Associando alguns pressupostos da Teoria de Princípios e Parâmetros (CHOMSKY, 1981), mais especificamente o Parâmetro do Sujeito Nulo (pro-drop), e da Sociolinguística Variacionista (WEINREICH, LABOV e HERZOG, 1968), analisamos uma amostra de língua oral composta de falas de 37 informantes, investigando as seguintes questões: (1) no português uruguaio teríamos uma mudança linguística em curso no que se refere ao Parâmetro do Sujeito Nulo, de modo que ele venha a se tornar um sujeito pronominal pleno?; (2) quais são os fatores linguísticos e sociais condicionantes dessa produção e em que direção vai essa tendência, português brasileiro (PB) ou espanhol (E)? A análise dos fatores sociais e linguísticos selecionados permitiu observar que o PU também passa por um processo de mudança paramétrica, ainda que mais lenta, devido ao fato de estar submetido à pressão simultânea de duas línguas, e se apresenta como uma língua em que, em alguns contextos, a realização do sujeito pronominal é plena e, em outros, ainda conserva as características das línguas pro-drop. Confirma-se, ainda, que essa disputa não está terminada, embora haja indícios nos dados da geração mais nova de que as regras do espanhol vêm ganhando alguma força, talvez pela pressão da escola e dos meios de comunicação. Tudo indica, então, que a base do PU é o PB, porém algumas características do E estão presentes nesse aspecto da gramática. A análise realizada confirma a maior parte das hipóteses iniciais e dá indícios de que o PU e o PB poderiam configurar-se como duas línguas distintas, da mesma forma que o PB e o PE, como aponta Galves (1998), isto é, tudo parece indicar que, mesmo quando os enunciados superficialmente se parecem, a língua interna (Língua-I) seria diferente e os enunciados dos falantes teriam estatutos diferentes, algo que, no entanto, será necessário demonstrar com um outro modelo de coleta de dados, de natureza mais introspectiva. / In this research we study the behavior of the pronominal subject in the Uruguayan Portuguese language (PU) spoken in the border region between Brazil and Uruguay (Santana do Livramento-Rivera). Associating some assumptions from the Theory of Principles and Parameters (CHOMSKY, 1981), specifically the Null Subject Parameter (pro-drop), and from the Variationist Sociolinguistics (WEINREICH, LABOV and HERZOG, 1968), we analyze a sample of spoken language consisting of 37 informants, in order to investigate the following questions: (1) would we have in the Uruguayan Portuguese language a language change in progress with regard to the Null Subject Parameter, so that it will become a full pronominal subject? (2) what are the linguistic factors and social conditions of production and in which direction will this trend, Brazilian Portuguese (BP) or Spanish (E)? The analysis of social factors and selected language programs suggests that the PU is also undergoing a process of parametric change, albeit slower, due to the fact of being subjected to the pressure of two languages simultaneously, and is presented as a language that, in some contexts, the performance of the pronominal subject is full, and in others it still retains the characteristics of pro-drop languages. It is also confirmed that this dispute is not over, although there are indications in the data of the younger generation that the rules of Spanish are gaining some strength, maybe due to the pressure of school and the media. The analysis confirms most of our initial hypothesis and provides evidence that the PU and CP could be framed as two distinct languages, in the same way as the PB and PE, as appointed by GALVES (1998), that is, everything seems to indicate that, even when the statements superficially resemble, the internal language (Language I) would be different and the production of the speakers would have different statutes, something which, however, would just be demonstrated by means of another more introspective model of data collection.

A presente dissertação trata de um estudo teórico-experimental sobre a perda de pressão em canais de diâmetro reduzido durante escoamento bifásico de refrigerantes halogenados. Trocadores de calor baseados na ebulição convectiva, em condições de micro-escala são amplamente estudados devido à intensificação da troca de calor proporcionada e a possibilidade de compactação de sistemas de resfriamento. Proporcionam também a redução do inventário de refrigerante e do material utilizado no processo de fabricação do trocador. Porém, o incremento da transferência de calor é acompanhada pelo aumento da perda de pressão, parâmetro também fundamental para o desempenho do sistema. Para o projeto satisfatório e otimizado destes dispositivos são necessários métodos de previsão de transferência de calor e perda de pressão. Entretanto, no caso de canais de diâmetro reduzido, tais ferramentas não encontram-se disponíveis e trocadores de calor baseados em escoamentos bifásicos no interior de canais de diâmetro reduzido vêm sendo desenvolvidos heuristicamente. Desta forma, inicialmente neste estudo, realizou-se uma revisão crítica da literatura envolvendo critérios de transição entre padrões de escoamento, fração de vazio superficial, perda de pressão no interior de canais com diâmetro reduzido durante escoamento bifásico e os principais métodos de estimativa da perda de pressão para macro e micro-escala. Resultados experimentais para perda de pressão levantados neste estudo em condições adiabáticas para os fluidos R245fa e R134a e tubo com 1,1 mm de diâmetro interno foram descritos e comparados aos métodos preditivos encontrados na literatura. Finalmente um novo método da previsão da perda de pressão foi proposto baseado na correlação de Müller-Steinhagen e Heck (1986), ajustando os valores do coeficiente e do expoente com base nos resultados experimentais levantados. / A theorical and experimental study on two-phase pressure drop inside micro-scale channels has been developed. Recently, the study of flow boiling in micro-scale channel have received special attention from academia and industry due to several advantages that they offer such as minimization of fluid inventory, high degree of compactness of the heat exchangers, better performance and the capacity of dissipate extremely high heat fluxes. The significant heat transfer coefficient enhancement provided by micro-scale channels comes together with a huge pressure drop penalty that impacts the efficiency of the overall cooling system. So, accurate predictive methods to evaluate the pressure drop are necessary for the appropriate design of the system and for its optimization. In the present study, firstly, a critical review on studies from literature was performed that covers criteria of transition between micro- and macro-scale flow boiling, void fraction, frictional pressure drop on micro-scale channels and the leading frictional pressure drop predictive methods. Experimental pressure drop results were acquired under adiabatic conditions for R245fa and R134a fluids and internal diameter tube of 1.1 mm. Then, the leading pressure drop predictive methods were compared against the present database. Also a new correlation based on Muller-Steinhagen e Heck (1986) method was proposed in this work by adjusting new empirical constants based on the present database together with previous results obtained by Tibiriçá et al. (2011) for a 2.3 mm ID tube.