Modelling hydrodynamics in the Rio Parana, Argentina : an evaluation and inter-comparison of reduced-complexity and physics based models applied to a large sand-bed river

Depth-averaged velocities and unit discharges within a 30 km reach of one of the world's largest rivers, the Rio Parana, Argentina, were simulated using three hydrodynamic models with different process representations: a reduced complexity (RC) model that neglects most of the physics governing fluid flow, a two-dimensional model based on the shallow water equations, and a three-dimensional model based on the Reynolds-averaged Navier-Stokes equations. Row characteristics simulated using all three models were compared with data obtained by acoustic Doppler current profiler surveys at four cross sections within the study reach. This analysis demonstrates that, surprisingly, the performance of the RC model is generally equal to, and in some instances better than, that of the physics based models in terms of the statistical agreement between simulated and measured flow properties. In addition, in contrast to previous applications of RC models, the present study demonstrates that the RC model can successfully predict measured flow velocities. The strong performance of the RC model reflects, in part, the simplicity of the depth-averaged mean flow patterns within the study reach and the dominant role of channel-scale topographic features in controlling the flow dynamics. Moreover, the very low water surface slopes that typify large sand-bed rivers enable flow depths to be estimated reliably in the RC model using a simple fixed-lid planar water surface approximation. This approach overcomes a major problem encountered in the application of RC models in environments characterised by shallow flows and steep bed gradients. The RC model is four orders of magnitude faster than the physics based models when performing steady-state hydrodynamic calculations. However, the iterative nature of the RC model calculations implies a reduction in computational efficiency relative to some other RC models. A further implication of this is that, if used to simulate channel morphodynamics, the present RC model may offer only a marginal advantage in terms of computational efficiency over approaches based on the shallow water equations. These observations illustrate the trade off between model realism and efficiency that is a key consideration in RC modelling. Moreover, this outcome highlights a need to rethink the use of RC morphodynamic models in fluvial geomorphology and to move away from existing grid-based approaches, such as the popular cellular automata (CA) models, that remain essentially reductionist in nature. In the case of the world's largest sand-bed rivers, this might be achieved by implementing the RC model outlined here as one element within a hierarchical modelling framework that would enable computationally efficient simulation of the morphodynamics of large rivers over millennial time scales. (C) 2012 Elsevier B.V. All rights reserved.

Stereoselective metabolism of citalopram in plasma and cerebrospinal fluid of depressive patients: relationship with 5-HIAA in CSF and clinical response.

Plasma and cerebrospinal fluid (CSF) concentrations of the enantiomers of citalopram (CIT), its N-demethylated metabolite demethylcitalopram (DCIT) and its deaminated metabolite citalopram propionic acid derivative (CIT-PROP) were measured in plasma and CSF in 22 depressed patients after a 4-week treatment with 40 mg/d citalopram, which was preceded by a 1-week washout period. CSF 5-hydroxyindoleacetic acid (5-HIAA) and homovanillic acid (HVA) were measured at baseline and after the 4-week CIT medication period. Patients were assessed clinically, using the Hamilton Depression Rating Scale (21-item HAM-D): at baseline and then at weekly intervals. CSF concentrations of S-CIT and R-CIT were 10.6 +/- 4.3 and 20.9 +/- 6 ng/mL, respectively, and their CSF/plasma ratios were 52% +/- 9% and 48% +/- 6%, respectively. The CIT treatment resulted in a significant decrease (28%) of 5-HIAA (P < 0.0001) and a significant increase (41%) of HVA in the CSF. Multiple linear regression analyses were performed to identify the impact of plasma and CSF CIT enantiomers and its metabolites on CSF monoamine metabolites and clinical response. There were 10 responders as defined by a > or =50% decrease of the HAM-D score (DeltaHAM-D) after the 4-week treatment. DeltaHAM-D correlated (Spearman) significantly with CSF S-CIT (r = - 0.483, P < 0.05), CSF S-CIT-PROP (r = -0.543, P = 0.01) (a metabolite formed from CIT by monoamine oxidase [MAO]) and 5-HIAA decrease (Delta5-HIAA) (r = 0.572, P = 0.01). The demonstrated correlations between pharmacokinetic parameters and the clinical outcome as well as 5-HIAA changes indicate that monitoring of plasma S-CIT, CSF S-CIT and CSF S-CIT-PROP may be of clinical relevance.

A reassessment of models for hydrocarbon generation in the Khibiny nepheline syenite complex, Kola Peninsula, Russia

Although hydrocarbon-bearing fluids have been known from the alkaline igneous rocks of the Khibiny intrusion for many years, their origin remains enigmatic. A recently proposed model of post-magmatic hydrocarbon (HC) generation through Fischer-Tropsch (FT) type reactions suggests the hydration of Fe-bearing phases and release of H-2 which reacts with magmatically derived CO2 to form CH4 and higher HCs. However, new petrographic, microthermometric, laser Raman, bulk gas and isotope data are presented and discussed in the context of previously published work in order to reassess models of HC generation. The gas phase is dominated by CH4 with only minor proportions of higher hydrocarbons. No remnants of the proposed primary CO2-rich fluid are found in the complex. The majority of the fluid inclusions are of secondary nature and trapped in healed microfractures. This indicates a high fluid flux after magma crystallisation. Entrapment conditions for fluid inclusions are 450-550 degrees C at 2.8-4.5 kbar. These temperatures are too high for hydrocarbon gas generation through the FT reaction. Chemical analyses of rims of Fe-rich phases suggest that they are not the result of alteration but instead represent changes in magma composition during crystallisation. Furthermore, there is no clear relationship between the presence of Fe-rich minerals and the abundance of fluid inclusion planes (FIPs) as reported elsewhere. delta C-13 values for methane range from -22.4% to -5.4%, confirming a largely abiogenic origin for the gas. The presence of primary CH4-dominated fluid inclusions and melt inclusions, which contain a methane-rich gas phase, indicates a magmatic origin of the HCs. An increase in methane content, together with a decrease in delta C-13 isotope values towards the intrusion margin suggests that magmatically derived abiogenic hydrocarbons may have mixed with biogenic hydrocarbons derived from the surrounding country rocks. (C) 2006 Elsevier BV. All rights reserved.

Matching stages of heavy-ion collision models

Heavy-ion reactions and other collective dynamical processes are frequently described by different theoretical approaches for the different stages of the process, like initial equilibration stage, intermediate locally equilibrated fluid dynamical stage, and final freeze-out stage. For the last stage, the best known is the Cooper-Frye description used to generate the phase space distribution of emitted, noninteracting particles from a fluid dynamical expansion or explosion, assuming a final ideal gas distribution, or (less frequently) an out-of-equilibrium distribution. In this work we do not want to replace the Cooper-Frye description, but rather clarify the ways of using it and how to choose the parameters of the distribution and, eventually, how to choose the form of the phase space distribution used in the Cooper-Frye formula. Moreover, the Cooper-Frye formula is used in connection with the freeze-out problem, while the discussion of transition between different stages of the collision is applicable to other transitions also. More recently, hadronization and molecular dynamics models have been matched to the end of a fluid dynamical stage to describe hadronization and freeze-out. The stages of the model description can be matched to each other on space-time hypersurfaces (just like through the frequently used freeze-out hypersurface). This work presents a generalized description of how to match the stages of the description of a reaction to each other, extending the methodology used at freeze-out, in simple covariant form which is easily applicable in its simplest version for most applications.

Fluid flow and dispersion predictions in porous media by utilizing advanced numerical methods

Diplomityön tavoitteena oli tarkastella numeerisen virtauslaskennan avulla virtaukseen liittyviä ilmiöitä ja kaasun dispersiota. Diplomityön sisältö on jaettu viiteen osaan; johdantoon, teoriaan, katsaukseen virtauksen mallinnukseen huokoisessa materiaalissa liittyviin tutkimusselvityksiin, numeeriseen mallinnukseen sekä tulosten esittämiseen ja johtopäätöksiin. Diplomityön alussa kiinnitettiin huomiota erilaisiin kokeellisiin, numeerisiin ja teoreettisiin mallinnusmenetelmiin, joilla voidaan mallintaa virtausta huokoisessa materiaalissa. Kirjallisuusosassa tehtiin katsaus aikaisemmin julkaistuihin puoliempiirisiin ja empiirisiin tutkimusselvityksiin, jotka liittyvät huokoisen materiaalin aiheuttamaan painehäviöön. Numeerisessa virtauslaskenta osassa rakennettiin ja esitettiin huokoista materiaalia kuvaavat numeeriset mallit käyttäen kaupallista FLUENT -ohjelmistoa. Työn lopussa arvioitiin teorian, numeerisen virtauslaskennan ja kokeellisten tutkimusselvitysten tuloksia. Kolmiulotteisen huokoisen materiaalinnumeerisessa mallinnuksesta saadut tulokset vaikuttivat lupaavilta. Näiden tulosten perusteella tehtiin suosituksia ajatellen tulevaa virtauksen mallinnusta huokoisessa materiaalissa. Osa tässä diplomityössä esitetyistä tuloksista tullaan esittämään 55. Kanadan Kemiantekniikan konferenssissa Torontossa 1619 Lokakuussa 2005. ASME :n kansainvälisessä tekniikan alan julkaisussa. Työ on hyväksytty esitettäväksi esitettäväksi laskennallisen virtausmekaniikan (CFD) aihealueessa 'Peruskäsitteet'. Lisäksi työn yksityiskohtaiset tulokset tullaan lähettämään myös CES:n julkaisuun.

Homeostatic proliferation and survival of naïve and memory T cells.

The immune system relies on homeostatic mechanisms in order to adapt to the changing requirements encountered during steady-state existence and activation by antigen. For T cells, this involves maintenance of a diverse repertoire of naïve cells, rapid elimination of effector cells after pathogen clearance, and long-term survival of memory cells. The reduction of T-cell counts by either cytotoxic drugs, irradiation, or certain viruses is known to lead to lymphopenia-induced proliferation and restoration of normal T-cell levels. Such expansion is governed by the interaction of TCR with self-peptide/MHC (p/MHC) molecules plus contact with cytokines, especially IL-7. These same ligands, i.e. p/MHC molecules and IL-7, maintain naïve T lymphocytes as resting cells under steady-state T-cell-sufficient conditions. Unlike naïve cells, typical "central" memory T cells rely on a combination of IL-7 and IL-15 for their survival in interphase and for occasional cell division without requiring signals from p/MHC molecules. Other memory T-cell subsets are less quiescent and include naturally occurring activated memory-phenotype cells, memory cells generated during chronic viral infections, and effector memory cells. These subsets of activated memory cells differ from central memory T cells in their requirements for homeostatic proliferation and survival. Thus, the factors controlling T-cell homeostasis can be seen to vary considerably from one subset to another as described in detail in this review.

Working memory load improves early stages of independent visual processing.

Increasing evidence suggests that working memory and perceptual processes are dynamically interrelated due to modulating activity in overlapping brain networks. However, the direct influence of working memory on the spatio-temporal brain dynamics of behaviorally relevant intervening information remains unclear. To investigate this issue, subjects performed a visual proximity grid perception task under three different visual-spatial working memory (VSWM) load conditions. VSWM load was manipulated by asking subjects to memorize the spatial locations of 6 or 3 disks. The grid was always presented between the encoding and recognition of the disk pattern. As a baseline condition, grid stimuli were presented without a VSWM context. VSWM load altered both perceptual performance and neural networks active during intervening grid encoding. Participants performed faster and more accurately on a challenging perceptual task under high VSWM load as compared to the low load and the baseline condition. Visual evoked potential (VEP) analyses identified changes in the configuration of the underlying sources in one particular period occurring 160-190 ms post-stimulus onset. Source analyses further showed an occipito-parietal down-regulation concurrent to the increased involvement of temporal and frontal resources in the high VSWM context. Together, these data suggest that cognitive control mechanisms supporting working memory may selectively enhance concurrent visual processing related to an independent goal. More broadly, our findings are in line with theoretical models implicating the engagement of frontal regions in synchronizing and optimizing mnemonic and perceptual resources towards multiple goals.

Modeling of non-isothermalvapor membrane separation with thermodynamic models and generalized mass transfer equations

A rigorous unit operation model is developed for vapor membrane separation. The new model is able to describe temperature, pressure, and concentration dependent permeation as wellreal fluid effects in vapor and gas separation with hydrocarbon selective rubbery polymeric membranes. The permeation through the membrane is described by a separate treatment of sorption and diffusion within the membrane. The chemical engineering thermodynamics is used to describe the equilibrium sorption of vapors and gases in rubbery membranes with equation of state models for polymeric systems. Also a new modification of the UNIFAC model is proposed for this purpose. Various thermodynamic models are extensively compared in order to verify the models' ability to predict and correlate experimental vapor-liquid equilibrium data. The penetrant transport through the selective layer of the membrane is described with the generalized Maxwell-Stefan equations, which are able to account for thebulk flux contribution as well as the diffusive coupling effect. A method is described to compute and correlate binary penetrant¿membrane diffusion coefficients from the experimental permeability coefficients at different temperatures and pressures. A fluid flow model for spiral-wound modules is derived from the conservation equation of mass, momentum, and energy. The conservation equations are presented in a discretized form by using the control volume approach. A combination of the permeation model and the fluid flow model yields the desired rigorous model for vapor membrane separation. The model is implemented into an inhouse process simulator and so vapor membrane separation may be evaluated as an integralpart of a process flowsheet.

Populating ACT-R's Declarative Memory with Internet Statistics

Decision situations are often characterized by uncertainty: we do not know the values of the different options on all attributes and have to rely on information stored in our memory to decide. Several strategies have been proposed to describe how people make inferences based on knowledge used as cues. The present research shows how declarative memory of ACT-R models could be populated based on internet statistics. This will allow to simulate the performance of decision strategies operating on declarative knowledge based on occurrences and co-occurrences of objects and cues in the environment.

Fluid flow processes at basin scale

S u b s u r face fluid flow plays a significant role in many geologic processes and is increasingly being studied in the scale of sedimentary basins and geologic time perspective. Many economic resources such as petroleum and mineral deposits are products of basin scale fluid flow operating over large periods of time. Such ancient flow systems can be studied through analysis of diagenetic alterations and fluid inclusions to constrain physical and chemical conditions of fluids and rocks during their paleohy d r og e o l ogic evolution. Basin simulation models are useful to complement the paleohy d r og e o l ogic record preserved in the rocks and to derive conceptual models on hydraulic basin evolution and generation of economic resources. Different types of fluid flow regimes may evo l ve during basin evolution. The most important with respect to flow rates and capacity for transport of solutes and thermal energy is gr avitational fluid flow driven by the topographic configuration of a basin. Such flow systems require the basin to be elevated above sea level. Consolidational fluid flow is the principal fluid migration process in basins below sea level, caused by loading of compressible rocks. Flow rates of such systems are several orders of magnitude below topogr a p hy driven flow. Howeve r, consolidation may create significant fluid ove rpressure. Episodic dewatering of ove rpressured compart m e n t s m ay cause sudden fluid release with elevated flow velocities and may cause a transient local thermal and chemical disequilibrium betwe e n fluid and rock. This paper gives an ove rv i ew on subsurface fluid flow processes at basin scale and presents examples related to the Pe n e d è s basin in the central Catalan continental margin including the offshore Barcelona half-graben and the compressive South-Pyrenean basin.

Multicontrast MRI Quantification of Focal Inflammation and Degeneration in Multiple Sclerosis.

INTRODUCTION: Local microstructural pathology in multiple sclerosis patients might influence their clinical performance. This study applied multicontrast MRI to quantify inflammation and neurodegeneration in MS lesions. We explored the impact of MRI-based lesion pathology in cognition and disability. METHODS: 36 relapsing-remitting MS subjects and 18 healthy controls underwent neurological, cognitive, behavioural examinations and 3 T MRI including (i) fluid attenuated inversion recovery, double inversion recovery, and magnetization-prepared gradient echo for lesion count; (ii) T1, T2, and T2(*) relaxometry and magnetisation transfer imaging for lesion tissue characterization. Lesions were classified according to the extent of inflammation/neurodegeneration. A generalized linear model assessed the contribution of lesion groups to clinical performances. RESULTS: Four lesion groups were identified and characterized by (1) absence of significant alterations, (2) prevalent inflammation, (3) concomitant inflammation and microdegeneration, and (4) prevalent tissue loss. Groups 1, 3, 4 correlated with general disability (Adj-R (2) = 0.6; P = 0.0005), executive function (Adj-R (2) = 0.5; P = 0.004), verbal memory (Adj-R (2) = 0.4; P = 0.02), and attention (Adj-R (2) = 0.5; P = 0.002). CONCLUSION: Multicontrast MRI provides a new approach to infer in vivo histopathology of plaques. Our results support evidence that neurodegeneration is the major determinant of patients' disability and cognitive dysfunction.

Commentary. The ontogeny of human memory : where are we going ?

In their review, Jabe`s and Nelson provide an update of Nelson's 1995 cognitive neuroscience model of human memory development. Here, we highlight the major changes in perspective after 20 years of advances in our understanding of the neural basis of memory, and advocate the need for more systematic investigations of memory processes across the lifespan, which combine different models and levels of analysis: from genes, to brain to behavior.

Does working memory training affect decision making ? : a neuroeconomic study

We all make decisions of varying levels of importance every day. Because making a decision implies that there are alternative choices to be considered, almost all decision involves some conflicts or dissatisfaction. Traditional economic models esteem that a person must weight the positive and negative outcomes of each option, and based on all these inferences, determines which option is the best for that particular situation. However, individuals rather act as irrational agents and tend to deviate from these rational choices. They somewhat evaluate the outcomes' subjective value, namely, when they face a risky choice leading to losses, people are inclined to have some preference for risk over certainty, while when facing a risky choice leading to gains, people often avoid to take risks and choose the most certain option. Yet, it is assumed that decision making is balanced between deliberative and emotional components. Distinct neural regions underpin these factors: the deliberative pathway that corresponds to executive functions, implies the activation of the prefrontal cortex, while the emotional pathway tends to activate the limbic system. These circuits appear to be altered in individuals with ADHD, and result, amongst others, in impaired decision making capacities. Their impulsive and inattentive behaviors are likely to be the cause of their irrational attitude towards risk taking. Still, a possible solution is to administrate these individuals a drug treatment, with the knowledge that it might have several side effects. However, an alternative treatment that relies on cognitive rehabilitation might be appropriate. This project was therefore aimed at investigate whether an intensive working memory training could have a spillover effect on decision making in adults with ADHD and in age-matched healthy controls. We designed a decision making task where the participants had to select an amount to gamble with the chance of 1/3 to win four times the chosen amount, while in the other cases they could loose their investment. Their performances were recorded using electroencephalography prior and after a one-month Dual N-Back training and the possible near and far transfer effects were investigated. Overall, we found that the performance during the gambling task was modulated by personality factors and by the importance of the symptoms at the pretest session. At posttest, we found that all individuals demonstrated an improvement on the Dual N-Back and on similar untrained dimensions. In addition, we discovered that not only the adults with ADHD showed a stable decrease of the symptomatology, as evaluated by the CAARS inventory, but this reduction was also detected in the control samples. In addition, Event-Related Potential (ERP) data are in favor of an change within prefrontal and parietal cortices. These results suggest that cognitive remediation can be effective in adults with ADHD, and in healthy controls. An important complement of this work would be the examination of the data in regard to the attentional networks, which could empower the fact that complex programs covering the remediation of several executive functions' dimensions is not required, a unique working memory training can be sufficient. -- Nous prenons tous chaque jour des décisions ayant des niveaux d'importance variables. Toutes les décisions ont une composante conflictuelle et d'insatisfaction, car prendre une décision implique qu'il y ait des choix alternatifs à considérer. Les modèles économiques traditionnels estiment qu'une personne doit peser les conséquences positives et négatives de chaque option et en se basant sur ces inférences, détermine quelle option est la meilleure dans une situation particulière. Cependant, les individus peuvent dévier de ces choix rationnels. Ils évaluent plutôt les valeur subjective des résultats, c'est-à-dire que lorsqu'ils sont face à un choix risqué pouvant les mener à des pertes, les gens ont tendance à avoir des préférences pour le risque à la place de la certitude, tandis que lorsqu'ils sont face à un choix risqué pouvant les conduire à un gain, ils évitent de prendre des risques et choisissent l'option la plus su^re. De nos jours, il est considéré que la prise de décision est balancée entre des composantes délibératives et émotionnelles. Ces facteurs sont sous-tendus par des régions neurales distinctes: le chemin délibératif, correspondant aux fonctions exécutives, implique l'activation du cortex préfrontal, tandis que le chemin émotionnel active le système limbique. Ces circuits semblent être dysfonctionnels chez les individus ayant un TDAH, et résulte, entre autres, en des capacités de prise de décision altérées. Leurs comportements impulsifs et inattentifs sont probablement la cause de ces attitudes irrationnelles face au risque. Cependant, une solution possible est de leur administrer un traitement médicamenteux, en prenant en compte les potentiels effets secondaires. Un traitement alternatif se reposant sur une réhabilitation cognitive pourrait être appropriée. Le but de ce projet est donc de déterminer si un entrainement intensif de la mémoire de travail peut avoir un effet sur la prise de décision chez des adultes ayant un TDAH et chez des contrôles sains du même âge. Nous avons conçu une tâche de prise de décision dans laquelle les participants devaient sélectionner un montant à jouer en ayant une chance sur trois de gagner quatre fois le montant choisi, alors que dans l'autre cas, ils pouvaient perdre leur investissement. Leurs performances ont été enregistrées en utilisant l'électroencéphalographie avant et après un entrainement d'un mois au Dual N-Back, et nous avons étudié les possibles effets de transfert. Dans l'ensemble, nous avons trouvé au pré-test que les performances au cours du jeu d'argent étaient modulées par les facteurs de personnalité, et par le degré des sympt^omes. Au post-test, nous avons non seulement trouvé que les adultes ayant un TDAH montraient une diminutions stable des symptômes, qui étaient évalués par le questionnaire du CAARS, mais que cette réduction était également perçue dans l'échantillon des contrôles. Les rsultats expérimentaux mesurés à l'aide de l'éléctroencéphalographie suggèrent un changement dans les cortex préfrontaux et pariétaux. Ces résultats suggèrent que la remédiation cognitive est efficace chez les adultes ayant un TDAH, mais produit aussi un effet chez les contrôles sains. Un complément important de ce travail pourrait examiner les données sur l'attention, qui pourraient renforcer l'idée qu'il n'est pas nécessaire d'utiliser des programmes complexes englobant la remédiation de plusieurs dimensions des fonctions exécutives, un simple entraiment de la mémoire de travail devrait suffire.

FOXC2 and fluid shear stress stabilize postnatal lymphatic vasculature.

Biomechanical forces, such as fluid shear stress, govern multiple aspects of endothelial cell biology. In blood vessels, disturbed flow is associated with vascular diseases, such as atherosclerosis, and promotes endothelial cell proliferation and apoptosis. Here, we identified an important role for disturbed flow in lymphatic vessels, in which it cooperates with the transcription factor FOXC2 to ensure lifelong stability of the lymphatic vasculature. In cultured lymphatic endothelial cells, FOXC2 inactivation conferred abnormal shear stress sensing, promoting junction disassembly and entry into the cell cycle. Loss of FOXC2-dependent quiescence was mediated by the Hippo pathway transcriptional coactivator TAZ and, ultimately, led to cell death. In murine models, inducible deletion of Foxc2 within the lymphatic vasculature led to cell-cell junction defects, regression of valves, and focal vascular lumen collapse, which triggered generalized lymphatic vascular dysfunction and lethality. Together, our work describes a fundamental mechanism by which FOXC2 and oscillatory shear stress maintain lymphatic endothelial cell quiescence through intercellular junction and cytoskeleton stabilization and provides an essential link between biomechanical forces and endothelial cell identity that is necessary for postnatal vessel homeostasis. As FOXC2 is mutated in lymphedema-distichiasis syndrome, our data also underscore the role of impaired mechanotransduction in the pathology of this hereditary human disease.

Using computational fluid dynamics to predict head losses in the auxiliary elements of a microirrigation sand filter

It is often assumed that total head losses in a sand filter are solely due to the filtration media and that there are analytical solutions, such as the Ergun equation, to compute them. However, total head losses are also due to auxiliary elements (inlet and outlet pipes and filter nozzles), which produce undesirable head losses because they increase energy requirements without contributing to the filtration process. In this study, ANSYS Fluent version 6.3, a commercial computational fluid dynamics (CFD) software program, was used to compute head losses in different parts of a sand filter. Six different numerical filter models of varying complexities were used to understand the hydraulic behavior of the several filter elements and their importance in total head losses. The simulation results show that 84.6% of these were caused by the sand bed and 15.4% were due to auxiliary elements (4.4% in the outlet and inlet pipes, and 11.0% in the perforated plate and nozzles). Simulation results with different models show the important role of the nozzles in the hydraulic behavior of the sand filter. The relationship between the passing area through the nozzles and the passing area through the perforated plate is an important design parameter for the reduction of total head losses. A reduced relationship caused by nozzle clogging would disproportionately increase the total head losses in the sand filter