977 resultados para fluid model
Resumo:
Propionibacterium acnes is an important cause of orthopedic-implant-associated infections, for which the optimal treatment has not yet been determined. We investigated the activity of rifampin, alone and in combination, against planktonic and biofilm P. acnes in vitro and in a foreign-body infection model. The MIC and the minimal bactericidal concentration (MBC) were 0.007 and 4 μg/ml for rifampin, 1 and 4 μg/ml for daptomycin, 1 and 8 μg/ml for vancomycin, 1 and 2 μg/ml for levofloxacin, 0.03 and 16 μg/ml for penicillin G, 0.125 and 512 μg/ml for clindamycin, and 0.25 and 32 μg/ml for ceftriaxone. The P. acnes minimal biofilm eradication concentration (MBEC) was 16 μg/ml for rifampin; 32 μg/ml for penicillin G; 64 μg/ml for daptomycin and ceftriaxone; and ≥128 μg/ml for levofloxacin, vancomycin, and clindamycin. In the animal model, implants were infected by injection of 10⁹ CFU P. acnes in cages. Antimicrobial activity on P. acnes was investigated in the cage fluid (planktonic form) and on explanted cages (biofilm form). The cure rates were 4% for daptomycin, 17% for vancomycin, 0% for levofloxacin, and 36% for rifampin. Rifampin cured 63% of the infected cages in combination with daptomycin, 46% with vancomycin, and 25% with levofloxacin. While all tested antimicrobials showed good activity against planktonic P. acnes, for eradication of biofilms, rifampin was needed. In combination with rifampin, daptomycin showed higher cure rates than with vancomycin in this foreign-body infection model.
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Background: Glutathione (GSH) is a major redox regulator and antioxidant and is decreased in cerebrospinal fluid and prefrontal cortex of schizophrenia patients [Do et al. (2000) Eur J Neurosci 12:3721]. The genes of the key GSH-synthesizing enzyme, glutamate- cysteine ligase catalytic (GCLC) and modifier (GCLM) subunits, are associated with schizophrenia, suggesting that the deficit in GSH synthesis is of genetic origin [Gysin et al. (2007) PNAS 104:16621]. GCLM knock-out (KO) mice, which display an 80% decrease in brain GSH levels, have abnormal brain morphology and function [Do et al. (2009) Curr Opin Neurobiol 19:220]. Developmental redox deregulation by impaired GSH synthesis and environmental risk factors generating oxidative stress may have a central role in schizophrenia. Here, we used GCLM KO mice to investigate the impact of a genetically dysregulated redox system on the neurochemical profile of the developing brain. Methods: The neurochemical profile of the anterior and posterior cortical areas of male and female GCLM KO and wild-type mice was determined by in vivo 1H NMR spectroscopy on postnatal days 10, 20, 30, 60 and 90, under 1 to 1.5% isoflurane anaesthesia. Localised 1H NMR spectroscopy was performed on a 14.1 T, 26 cm VNMRS spectrometer (Varian, Magnex) using a home-built 8 mm diameter quadrature surface coil (used both for RF excitation and signal reception). Spectra were acquired using SPECIAL with TE of 2.8 ms and TR of 4 s from VOIs placed in anterior or posterior regions of the cortex [Mlynárik et al. (2006) MRM 56:965]. LCModel analysis allowed in vivo quantification of a neurochemical profile composed of 18 metabolites. Results: GCLM KO mice displayed nearly undetectable GSH levels as compared to WT mice, demonstrating their drastic redox deregulation. Depletion of GSH triggered alteration of metabolites related to its synthesis, namely increase of glycine and glutamate levels during development (P20 and P30). Concentrations of glutamine and aspartate that are produced from glutamate were also increased in GCLM KO animals relative to WT. In addition, GCLM KO mice also showed higher levels of N-acetylaspartate that originates from the acetylation of aspartate. These metabolites are particularly implicated in neurotransmission processes and in mitochondrial oxidative metabolism. Their increase may indicate impaired mitochondrial metabolism with concomitant accumulation of lactate in the adult mice (P60 and P90). In addition, the GSH depletion triggers reduction of GABA concentration in anterior cortex of the P60 mice, which is in accordance with known impairment of GABAergic interneurons in that area. Changes were generally more pronounced in males than in females at P60, which is consistent with earlier disease onset in male patients. Discussion: In conclusion, the observed metabolic alterations in the cortex of a mouse model of redox deregulation suggest impaired mitochondrial metabolism and altered neurotransmission. The results also highlight the age between P20 and P30 as a sensitive period during the development for these alterations.
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Enterococcal implant-associated infections are difficult to treat because antibiotics generally lack activity against enterococcal biofilms. We investigated fosfomycin, rifampin, and their combinations against planktonic and adherent Enterococcus faecalis (ATCC 19433) in vitro and in a foreign-body infection model. The MIC/MBClog values were 32/>512 μg/ml for fosfomycin, 4/>64 μg/ml for rifampin, 1/2 μg/ml for ampicillin, 2/>256 μg/ml for linezolid, 16/32 μg/ml for gentamicin, 1/>64 μg/ml for vancomycin, and 1/5 μg/ml for daptomycin. In time-kill studies, fosfomycin was bactericidal at 8× and 16× MIC, but regrowth of resistant strains occurred after 24 h. With the exception of gentamicin, no complete inhibition of growth-related heat production was observed with other antimicrobials on early (3 h) or mature (24 h) biofilms. In the animal model, fosfomycin alone or in combination with daptomycin reduced planktonic counts by ≈4 log10 CFU/ml below the levels before treatment. Fosfomycin cleared planktonic bacteria from 74% of cage fluids (i.e., no growth in aspirated fluid) and eradicated biofilm bacteria from 43% of cages (i.e., no growth from removed cages). In combination with gentamicin, fosfomycin cleared 77% and cured 58% of cages; in combination with vancomycin, fosfomycin cleared 33% and cured 18% of cages; in combination with daptomycin, fosfomycin cleared 75% and cured 17% of cages. Rifampin showed no activity on planktonic or adherent E. faecalis, whereas in combination with daptomycin it cured 17% and with fosfomycin it cured 25% of cages. Emergence of fosfomycin resistance was not observed in vivo. In conclusion, fosfomycin showed activity against planktonic and adherent E. faecalis. Its role against enterococcal biofilms should be further investigated, especially in combination with rifampin and/or daptomycin treatment.
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BACKGROUND: Regulatory T cells (Tregs) are key players in controlling the development of airway inflammation. However, their role in the mechanisms leading to tolerance in established allergic asthma is unclear. OBJECTIVE: To examine the role of Tregs in tolerance induction in a murine model of asthma. METHODS: Ovalbumin (OVA) sensitized asthmatic mice were depleted or not of CD25(+) T cells by anti-CD25 PC61 monoclonal antibody (mAb) before intranasal treatment (INT) with OVA, then challenged with OVA aerosol. To further evaluate the respective regulatory activity of CD4(+)CD25(+) and CD4(+)CD25(-) T cells, both T cell subsets were transferred from tolerized or non-tolerized animals to asthmatic recipients. Bronchoalveolar lavage fluid (BALF), T cell proliferation and cytokine secretion were examined. RESULTS: Intranasal treatment with OVA led to increased levels of IL-10, TGF-beta and IL-17 in lung homogenates, inhibition of eosinophil recruitment into the BALF and antigen specific T cell hyporesponsiveness. CD4(+)CD25(+)Foxp3(+) T cells were markedly upregulated in lungs and suppressed in vitro and in vivo OVA-specific T cell responses. Depletion of CD25(+) cells before OVA INT severely hampered tolerance induction as indicated by a strong recruitment of eosinophils into BALF and a vigorous T cell response to OVA upon challenge. However, the transfer of CD4(+)CD25(-) T cells not only suppressed antigen specific T cell responsiveness but also significantly reduced eosinophil recruitment as opposed to CD4(+)CD25(+) T cells. As compared with control mice, a significantly higher proportion of CD4(+)CD25(-) T cells from OVA treated mice expressed mTGF-beta. CONCLUSION: Both CD4(+)CD25(+) and CD4(+)CD25(-) T cells appear to be essential to tolerance induction. The relationship between both subsets and the mechanisms of their regulatory activity will have to be further analyzed.
Dimethylarginines, homocysteine metabolism, and cerebrospinal fluid markers for Alzheimer's disease.
Resumo:
Dimethylarginine and homocysteine metabolism are closely linked and alterations of both were observed in plasma and cerebrospinal fluid (CSF) of patients with Alzheimer's disease (AD). CSF parameters of homocysteine metabolism have recently been found to be associated with the CSF level of the AD biomarker phosphorylated tau (ptau) in AD patients. To investigate possible relationships between homocysteine and dimethylarginine metabolism and the AD CSF biomarkers ptau181 and amyloid-β 1-42 (Aβ42), we assessed parameters of homocysteine metabolism (CSF homocysteine, S-adenosylmethionine (SAM), S-adenosylhomocysteine (SAH), 5-methyltetrahydrofolate (5-MTHF)) and dimethylarginine metabolism (plasma and CSF asymmetric dimethylarginine (ADMA), symmetric dimethylarginine, L-arginine) as well as CSF Aβ42 and ptau181 in 98 controls and 51 AD patients. Multivariate linear regression analyses were performed to assess associations between the considered parameters. SAH concentrations show significant associations to CSF ADMA levels, and CSF ADMA and L-arginine to ptau181, but not to Aβ42 concentrations in AD patients. When including concentrations of homocysteine, 5-MTHF, SAM, and SAH into the analysis, CSF ADMA concentrations independently predicted ptau181 levels in AD patients but homocysteine-related metabolites were associated with ptau181 only when ADMA was removed from the analysis model. These results suggest that CSF ADMA may interact with CNS homocysteine metabolism and may contribute to neurodegeneration and accumulation of phosphorylated tau in AD. Functional and interventional studies are needed to further proof this hypothesis.
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BACKGROUND: So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. RESULTS: We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. CONCLUSION: It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.
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The activity of dalbavancin, a representative of the lipoglycopeptide antibiotics, alone and in combination with rifampicin, was investigated against meticillin-resistant Staphylococcus aureus (MRSA) in a foreign-body infection model in guinea pigs. The MIC, MBC and time-kill profile of dalbavancin were determined for MRSA ATCC 43300 in the logarithmic (MBClog) and stationary (MBCstat) growth phases. The pharmacokinetic profile of dalbavancin was determined in sterile cage fluid in guinea pigs. The activity of intraperitoneal dalbavancin (40, 60 or 80mg/kg as a single dose), rifampicin (12.5mg/kg/12h for 4 days) and their combination was assessed against planktonic and biofilm MRSA. The MIC of dalbavancin was 0.078mg/L; MBClog and MBCstat were both >128Ã- MIC. In time-kill studies, bacterial reduction of 3log10CFU/mL was achieved after 48h at â0/00¥32Ã- MIC (logarithmic growth) and at â0/00¥1Ã- MIC (stationary growth). Dalbavancin was neither synergistic nor antagonistic with rifampicin, and prevented the emergence of rifampicin resistance in vitro. The half-life of dalbavancin in cage fluid was 35.8-45.4h and the concentration remained above the MIC of MRSA during 7 days after a single dose. Dalbavancin reduced planktonic MRSA in cage fluid at high dose (60mg/kg and 80mg/kg) but failed to eradicate biofilm MRSA from cages. In combination with rifampicin, dalbavancin at 80mg/kg cured 36% of infected cages, and emergence of rifampicin resistance was completely prevented. Dalbavancin at 80mg/kg and in combination with rifampicin eradicated approximately one-third of cage-associated MRSA infections and prevented emergence of rifampicin resistance.
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Endometriosis, a leading cause of pelvic pain and infertility, is characterized by ectopic growth of endometrial-like tissue and affects approximately 176 million women worldwide. The pathophysiology involves inflammatory and angiogenic mediators as well as estrogen-mediated signaling and novel, improved therapeutics targeting these pathways are necessary. The aim of this study was to investigate mechanisms leading to the establishment and progression of endometriosis as well as the effect of local treatment with Lipoxin A4 (LXA₄), an anti-inflammatory and pro-resolving lipid mediator that we have recently characterized as an estrogen receptor agonist. LXA₄ treatment significantly reduced endometriotic lesion size and downregulated the pro-inflammatory cytokines IL-1β and IL-6, as well as the angiogenic factor VEGF. LXA₄ also inhibited COX-2 expression in both endometriotic lesions and peritoneal fluid cells, resulting in attenuated peritoneal fluid Prostaglandin E₂ (PGE₂) levels. Besides its anti-inflammatory effects, LXA₄ differentially regulated the expression and activity of the matrix remodeling enzyme matrix metalloproteinase (MMP)-9 as well as modulating transforming growth factor (TGF)-β isoform expression within endometriotic lesions and in peritoneal fluid cells. We also report for first time that LXA₄ attenuated aromatase expression, estrogen signaling and estrogen-regulated genes implicated in cellular proliferation in a mouse model of disease. These effects were observed both when LXA₄ was administered prior to disease induction and during established disease. Collectively, our findings highlight potential targets for the treatment of endometriosis and suggest a pleotropic effect of LXA₄ on disease progression, by attenuating pro-inflammatory and angiogenic mediators, matrix remodeling enzymes, estrogen metabolism and signaling, as well as downstream proliferative pathways.
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In this study, a model for the unsteady dynamic behaviour of a once-through counter flow boiler that uses an organic working fluid is presented. The boiler is a compact waste-heat boiler without a furnace and it has a preheater, a vaporiser and a superheater. The relative lengths of the boiler parts vary with the operating conditions since they are all parts of a single tube. The present research is a part of a study on the unsteady dynamics of an organic Rankine cycle power plant and it will be a part of a dynamic process model. The boiler model is presented using a selected example case that uses toluene as the process fluid and flue gas from natural gas combustion as the heat source. The dynamic behaviour of the boiler means transition from the steady initial state towards another steady state that corresponds to the changed process conditions. The solution method chosen was to find such a pressure of the process fluid that the mass of the process fluid in the boiler equals the mass calculated using the mass flows into and out of the boiler during a time step, using the finite difference method. A special method of fast calculation of the thermal properties has been used, because most of the calculation time is spent in calculating the fluid properties. The boiler was divided into elements. The values of the thermodynamic properties and mass flows were calculated in the nodes that connect the elements. Dynamic behaviour was limited to the process fluid and tube wall, and the heat source was regarded as to be steady. The elements that connect the preheater to thevaporiser and the vaporiser to the superheater were treated in a special way that takes into account a flexible change from one part to the other. The model consists of the calculation of the steady state initial distribution of the variables in the nodes, and the calculation of these nodal values in a dynamic state. The initial state of the boiler was received from a steady process model that isnot a part of the boiler model. The known boundary values that may vary during the dynamic calculation were the inlet temperature and mass flow rates of both the heat source and the process fluid. A brief examination of the oscillation around a steady state, the so-called Ledinegg instability, was done. This examination showed that the pressure drop in the boiler is a third degree polynomial of the mass flow rate, and the stability criterion is a second degree polynomial of the enthalpy change in the preheater. The numerical examination showed that oscillations did not exist in the example case. The dynamic boiler model was analysed for linear and step changes of the entering fluid temperatures and flow rates.The problem for verifying the correctness of the achieved results was that there was no possibility o compare them with measurements. This is why the only way was to determine whether the obtained results were intuitively reasonable and the results changed logically when the boundary conditions were changed. The numerical stability was checked in a test run in which there was no change in input values. The differences compared with the initial values were so small that the effects of numerical oscillations were negligible. The heat source side tests showed that the model gives results that are logical in the directions of the changes, and the order of magnitude of the timescale of changes is also as expected. The results of the tests on the process fluid side showed that the model gives reasonable results both on the temperature changes that cause small alterations in the process state and on mass flow rate changes causing very great alterations. The test runs showed that the dynamic model has no problems in calculating cases in which temperature of the entering heat source suddenly goes below that of the tube wall or the process fluid.
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PURPOSE: To characterize perifoveal intraretinal cavities observed around full-thickness macular holes (MH) using en face optical coherence tomography and to establish correlations with histology of human and primate maculae. DESIGN: Retrospective nonconsecutive observational case series. METHODS: Macular en face scans of 8 patients with MH were analyzed to quantify the areas of hyporeflective spaces, and were compared with macular flat mounts and sections from 1 normal human donor eye and 2 normal primate eyes (Macaca fascicularis). Immunohistochemistry was used to study the distribution of glutamine synthetase, expressed by Müller cells, and zonula occludens-1, a tight-junction protein. RESULTS: The mean area of hyporeflective spaces was lower in the inner nuclear layer (INL) than in the complex formed by the outer plexiform (OPL) and the Henle fiber layers (HFL): 5.0 × 10(-3) mm(2) vs 15.9 × 10(-3) mm(2), respectively (P < .0001, Kruskal-Wallis test). In the OPL and HFL, cavities were elongated with a stellate pattern, whereas in the INL they were rounded and formed vertical cylinders. Immunohistochemistry confirmed that Müller cells followed a radial distribution around the fovea in the frontal plane and a "Z-shaped" course in the axial plane, running obliquely in the OPL and HFL and vertically in the inner layers. In addition, zonula occludens-1 co-localized with Müller cells within the complex of OPL and HFL, indicating junctions in between Müller cells and cone axons. CONCLUSION: The dual profile of cavities around MHs correlates with Müller cell morphology and is consistent with the hypothesis of intra- or extracellular fluid accumulation along these cells.
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OBJECTIVES: Repair of the right ventricular outflow tract (RVOT) in paediatric cardiac surgery remains challenging due to the high reoperation rate. Intimal hyperplasia and consequent arteriosclerosis is one of the most important limitation factors for graft durability. Since local shear stress and pressure are predictive elements for intimal hyperplasia and wall degeneration, we sought to determine in an oversized 12-mm RVOT model, with computed fluid dynamics simulation, the local haemodynamical factors that may explain intimal hyperplasia. This was done with the aim of identifying the optimal degree of oversizing for a 12-mm native RVOT. METHODS: Twenty domestic pigs, with a weight of 24.6 ± 0.89 kg and a native RVOT diameter of 12 ± 1.7 mm, had valve conduits of 12, 16, 18 and 20 mm implanted. Pressure and flow were measured at 75, 100 and 125% of normal flow at RVOT at the pulmonary artery, pulmonary artery bifurcation and at the left and right pulmonary arteries. Three-dimensional computed fluid dynamics (CFD) simulation in all four geometries in all flow modalities was performed. Local shear stress and pressure conditions were investigated. RESULTS: Corresponding to 75, 100 and 125% of steady-state flow, three inlet velocity profiles were obtained, 0.2, 0.29 and 0.36 m/s, respectively. At inflow velocity profiles, low shear stress areas, ranged from 0 to 2 Pa, combined with high-pressure areas ranging from 11.5 to 12.1 mmHg that were found at distal anastomosis, at bifurcation and at the ostia of the left and right pulmonary arteries in all geometries. CONCLUSIONS: In all three oversized geometries, the local reparation of shear stress and pressure in the 16-mm model showed a similar local profile as in the native 12 mm RVOT. According to these findings, we suggest oversizing the natural 12-mm RVOT by not more than 4 mm. The elements responsible for wall degeneration and intimal hyperplasia remain very similar to the conditions present in native RVOT.
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In recent years, the emergence of Staphylococcus aureus strains with reduced susceptibility to glycopeptides has raised considerable concern. We studied the efficacy of vancomycin and teicoplanin, as well as cloxacillin and cefotaxime, against the infection caused by four S. aureus strains with different glycopeptide and β-lactam susceptibilities (strains A, B, C, and D; MICs for vancomycin of 1, 2, 4, and 8 µg/ml respectively), using a modified model of mouse peritonitis. This optimized model appeared to be straightforward and reproducible, and was able to detect low differences in bacterial killing between antibiotics and also between different S. aureus strains. Bactericidal activities in peritoneal fluid for vancomycin, teicoplanin, cloxacillin, and cefotaxime decreased from -2.98, -2.36, -3.22, and -3.57 log10 cfu/ml, respectively, in infection by strain A (MICs for vancomycin and cloxacillin of 1 and 0.38 µg/ml, respectively) to -1.22, -0.65, -1.04, and +0.24 in peritonitis due to strain D (MICs for vancomycin and cloxacillin of 8 and 1,024 µg/ml). Our data confirm the superiority of β-lactams against methicillin-susceptible S. aureus and show that bactericidal activity of glycopeptides decreases significantly with slight increases in MICs; this finding suggests a reduced efficacy of glycopeptides in the treatment of serious glycopeptide-intermediate S. aureus infections
Resumo:
In recent years, the emergence of Staphylococcus aureus strains with reduced susceptibility to glycopeptides has raised considerable concern. We studied the efficacy of vancomycin and teicoplanin, as well as cloxacillin and cefotaxime, against the infection caused by four S. aureus strains with different glycopeptide and β-lactam susceptibilities (strains A, B, C, and D; MICs for vancomycin of 1, 2, 4, and 8 µg/ml respectively), using a modified model of mouse peritonitis. This optimized model appeared to be straightforward and reproducible, and was able to detect low differences in bacterial killing between antibiotics and also between different S. aureus strains. Bactericidal activities in peritoneal fluid for vancomycin, teicoplanin, cloxacillin, and cefotaxime decreased from -2.98, -2.36, -3.22, and -3.57 log10 cfu/ml, respectively, in infection by strain A (MICs for vancomycin and cloxacillin of 1 and 0.38 µg/ml, respectively) to -1.22, -0.65, -1.04, and +0.24 in peritonitis due to strain D (MICs for vancomycin and cloxacillin of 8 and 1,024 µg/ml). Our data confirm the superiority of β-lactams against methicillin-susceptible S. aureus and show that bactericidal activity of glycopeptides decreases significantly with slight increases in MICs; this finding suggests a reduced efficacy of glycopeptides in the treatment of serious glycopeptide-intermediate S. aureus infections
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Boiling two-phase flow and the equations governing the motion of fluid in two-phase flows are discussed in this thesis. Disposition of the governing equations in three-dimensional complex geometries is considered from the perspective of the porous medium concept. The equations governing motion in two-phase flows were formulated, discretized and implemented in a subroutine for pressure-velocity solution utilizing the SIMPLE algorithm modified for two-phase flow. The subroutine was included in PORFLO, which is a three-dimensional 5-equation porous media model developed at VTT by Jaakko Miettinen. The development of two-phase flow and the resulting void fraction distribution was predicted in a geometry resembling a section of BWR fuel bundle in a couple of test cases using PORFLO.
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The aim of this work is to study flow properties at T-junction of pipe, pressure loss suffered by the flow after passing through T-junction and to study reliability of the classical engineering formulas used to find head loss for T-junction of pipes. In this we have compared our results with CFD software packages with classical formula and made an attempt to determine accuracy of the classical formulas. In this work we have studies head loss in T-junction of pipes with various inlet velocities, head loss in T-junction of pipes when the angle of the junction is slightly different from 90 degrees and T-junction with different area of cross-section of the main pipe and branch pipe. In this work we have simulated the flow at T-junction of pipe with FLUENT and Comsol Multiphysics and observed flow properties inside the T-junction and studied the head loss suffered by fluid flow after passing through the junction. We have also compared pressure (head) losses obtained by classical formulas by A. Vazsonyi and Andrew Gardel and formulas obtained by assuming T-junction as combination of other pipe components and observations obtained from software experiments. One of the purposes of this study is also to study change in pressure loss with change in angle of T-junction. Using software we can have better view of flow inside the junction and study turbulence, kinetic energy, pressure loss etc. Such simulations save a lot of time and can be performed without actually doing the experiment. There were no real life experiments made, the results obtained completely rely on accuracy of software and numerical methods used.