The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor . To date, the captured flow friction factor can be extracted from the logarithmic form analytically only in the term of the Lambert -function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert -function also known as the Wright -function. The Wright -function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term of the Lambert -function to the series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert -function is identical to the original expression in term of accuracy, a further evaluation of the Lambert -function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contains only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with the relative error of no more than 0.0096%. The presented approximations are in the form suitable for everyday engineering use, they are both accurate and computationally efficient.

To achieve rapid post-earthquake repair of self-centering ribbed floor flat beam frame structures, a ductile hybrid joint consisting of dog bone weakened energy dissipating steel bars connected to the upper and lower column sections through high-strength threads based on the damage control design concept is proposed. By moving the ductile energy dissipating zone out to the locally weakened section of the energy dissipating steel bars and the locally unbonded prestressed steel bars in the core area, the residual deformation was limited and the seismic performance was improved. Based on the working principle of hybrid joints, low cycle loading tests were conducted on two joint specimens to analyze the influence of lateral prestress on the seismic performance of the hybrid joints. Numerical modeling methods were used to compare the position of the energy-consuming steel bars in the composite layer and the friction performance of joints. The research results indicated that the hybrid joint had stable load-bearing, deformation, and energy dissipation capabilities, with damage primarily concentrated on the energy-consuming steel bars. Even at an inter-story displacement angle of 5.5%, the upper and lower column segments remained elastic. After unloading, the connection seam at the joint was closed, and the self-centering performance was good. When the inter-story displacement angle reached 5.5%, the lateral prestress increased from 150 kN to 250 kN, the ultimate bearing capacity of the joint increased by 16.3%, and the cumulative energy consumption increased by 30.0%. The influence of the friction coefficient of the joint surface on the structural performance was set at a threshold of 0.7. When it was less than the threshold, the ultimate bearing capacity and initial stiffness of the joint increased with an increase in the friction coefficient. After reaching the threshold, the increase in the ultimate bearing capacity of the joint slowed down, and the rate of stiffness degradation gradually accelerated. This joint had excellent seismic performance and can also achieve post-earthquake repair of structures.

Employing numerical methods to simulate manufacturing processes and study their influential factors is increasing. The development of computers and engineering software has increased the ability and accuracy of numerical methods in simulating various aspects of different processes. One of the manufacturing processes that has been considered by many industries in recent years to join metals in solid-state with unique properties is called friction stir welding. It is challenging and, in some cases, impossible to experimentally study the various aspects of this process, such as temperature distribution, stress distribution, and material flow, due to severe plastic deformation in the weld zone. In this case, numerical methods are used to investigate these parameters and better understand the process. This study first investigates various numerical methods researchers use to simulate the process. The ability, pros, and cons of these methods to simulate the process are also examined. Then, the applications of numerical models in simulating the temperature distribution during the process as well as the effects of input parameters on the temperature history of the process, are deeply considered. Next, the application of numerical methods in material flow modeling during the process is investigated. Finally, the modeling of the microstructure of the welding zone is investigated using numerical methods that help significantly in predicting the weld microstructure.

In this study, an investigation on the influence of In-situ tribo-oxide-layer on non-lubricated tribological behaviours of LM27/SiCp composites was carried out at different applied loads. The variations in wear performance and microstructure of brake lining friction material (LM27) with the addition of different amounts and sizes of SiCp are explored. For this purpose, LM27/SiCp composite materials were manufactured by stir casting route varying the amount of particle reinforced from 3wt.% to 12wt.% with a different size range (fine: 1-20µm and coarse: 106-125µm). Non-lubricated dry wear tests of LM27/SiCp composites samples were trialled at different loads from 9.8N to 49N by using a pin-on-disc machine system. At a contact pressure of 0.2-1 MPa, LM27/SiCp composites with 12wt.% reinforcement showed a lower coefficient of friction than other composites. In-situ formation of oxide layers on the contact region of the specimen supports the self-lubrication during the wear test, which is responsible for better wear performance of LM27/SiCp composites. However, these study portraits that composite with 12wt. % fine size SiCp exhibits better wear performance in comparison to the other developed composites.

Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction. The presented approximations are based on the asymptotic series expansion of the Wright ω-function and symbolic regression. The results are verified with 8 million of Quasi-Monte Carlo points covering the domain of interest for engineers. In comparison with the built-in “wrightOmega” feature of Matlab R2016a, the herein introduced related approximations of the Wright ω-function significantly accelerate the computation. With only two logarithms and several basic arithmetic operations used, the presented approximations are not only computationally efficient but also extremely accurate. The maximal relative error of the most promising approximation which is given in the form suitable for engineers’ use is limited to 0.0012%, while for a little bit more complex variant is limited to 0.000024%.

The occurrence rate of occupational accidents caused by slipping and falling is 50% worldwide. Determining the slip safety risk is necessary to minimize the accidents caused by slipping in pedestrian walking areas. By on-site testing, this study aims to determine the slip risks of floor coverings used in walking areas with many pedestrians in public service buildings (PSB). For this purpose, on-site measurements were performed in two environments and six locations in PSB using portable GMG 200 and pendulum testers operating according to DIN 51131 and TS EN 14231 standards. These tests were performed on four-floor coverings with polished surface treatment in PSB. Since the floor coverings measured have a polished surface, it can be seen that the dynamic friction coefficients (DCOF) values are very low, and the slip risks are high. By statistically analyzing the slip test data using the K-means method, a new safety classification was made according to the usage areas of floor coverings. To minimize the risk of slip safety, especially for students, patients, and employees in PSB, it is recommended to use floor coverings with high DCOF values and low slip risk.

Environment approachable products such as fuels and lubricants are among the best choices in several countries that contain renewable products as alternatives. To protect human life, alternative methods of saving the environment and production balance is needed to reduce the effects of the crisis and the contamination of the Environment. This research concentrated on the Manufacturing and testing of bio- grease from sugar cane filter mud vegetable oil as a lubricant for friction reduction and determining the properties of both bio grease and Mineral oil grease with environmental problems. SC filter mud oil as an alternative use for bio-grease preparation in addition to mineral oil grease. The Testing was accepted to determine the quality of the eco-friendly grease produced. For the preparation of this bio- grease, the SC Filter cake sample is taken from different sugar factory which found in Ethiopia. The sample has a moisture content of 78%. Using this sample first oil is extracted by Soxhlet apparatus, n-hexane solvent and temperature for extraction from 42 -68℃. The maximum temperature and time for extraction of oil were 68 and 7hrs respectively. The extracted oil's physical properties include color, acid value, specific graphite, saponification value, iodine value, density, and viscosity. Finally, the friction behavior in function of time for both grease at identical load, the friction coefficient vs time for SC filter Cake Grease_ Na_ MoS2 and industrial mineral one (I_ Greasily _ MoS2), grease was determined.

The efficiency of cold sheet and strip rolling of steels and non-ferrous metals in the main depends on the quality of the technological lubricant and its cost. In this regard, it is important to develop new compositions of effective metal-working coolants (MWC) having low cost and providing the maximum reduction in the friction coefficient. We developed and tested the new compositions of the MWC on basis of chicken fat, and mono- and diglycerides and their esters of boric acid synthesized from the wastes of sunflower oil production. The MWC were tested in DSEA on laboratory rolling mill 100x100 with a roll diameter of 260 mm during steel 08Kp rolling. The efficiency of the coolants was determined by the factor of metal stretch forming λ and the coefficient of friction μ in the deformation zone which was found by forward slip method. We found the metal-working coolant with 100 % concentration of boric acid esters of mono- and diglycerides is the most effective in steel rolling. Thus the new MWC on basis of boric acid esters of mono- and diglycerides synthesized from the wastes of sunflower oil production can be recommended for use in rolling of structural steels on account of availability, high efficiency, and a low cost.

This paper presents results on tribological characteristics for polymer blends made of polybutylene terephthalate (PBT) and polytetrafluoroethylene (PTFE). This blend is relatively new in research as PBT has restricted processability because of its processing temperature near the degradation one. Tests were done block-on-ring tribotester, in dry regime, the variables being the PTFE concentration (0%, 5%, 10% and 15%wt) and the sliding regime parameters (load: 1 N, 2.5 N and 5 N, the sliding speed: 0.25 m/s, 0.5 m/s and 0.75 m/s, and the sliding distance: 2500 m, 5000 m and 7500 m). Results are encouraging as PBT as neat polymer has very good tribological characteristics in terms of friction coefficient and wear rate. SEM investigation reveals a quite uniform dispersion of PTFE drops in the PBT matrix.

The annual demand for fibres continues to rise worldwide. Consequently, more and more fibres must be produced to meet this demand, most of which are melt-spun polymeric man-made fibres. [1] Smooth filaments made of polymers are mainly used for technical applications in industry. For use in clothing or home textiles, for example, a texturing process is used to give the filaments a crimp and thus a feel like that of natural fibres. In this state, they can be processed together with natural fibres and used in textiles. Partially oriented yarns (POY) are of great importance in tex-turing. The yarns are mainly crimped with the help of the so-called false-twist texturing process (FTTP). [2] Since POY accounts for about 60 % of the melt-spun filament yarn produced world-wide, the FTTP is the most important texturing process in the textile industry [3]. In this paper, the main components of false-twist texturing (FTT) machines are explained along with the state of the art and research for each component and its influence on the process. Relevant patents are dis-cussed as well as process optimisation techniques, innovative polymers and yarn types recently used in FTT, followed by a conclusion and an outlook for the process.

The loads generated inside agricultural silos under static and dynamic conditions depend on the mechanical properties of the materials stored inside them. The silo calculation methodologies are based on these mechanical properties. Although it is known that moisture content greatly influences the values reached by these mechanical properties, just few studies have been conducted to determine them. The present work determines the angle of internal friction, the apparent cohesion, the dilatancy angle and the apparent specific weight of wheat when subjected to different moisture contents. Direct shear and oedometer assay devices were used. In addition, a climatic chamber was used to moisten the wheat samples used in this work. The moisture content applied to the samples ranged from 7.5% to 15.5%. From the different assays carried out it could be observed that the values of the angle of internal friction and apparent cohesion obtained from direct shear assays, as well as those related to the apparent specific weight obtained from oedometer assays were like those found in the literature. The apparent specific weight increased as moisture content increased, reaching a peak value at a moisture content of 13.4%, followed by a drop at a moisture content of 15.5%. The values here provided can be used in silo load calculations involving numerical methods.

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite thin elastic plate with a circular orifice of radius lying on a rough base. In the field of motion, an exact analytical solution of a nonlinear boundary value problem for tangential stresses and transversal velocities is obtained in quadratures by the method of Laplace transformations. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance from the center of the hole and an elementary formula is given for this distance (the case of tangential forces instantly applied to the orifice boundary, and then constant in time, is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the trailing wave fronts are obtained, after which a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual deformations is established in the region .

The paper presents the measured values of tensile forces acting on transmission idlers in the upper and lower run of a conveyor belt placed on a laboratory machine designed at the Department of Machine and Industrial Design, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava). The tensile forces detected by two strain gauge load cells and recorded using DEWESoft software were used to calculate the friction coefficient which acts on the surface of the driving drum casing and the conveyor belt. The friction coefficient at the slip point, or during the slippage of the conveyor belt on the rubber or steel casing of the driving drum was determined for two states of the surfaces which are in contact. Experimental measurements on a laboratory machine determined four values of friction coefficients, for two types of drum surfaces and for two states of contact surfaces, which were compared with the recommended standard values. The measured values reached higher values in comparison with the values given by the CSN standards. The highest deviation of 273.3% is achieved using a steel wet surface, and the lowest deviation of 106.3% is achieved when using a rubber dry lining for the driving drum casing. On the presented laboratory machine, it is possible to measure tensile forces for different speeds of movement, different belt angles on the driving drum, various types of belt surfaces, different types of drum casing linings and different sizes of tension forces for the endless loop of the conveyor belt. For these characteristics of the conveyor belt, the magnitude of the friction coefficient, acting between the belt and the drum surfaces, can be determined.

A model of space-time is presented, whose origin is set before the appearance of any universe. It uses concepts of previous work, a central one being that the information about the laws of nature is stored locally everywhere in space such that all physical processes obey them. Since information storage is bound to matter or energy, space is assumed to consist of dark energy (DE), which thus assumes an importance far beyond its function as a stopgap for an energy deficit in our universe (U). The primordial state (PS) is a timeless and relatively large space of 3 dimensions described by a Wheeler DeWitt (WDW) equation, whose solution is interpreted as an arrangement of very many space quanta and possesses all the characteristics of the time-honored concept of the unmoved mover. The comparison of WDW solutions belonging to different mass densities of the DE favors one in which the space quanta are mini black holes, and allows the space quanta to be imagined as mass points that are kept at a distance compatible with the quantum volume by the Pauli principle or something equivalent. Triggered by an increase in probability, the PS is followed by a time-dependent state of space expansion (ES). The concomitant emergence of time occurs in a lightning huge crash, consuming almost all DE of the PS. The subsequent expansion proceeds in quantum leaps, whose huge size emerges from a WDW equation novelly derived from the time-dependent classical expansion solution, and is also used as size of the PS. Information is assumed to be geometrically stored in arrangements of space quanta similar to how genetic information is stored in DNA molecules. During space expansion information must be transferred from already existing "information quanta" to new ones. This requires time, slows down the expansion and is taken into account by a friction term in the cosmological momentum equation. Sinc e the Friedmann-Lemaître (FL) equation remains fully valid, the model can exclusively be based on recognized equations, so that the assumptions used to build it can be understood as interpretations.

Abstract: In this study, a computational fluid dynamics (CFD) simulation was conducted to validate the CFD model with experimental data from Zimparov et.al (2012), which investigates the heat transfer performance in a spirally corrugated tube that has a twisted tape inserted. The heat transfer was then compared to a simple corrugated tube without the twisted tape and to a smooth tube with no corrugations and no twisted tape. This simulation is compared with a previous experimental study conducted by (Zimparov et al. 2012), which focuses on tubes with a height-to-diameter ratio e/Di > 0.04 and small relative pitches of the twisted tape, H/Di. The largest improvement was noticed in the tube with e/Di= 0.057 and ridge pitch-to-height ratio p/e=6.77 with a twisted tape of H/Di= 4.7. This tube is labeled 5035. Tube 5035 was found to have the most significant enhancement, hence the focus of the CFD simulation will be on this tube, and the simulation will range for Reynolds numbers, 3.5 x 103 < Re < 5.0 x 104. The focus of this simulation is the evaluation of heat transfer and friction factors; a metric was used to obtain an empirical representation of the tube’s performance. Keywords: Spirally corrugated tube; Twisted tape; Heat transfer enhancement; Friction factor; Nusselt number; Computational fluid dynamics (CFD); Star CCM+

The tribological performance of metalwork steel tools is of vital importance in both cold and hot working processes. One solution for improving metal tool life is the application of coatings. This paper investigates the effect of CrAlSiN thin-film PVD-deposition on the tribological behaviour of tool steel K340. The sliding wear performance of the coated K340 steel is analysed in relation to both the uncoated K340 steel and a range of tool steels dedicated to hot- and cold-working, such as X155CrVMo12-1, X37CrMoV5-1, X40CrMoV5-1, 40CrMnMo7 and 90MnCrV8. The investigated tool steels were heat-treated, while K340 was subjected to thermochemical treatment and then coated with a CrAlSiN hard film (K340/CrAlSiN). The hardness, chemical composition, phase structure and microstructure of steels K340 and K340/CrAlSiN are examined. Tribological tests were conducted using the ball-on-disc tester in compliance with the ASTM G99 standard. The tests were performed under dry unidirectional sliding conditions, using an Al2O3 ball as a counterbody. The wear factor and coefficient of friction are estimated and analysed with respect to hardness and alloying composition of the materials under study. SEM observations are made to identify the sliding wear mechanisms of the analysed tool steels and PVD-coated K340 steel. In contrast to the harsh abrasive-adhesive wear mechanism observed for uncoated tool steels, the abrasive wear dominates in case of the AlCrSiN. The deposited thin film effectively prevents the K304 substrate from harsh wear severe degradation. Moreover, thanks to the deposited coating, the K304/CrAlSiN sample has a COF of 0.529 and a wear factor of K=5.68×10−7 m3 N−1 m−1, while the COF of the reference tool steels ranges from 0.702 to 0.885 and their wear factor ranges from 1.68×10−5 m3 N−1 m−1 to 3.67×10−5 m3 N−1 m−1. The CrAlSiN deposition reduces the wear of the K340 steel and improves its sliding properties, which makes it a promising method for prolonging the service life of metalwork tools.

This study presents a new form of velocity distribution in laminar liquid flow in rectangular microchannels using the eigenfunction expansion technique. Darcy friction factor and Poiseuille number are also obtained analytically. Due to the symmetry of the solutions, the effects of changing the aspect ratio from 0 to ∞ are also discussed. Using finite element method (FEM), the obtained analytical results are further compared with the 3D numerical simulations for the rectangular microchannels with different range of aspect ratio and pressure gradient, and excellent agreements were found. These findings provide additional insights in interpreting the results of the pressure-driven flows in finite aspect ratio microchannels, in which very precise comparison with the macroscale theory is crucial.

The present review paper aims at collecting and discussing the research work, numerical and experimental, carried out in the field of Fluid-Structure Interaction (FSI) in one-dimensional (1D) pressurized transient flow in the time-domain approach. Background theory and basic definitions are provided for the proper understanding of the assessed literature. A novel frame of reference is proposed for the classification of FSI models based on pipe degrees-of-freedom. Numerical research is organized according to this classification, while an extensive review on experimental research is presented by institution. Engineering applications of FSI models are described and historical accidents and post-accident analyses documented.

The eighty years old empirical Colebrook function widely used as an informal standard for hydraulic resistance relates implicitly the unknown flow friction factor , with the known Reynolds number and the known relative roughness of a pipe inner surface ; . It is based on logarithmic law in the form that captures the unknown flow friction factor in a way from which it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one -call in total for the whole procedure (expensive -calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.

This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent regimes: smooth turbulent regime, partial non-fully developed turbulent and fully developed rough turbulent regime. The formula follows the inflectional form of curves as suggested in Nikuradse’s experiment rather than monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula consists of switching functions and of the interchangeable formulas for laminar, smooth turbulent and fully rough turbulent flow. The proposed switching functions provide a smooth and a computationally cheap transition among hydraulic regimes. Thus, the here presented formulation represents a coherent hydraulic model suitable for engineering use. The model is compared to existing literature models, and shows smooth and computationally cheap transitions among hydraulic regimes.

Today, Colebrook’s equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook’s equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook’s equation and its Moody’s plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

It is known that the elastic characteristics of polyamides change with increasing temperature, in particular, the Young's modulus decreases significantly. This fact is practically not taken into account in design calculations of metal-polymer plain (MP) bearings, operating under conditions of the boundary and dry friction. The purpose of the study is the analysis of the effect of temperature on the change of the Young's modulus and, accordingly, the contact strength and triboresource according to the developed method of calculating MP bearings. MP bearings with a bushing made of polyamide PA6 reinforced with glass or carbon dispersed fibers were investi-gated. Quantitative and qualitative regularities of change of the maximum contact pressures and resource of the bearings at temperature increase under conditions of boundary and dry friction are established. The pressures in the bearing bushing made of PA6+30GF will be lower than for the bushing made of PA6+30CF. The resource of the bushing made of PA6+30CF will be significantly greater than for PA6+30GF. For thermoplastic polymers, the increase in temperature will have a useful practical effect due to the decrease in the rigidity of the polymer composites of the bearing bushing.

This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ω-function). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.

The various methods used to choose the profile shift coefficients, primarily the so-called equalizations, were based on assumed advantages without physical evidence proving them. In this paper a new calculation method is presented for determining profile shift coefficient. The procedure gives the pair of values ​​of the profile shift coefficients, in which case, under the given load, the resulting bending stress will be of the lowest possible value.

Polyvinyl Alcohol (PVA)/ Graphene Quantum Dots (GQDs) polymer nanocomposite films have been prepared, and the relationship between their structural, thermal and nanoscale morphologi-cal properties, and their photoluminescent response, has been investigated. Although according to X-ray Diffraction (XRD), Fourier-Transform Infrared Spectroscopy (FT-IR) and Differential Thermal Analysis (DTA) the incorporation of GQDs does not significantly affect the percentage crystallinity of the PVA matrix, for a range of added GQD concentrations, Atomic Force Micros-copy (AFM) showed the formation of islands with apparent crystalline morphology on the surface of the PVA/GQD films, with GQD presumably acting as a nucleating agent for island growth. The incorporation of GQD also led to the formation of characteristic surface pores with increased stiffness and frictional contrast, according to Ultrasonic Force Microscopy (UFM) and Frictional Force Microscopy (FFM) data. The photoluminescence (PL) spectra of the films were found to de-pend both on the amount of GQD incorporated and on the film morphology. For GQD loads > 1,2wt%, a GQD-related band was observed at ~ 1650 cm-1 in FT-IR, along with an increase in the PL band at lower energy. For a load of ~2wt% GQD, the surface morphology was characterized by extended cluster aggregates with lower stiffness and friction than the surrounding matrix, and the PL signal decreased.

Pavement friction plays a crucial role in ensuring the safety of road networks. Accurately assessing friction levels is vital for effective pavement maintenance and management strategies employed by state highway agencies. Traditionally, friction evaluations have been conducted on a case-by-case basis, focusing on specific road sections. However, this approach fails to provide a comprehensive assessment of friction conditions across the entire road network. This paper introduces a hybrid clustering algorithm, namely the combination of density-based spatial clustering of applications with noise (DBSCAN) and Gaussian mixture model (GMM), to perform pavement friction performance rating across a statewide road network. A large, safety-oriented dataset is first generated by integrating network friction and vehicle crash data based on the attributes contributing possibly to friction related crashes. One-, two-, and multi-dimensional clustering analyses, respectively, are then performed to rate pavement friction. The Chi-square test is further employed to validate and identify the practical ratings. It is shown that by effectively capturing the hidden, intricate patterns within the integrated, complex dataset and prioritizing friction-related safety attributes, the hybrid clustering algorithm can produce pavement friction ratings that align effectively with the current practices of the Indiana Department of Transportation (INDOT) in friction management.

The aim of the studies was to test the hydraulic pressure losses along the length, local pressure losses, absolute and relative roughness values of the pipeline walls made of modern polymer material. The article presents the results of the experimental studies of hydraulic resistance of pipelines from modern polymer materials, the method of theoretical determination of resistance coefficients in the VALTEC ISO 21003 metal polymer pipeline, the classification and method of determining the values of local hydraulic resistance coefficients of T-Junctions are given, the dependence for determining the Darcy λ hydraulic friction coefficient associated with the value of the equivalent hydraulic roughness coefficient of the inner surface of pipes and the Reynolds number. The experimental data of the hydraulic coefficient of friction Darcy λ was compared with the known theoretical relationships of A.D. Altschul, Colbrooke for smooth pipes, Colbrooke and White, an alternative to the Colbrooke-White, Offengenden equation for low-shear pipes and pipes from polymer materials with Reynolds numbers Re>10^4. Dependence of hydraulic coefficient of friction on relative equivalent roughness of pipeline walls and Reynolds number, specific energy loss per one linear meter on total flow rate in system of hydraulically short pipeline is obtained. The empirical dependence of values of coefficients of local resistance ζ=f(Q2/Q3) from a ratio of the divided expenses of Q2/Q3 of the equal-pass T-Junction α=90 the pipeline to a branch up, on pass in the direct T-Junction and division of streams at various internal pipeline diameters of VALTEC.