Constant Friction Factor Research Articles

Acclimatize experimental approach to adjudicate hydraulic coefficients under different bed material configurations and slopes with and without weir

The primary purpose of this study was to evaluate the hydraulic coefficient of coarse aggregate grain size beds and hydraulic parameters under random and perpendicular bed configurations, as well as to explore the discharge coefficient for rectangular weirs. The research objectives were to compare flow resistance coefficients, evaluate the discharge coefficient for rectangular weirs, investigate the relationship between roughness coefficient and hydraulic parameters, and validate the theoretical hydraulic equation for the rectangular weir. This was achieved by analysing different bed configurations, bed slopes, and 20 and 30-mm bed materials. Sieve analysis was conducted on bed materials using American-standard sieves to determine their particle size distribution. The experiment was performed in a rectangular flume measuring 12 m in length, 0.31 m in width, and 0.45 m in depth. In a laboratory experiment, water was pumped into a flume using centrifugal pumps, and a rectangular weir was attached downstream for discharge measurement. The experiment investigated factors such as Manning roughness coefficient, bed material geometry, bed slope, and weir shapes. Approximately 1680 tests were conducted to analysed the impact of these factors on discharge and the coefficient of discharge. The average Manning's roughness coefficients for a grain size of 20 mm were 0.019 (with weir) and 0.019 (without weir) in a random bed configuration, and 0.028 (with weir) and 0.027 (without weir) in a perpendicular flow bed configuration. For a grain size of 30 mm, the coefficients were 0.023 (with weir) and 0.022 (without weir) in a random bed configuration, and 0.033 (with weir) and 0.026 (without weir) in a perpendicular flow bed configuration. The presence of a weir has affected Manning's roughness coefficients and discharge coefficients. With a weir, the roughness coefficients have generally been higher compared to without a weir, indicating increased roughness in the channel. The discharge coefficient for a rectangular weir with a grain size of 20 mm ranged from 0.39 to 0.84 (random bed) and 0.27 to 0.68 (perpendicular flow bed), while for a grain size of 30 mm it ranged from 0.31 to 0.81 (random bed) and 0.23 to 0.48 (perpendicular flow bed). The discharge coefficients have varied depending on the grain size and bed configuration, reflecting different flow efficiencies over the weir. Rough particles influenced flow and Manning's roughness coefficient value, then reduced discharge and velocity values. Under two bed configurations and slopes, beds with a grain size of 30 mm have higher roughness coefficients compared to those with a grain size of 20 mm. The models have shown that the roughness coefficient is inversely proportional to the discharge and directly proportional to the tailgate water levels. The coefficient of roughness and discharge coefficient are mainly influenced by the channel slopes, bed roughness, bed grain size, and bed configuration. A randomly configured bed with a 20 mm grain size gravel bed is preferred over a perpendicular bed configuration to handle high discharges. Using a 20 mm grain-size gravel bed in open-channel flow is more suitable than a 30 mm grain-size bed. Relying on the constant friction factor, Manning's n, is not recommended as it may result in design errors. These findings have the potential to improve hydraulic engineering design practices, enhancing the accuracy and efficiency of open-channel flow systems.

Identification Algorithm for Simultaneous Leaks in a Pipeline

This work addresses the problem of simultaneous leaks’ identification in a main pipeline by assuming a constant friction factor. The solution is based on the invariance of the physical leak parameters for any operation point. By considering a quadratic function of the errors between one and two leaks in a pipeline with a steady-state behavior, a new procedure is proposed for the estimation of four parameters associated with the two leaks. In comparison with the algorithm reported in Peralta and Verde (2023), the new one simultaneously adjusts both unknown positions with their gradients. The advantages of the new algorithm are the reduction of maneuvers for obtaining satisfactory estimated parameters and the straightforward estimation of the parameters associated with the orifices through direct nonlinear functions. The results with synthetic data show a considerable improvement regarding the estimation previously reported.

Overall Pressure Loss and Heat Transfer Performance of Additively Manufactured Offset Strip Fins Used in Compact Heat Exchangers

Abstract Preliminary heat exchanger design relies heavily on correlations for overall heat transfer and pressure drop performance, particularly for heat transfer augmentation features such as fins. Extensive work has been performed by the research community to develop these correlations for the numerous designs. However, with the new technology of metal additive manufacturing and the resultant surface roughness, the traditional correlations and design considerations related to performance need to be adjusted. As a result, two metal additively manufactured offset strip fin heat exchanger geometries with different fin spacing are studied for heat transfer and pressure drop performance and compared with traditional correlations. Deviations between the additively manufactured geometries and previous correlations for smooth fins are found and are further amplified as the surface roughness-to-hydraulic diameter ratio is increased. Furthermore, the surface roughness from the additive process results in a constant friction factor behavior at high Reynolds numbers, which is unlike behavior observed for conventionally manufactured fins. Considerations for both the laminar and turbulent flow regimes are needed for correct performance prediction. A final offset strip fin geometry with a change in the fin spacing every third of the way through the flow path is tested. This study found that the orientation of fin spacing, wider spaced to tightly spaced or tightly spaced to wider spaced, did not have a significant effect on pressure drop or heat transfer. However, the study found a method for predicting the performance which will become important as additive manufacturing increases the complexity of heat exchanger designs.

Numerical investigations on the difference between aiding and opposing flows in the developing regime of laminar mixed convection in vertical tubes

The present article discusses the numerical simulation results of laminar mixed convection flow in vertical tubes. A comparative analysis of the thermal and hydrodynamic features of both buoyancy-assisted and opposed flows was performed for Reynolds number (), Grashof number () and Richardson number () with uniform heat flux boundary condition. 2-D axisymmetric steady state simulations were carried out for a length-to-diameter () ratio of with water as the working fluid. Numerical simulations were performed by employing SIMPLE scheme for pressure–velocity coupling in momentum equations and second order UPWIND scheme for solving energy equations. In case of assisting flow (), at fully developed state the centerline velocity decreases, and velocity is increased near the tube wall due to heat flux induced free convection. With increasing heat flux, the decrement in centerline velocity compared to the no-heat flux condition increases. Further, with increasing heat flux, the increase in friction factor and Nusselt number was observed. Therefore, at the same the variation of heat flux led to unique velocity profiles and temperature gradients. The variation of centerline velocity and temperature in developing region was also studied. While centerline temperature was monotonically increasing with length, the centerline velocity increased up to a maximum in the developing region and then attained the steady state at a lower value in the fully developed state. Subsequently we studied the dependence of on the hydrodynamic and thermal features. For constant friction factor and Nusselt number was observed to increase with increase in from 0.1 to 1.5 range. At fixed variation of heat flux leads to variation of or Hence, the buoyancy effect has a significant role in the entrance length development. The hydrodynamic entry length after an initial increase, attained an almost constant value with increasing On the other hand, the thermal entry length exhibited a decreasing trend with increasing Similarly, at constant Nusselt number increased with increasing for a range of 100–1000. It was evident that for a given and the heat transfer in the developing flow is always higher as that of the fully developed flow. Contrasting observations were observed for buoyancy-opposed flow. Velocity is accelerated at the center as compared to the tube wall in case of opposing flow for same and For a fixed the friction factor and Nusselt number decreased with increasing the Both the hydrodynamic and thermal entry length increases for opposing flows. Finally, we have developed correlations for fully developed friction factor () with as well as and Nusselt number () with for buoyancy-assisting and buoyancy-opposing flows. Two independent correlations are also produced for with Graetz number () for developing and fully developed regimes in both assisting as well as opposing flows.

Derivation of the Coefficients in the Coulomb Constant Shear Friction Law from Experimental Data on the Extrusion of a Material into V-Shaped Channels with Different Convergence Angles: New Method and Algorithm

The combined Coulomb constant shear friction law is widely used in commercial and research software for the finite-element analysis (FEA) of metalworking and is naturally more flexible and hence, more relevant to real-life manufacturing than the individual Coulomb and constant shear friction laws. In this work, a new mathematical model of coefficients in the Coulomb constant shear friction law for extruding a metal through narrow V-shaped channels with small convergence angles has been developed and evaluated and compared with laboratory measurements. The extrusion of the model material (lead) through narrow V-shaped channels with small convergence angles varying from 0 to 3.5 degrees has been studied. The Coulomb friction coefficient µ and the constant friction factor m appear to be independent of the dimension ratio and are influenced mostly by roughness and range from µ = 0.363 (with lubricant) to µ = 0.488 (without lubricant) and from m = 0.726 (with lubricant) to 0.99 (without lubricant). The relative length dominated by the Coulomb friction law is less than 1%, and the Coulomb’s coefficient of friction can be approximated as ½ the constant shear friction factor for all tested cases. The developed method and algorithm can be used in both FEA of manufacturing processes and efficiency tests for lubricants used in metalworking.

Drainage of an ice-dammed lake through a supraglacial stream: hydraulics and thermodynamics

Abstract. The glacier-dammed Lac des Faverges, located on Glacier de la Plaine Morte (Swiss Alps), has drained annually as a glacier lake outburst flood since 2011. In 2018, the lake volume reached more than 2 × 106 m3, and the resulting flood caused damage to the infrastructure downstream. In 2019, a supraglacial channel was dug to artificially initiate a surface lake drainage, thus limiting the lake water volume and the corresponding hazard. The peak in lake discharge was successfully reduced by over 90 % compared to 2018. We conducted extensive field measurements of the lake-channel system during the 48 d drainage event of 2019 to characterize its hydraulics and thermodynamics. The derived Darcy–Weisbach friction factor, which characterizes the water flow resistance in the channel, ranges from 0.17 to 0.48. This broad range emphasizes the factor's variability and questions the choice of a constant friction factor in glacio-hydrological models. For the Nusselt number, which relates the channel-wall melt to the water temperature, we show that the classic, empirical Dittus–Boelter equation with the standard coefficients does not adequately represent our measurements, and we propose a suitable pair of coefficients to fit our observations. This hints at the need to continue research into how heat transfer at the ice–water interface is described in the context of glacial hydraulics.

Process design and finite element analysis of multi-station two-roller cassette hot rolling for aluminum alloy 6061 wire

In this paper, a round-oval-round roller cassette wire rolling process of the aluminum alloy 6061 was studied for the process and the roller design evaluation. The elliptic groove of roller was designed for the stand of oval cross-sectional profiles. The billet diameter for this 10- stand rolling process simulation is 20mm. The diameters for the round cross-section profile stands are 16mm,12.8mm,10.2mm,8.2mm, and 6mm, respectively. The forming conditions for the CAE simulation is 400 °C for billet temperature, 0.45 for the constant shear friction factor, 20mm/s for the initial rolling speed. The CAE (Computer Aided Engineering, CAE) results had shown the maximum dimension deviation of the billet is less than 0.25 mm at the location of the roller gap and almost perfect match at the other locations. The maximum principal stress distribution on the cross section had shown a two third area was deformed under the rolling process. The CAE results had demonstrated the proposed process and die design was able to make the smaller wire with good geometrical accuracy without breaking the wire during the rolling process because of the more uniform stress distribution at the cross section of wire.

Upper-Bound Analysis for Equal Channel Angular Pressing (ECAP) with an Intersecting Channel Angle of 120°

Abstract The exact calculations of the stress and strain distributions based on the controlling equations for a forming process with large deformation are often difficult. To circumvent such difficulties, some analytical methods such upper-bound analysis and slip-line field theory have been established by making a number of simplifying assumptions regarding the material properties and deformation modes. In this work an analytical model based on the upper-bound theory was successfully developed to predict material flow pattern and maximum process loads for an Equal Channel Angular Pressing (ECAP) die with circular cross-section and an intersecting channel angle of 120°. Based on the model, the power dissipated on all frictional and velocity discontinuity surfaces were determined and optimized in order predict the maximum process force as function of the channel geometry and the material plastic behavior. To validate the developed model, the ECAP die were produced and used to determine experimental load-displacement curves of AA6061-T6 specimens with different lengths. A good correlation between theoretical and experimental results was observed. In addition, the constant friction factor demonstrated to have a strong effect on the relative extrusion pressure.

On the Friction Conditions in FEM Simulations of Cold Extrusion

Friction is a very important issue for calculating the punch force and energy consumption in cold extrusion. FEM simulations are commonly used to investigate this process, but the choice of the friction’s model and set-up parameter have influence on the results. In this work FEM simulations of cold forward extrusion of rods were performed using the commercial code DEFORMTM in axisymmetric 2D deformation mode with Lagrangian formulation considering Tresca’s friction model and two parameters as set-up: constant friction factor m or constant frictional shear stress τ. Over the deformation stages of the process, the influence of the friction parameters on the simulated force-displacement curves was analyzed. In addition, metal flow prediction and the profile of the actual frictional stress at the billet-container interface were studied. For the investigated tooling geometry and dimensions, it was found that for low levels of friction (m ≤ 0.1), both parameters can be suitably used to study the forming process, since they provided similar force-displacement curves and metal flow prediction. For higher levels of friction, the use of □ as input provided most stable and reliable results, since in this case, the simulated force-displacement curves agreed very well with experimental result, the effective frictional stresses values were more constant, and the relative frictional stresses resulted closest to the input value.

Friction Correction of Austenite Flow Stress Curves Determined under Axisymmetric Compression Conditions

The experimental flow stress curves of structural steels obtained from axisymmetric compression tests conducted under hot-working conditions very often include the frictional effects present at the tool/specimen interface. Such effects have a significant influence on the flow stress and therefore, should be corrected prior to any quantitative analysis aimed at determining the constitutive description of these materials. Commonly, such a correction is carried out by assuming a constant friction coefficient (μ) or friction factor (m) independent of deformation conditions, which is an unrealistic approach. The present investigation analyzes experimentally the frictional effects that occur when steel is deformed under axisymmetric compression conditions in the temperature range of 850 to 1200 °C at a strain rate of 0.1 s−1 and applied effective strains of 1, employing cylindrical samples with an initial diameter to initial height ratio (d0/h0) in the range of 0.5 to 2. Finite element modeling (FEM), as well as element-free Galerkin modeling (EFGM), have been employed for the analysis and prediction of the von Mises stress distribution, barreling and amount of metal folding undergone by the compression specimens. It has been shown that the increase in flow stress due to frictional effects can be corrected on the basis of either μ or m, by assuming that these parameters vary in the course of plastic deformation and are strongly dependent on deformation temperature. A novel procedure for the systematic correction of the flow stress curves, taking into consideration the changes in friction conditions during plastic deformation, has been proposed.

Compressible Fanno flows in micro-channels: An enhanced quasi-2D numerical model for laminar flows

Micro-scale fluid systems are becoming common in many applications ranging from electronic cooling to refrigeration systems and more. One-dimensional numerical models represent a simple and fast tool for the design of such devices, yet they struggle to accurately predict the flow characteristics in compressible micro-flows. Under the adiabatic assumption, the elegant theory developed by Fanno allows models for the viscous compressible flow in constant cross-section channels to be easily built. Although reasonably accurate, these models suffer from drawbacks inherent to their being one-dimensional, as such they cannot take into account the local profiles of quantities like the velocity and the temperature. In cascade, this results into incorrect evaluations of other dependent quantities, such as the dynamic pressure and the fluid thermophysical properties. The mismatch turns large when the fluid compressibility becomes important. As the Mach number grows, the velocity profile changes, and so the friction factor, even though a reliable model for predicting this change is still missing. In fact, a constant friction factor throughout the channel is generally assumed, following the incompressible flow theory. Here, a set of correlations is proposed improving the 1D theory accuracy by taking into account the effects of the non-uniform velocity and temperature profiles in a quasi-2D fashion. A detailed analysis of the velocity profiles at different Mach numbers coming from a large set of CFD simulations results in a model for assessing the impact of compressibility on friction and other quantities. The numerical model proposed, being able to properly account for the compressibility effects, offers an improved tool for the design of micro-scale fluid systems. Extending the analysis to include heat transfer is not difficult as the effect of heat flux will be analogous to the effect of pressure drop due to friction.

Advancing mechanics of Barrelling Compression Test

Compression Test (CT) plays a fundamental role in our understanding of materials science and engineering. This is due to the test's capacity to physically simulate different deformation scenarios. Mechanics of CT is critical to model stored energy, microstructure and behaviours in a deforming material. To simulate “shear and heterogeneous” deformation, friction, constitutive behaviour, etc., new closed form solutions of CT are needed. Developing detailed solutions for the test is a fundamental priority to represent the deformation more reliably.Expressions for effective strain and the test sample's free surface were derived here to extend “Avitzur's solution” beyond a limit analysis. The extended Avitzur (EA) solution was employed in a “constant friction factor mode” to make it more comparable with other reference solutions such as the Cylindrical Profile Model (CPM) and the Finite Element (FE). Example EA and CPM solutions were obtained and compared to those of a FE model. Partial enforcement of incompressibility and a rough estimation of barrelling parameter in Avitzur solution were found to be responsible for unrealistic prediction of the sample's profile and friction factor. EA's effective strain and strain rate along the sample's centre line, particularly at its centre, agreed well with the FE predictions. Therefore, the sample centre was suggested as the representative point at which the deformation path can be traced for the constitutive modelling using EA solution.

Experimental Investigation of the Dynamics of Laboratory Simple Surge Tank

The surge tank is one of important control devices inreducing water Hummer effect on distributed network pipingsystem and hydropower stations. An experimental study wasconducted into a simple surge tank of 0.044 m in a diameterwith upstream constant head reservoir of a height, 0.881 mand a water transporting pipe of a size 0.0202 m.Results indicate that rapid closure of a downstream valvecauses under-damped stable oscillation in a surge tank.Experimental response agreed well with theoretical resultswhen friction factor is considered to be variable, but with 85% increases in settle time and more oscillations when constantfriction factor is recognized at initial value before valveclosure. Doubling surge tank area does not improve thedynamics properties; otherwise, Thoma area must be avoidedfor small sizes. Comsol multiphysics software 3.5 is used todeal with the dynamics of the surge tank numerically.

Numerical investigation of the pressure-time method

The pressure-time method is a discharge measurement technique commonly used to estimate the flow rate in hydro-power plants to assess the turbine hydraulic efficiency. In this paper two-dimensional Reynolds-averaged Navier-Stokes equations with the low-Reynolds k-ω SST turbulence model are used to model and evaluate the pressure-time method. The flow rate decrease is modeled by valve closure and use of the dynamic mesh technique. The results are compared with experimental data showing the close trend. Moreover, the affecting parameters in the pressure-time method including compressibility, calculation of the losses and finding the upper time limit of integration of the pressure-time diagram are studied in detail. Furthermore, the flow characteristics with both compressible and incompressible assumptions are investigated. The obtained results demonstrated the compressibility effect even before the complete valve closure. The physics of the flow, in the closed conduit in the pressure-time method, before the complete valve closure is studied based on the time variation of the wall shear stress and the γ parameter. The γ parameter represents the difference between the turbulence structure in a transient accelerating or decelerating flow and the one in the quasi-steady condition. It is demonstrated that for the pressure-time method, some part of the flow decrease excursion can be characterized as quasi-steady and the rest is unsteady. The dominance of inertia and turbulence dynamics is investigated to evaluate the wall shear stress in the part of the excursion with the unsteady assumption. It is found that the inertia has a dominant effect during the excursion. The flow rate is calculated by evaluating all the terms of losses, e.g., wall shear stress, normal stresses, Reynolds stresses and density variation. Based on the relative magnitude of each term the results indicate that the wall shear stress is a good approximation of the losses for the flow rate calculation and the other terms can be neglected. Due to the primary role of losses in the flow rate calculation other methods in losses calculation are also considered for comparison (e.g., quasi-steady friction or constant friction factor). The available methods to find the upper time limit of the flow rate approximation integral still have significant errors. The flow rate reduction is calculated at each time step before complete valve closure using CFD methods.

Modeling study of three-phase low liquid loading flow in horizontal pipes

A theoretical study is conducted to model the flow characteristics of three-phase stratified wavy flow in horizontal pipelines with a focus on the low liquid loading condition, which is commonly observed in wet gas pipelines. The model predictions are compared to the experimental data of Karami et al. (2016a, b). These experiments were conducted with water or 51 wt% of MEG in the aqueous phase, and inlet aqueous phase fraction values from 0 to100%.Modeling of three-phase flow can be described as a combination of two-phase gas-liquid flow modeling, and a liquid phase oil-water mixing modeling. A mechanistic model is proposed to predict flow characteristics of three-phase stratified wavy flow in pipeline. For the gas-liquid interactions, Watson's (1989) combined momentum balance equation derivation was applied. However, the calculation procedure was reversed, and the wave celerity was assumed as an input, while interfacial friction factor was one of the model's outputs. The liquid-liquid interactions were modeled using a simple energy balance equation and shift in liquid phase center of gravity calculations. The liquid phases can be separated, partially mixed, or fully mixed. The bottom aqueous film velocity was calculated using the law of the wall formulation, and was used to calculate the flowing aqueous phase fraction.The model predictions of different flow characteristics for two and/or three-phase flows were compared with available experimental data. The pressure gradient, wave amplitude, and aqueous phase fraction predictions were in good agreement with the experimental data. However, the liquid holdup predictions were slightly under-predicted by the model. Overall, an acceptable agreement was observed for all cases.Most of the common multiphase stratified flow models are developed with the assumption of steady-state conditions and with constant interfacial friction factor value. This study proposes a novel method to model stratified flow. The predictions are in acceptable agreement with experimental data conducted under stratified wavy flow pattern conditions.

Numerical solutions of metal plastic flow in compression tests with sinusoidal profile of die roughness

During metal bulk-forming in microscale the so-called size effect, making changes in the material deformation process should be taken into account. One of the factors having a significant influence on the flow mechanics is a die roughness. Paper contains results of numerical analysis of the cylindrical sample compression between anvils with sinusoidal profile of roughness and with zero friction factor at the tool-workpiece interface in dry conditions. Two models of dies were used: parallel and conical one. Obtained data were compared to analogous, conventional models of compression tests with flat dies and with constant friction factor – equivalent to sinusoidal wave. Sinusoidal curve modeling the die roughness was determined from the surface roughness profile and using the motifs method. Presented analysis revealed increase in value and in variability of stress and strain in layers flowing in the vicinity of the wave – size effect. No impact of the wave presence on the compression forces values was obtained. DOI: http://dx.doi.org/10.5755/j01.mech.22.6.13574

Determination of Actual Friction Factors in Metal Forming under Heavy Loaded Regimes Combining Experimental and Numerical Analysis.

Tribological conditions can change drastically during heavy loaded regimes as experienced in metal forming; this is especially critical when lubrication can only be applied at the early stage of the process because the homogeneous lubricant layer can break along the die-workpiece interface. In these cases, adopting a constant friction factor for the lubricant-surface pair may not be a valid assumption. This paper presents a procedure based on the use of dual friction factor maps to determine friction factors employed in heavy loaded regimes. A finite element (FE) simulation is used to obtain the friction factor map for the alloy UNS A96082. Experiments were conducted using four lubricants (aluminum anti-size, MoS2 grease, silicone oil, and copper paste) to determine the actual friction curves. The experimental procedure is based on the application of lubricant only at the beginning of the first stage of ring compression, and not at intermediate stages as is usual in typical ring compression tests (RCTs). The results show that for small reductions (rh < 20%), the conventional RCT can be applied because the tribological conditions remain similar. For large reductions (rh > 20%), it is recommended to obtain an average value of the friction factor for every lubricant-surface pair in the range of deformation considered.

Influence of rock mechanical properties and rake angle on the formation of rock fragments during cutting operation

Mechanical rock cutting is a process encountered in different engineering applications including rock excavation, mining, and deep oil well drilling. Rock mechanical properties vary with depth in the subsurface and also at different geographical locations due to different environmental conditions. Understanding of fragmentation mechanisms in specific rock materials allows the determination of optimum cutting parameters that improve cutting efficiency and increase tool life during cutting operations. In the present investigation, numerical models that accurately predict the rock fragmentation and stress profiles in the rock slab during cutting were developed using the explicit finite element method (FEM). In the numerical method, a damage material model was utilized to capture the rock fragmentation process when a rigid cutter of different rake angles was displaced at different velocities against a stationary rock slab for a cutting depth of 1 mm. Rock slabs with significantly different mechanical properties were incorporated in the material model, and a constant friction factor is utilized in the contact model. The variation of cutting forces and stresses and the size and morphology of rock fragmentation were analyzed. The simulation results indicated that the explicit FEM is a powerful tool for simulating rock cutting as the formation of discontinuous rock fragments were distinctly observed at different cutting conditions. The rock mechanical properties and tool rake angle were found to have the most significant effect on the rock fragmentation during cutting operations. The cutting forces were also influenced by mechanical properties of the rock and tool rake angle. The experimental and numerical results obtained in the literature found a good agreement with the current numerical predictions.

An analytical approach for simple shear extrusion process with a linear die profile

Abstract In the present work, for the first time, an analytical approach based on upper-bound theorem is proposed to analyze the simple shear extrusion process. In this regard new die parameter named maximum inclination angle is introduced. By this model, the power dissipated on all frictional and velocity discontinuity surfaces is determined and the total power is optimized for two types of die, fixed and movable inlet channel die. To check the validation of the upper-bound model, the process is simulated by the commercial finite element code, Deform-3D. To compare the theoretical results with experiments, a fixed inlet channel die and two dies with movable inlet channel are used to determine the processing force for different cross sections. The developed model predicts that the relative extrusion pressure increases with increasing the constant friction factor; also, for a given value of the constant friction factor and the maximum distortion angle, there is an optimized maximum inclination angle which minimizes the power. Comparing the fixed inlet channel die with the movable inlet channel one, it is seen that the optimized maximum inclination angle is higher in the FIC die.

Design of Zero Slope Microirrigation Laterals: Effect of the Friction Factor Variation

AbstractMicroirrigation has become quite a common practice in agricultural production in various parts of the world. To achieve the optimum (hydraulic and economic) system performance, designers are often faced with the problem of designing a maximum lateral length which results in a desired coefficient of uniformity (CU) or an allowable pressure head variation (δH). Previous theoretical design approaches are usually based on a constant Darcy–Weisbach (DW) friction factor along the lateral and this assumption can lead to substantial errors. In the research reported in this paper, a new analytical design approach does not require the constant DW assumption for zero-slope laterals while it still takes into account the emitter exponent and the effect of minor friction losses caused by emitters. Assuming a constant friction factor along the lateral might result in errors up to 14% in the calculation of the maximum lateral length. Conversely, the maximum relative error caused by the application of the proposed...