Theoretical Equations Research Articles

Flow features of a horseshoe tunnel bend

Previous research on bend flow has mainly focused on rectangular channels or circular conduits with small bend radii. This study investigates the dynamics of bend flow in an unexplored geometry: the horseshoe cross-section with large bend radii, a typical configuration in hydraulic tunnels. We examine two critical flow features, energy losses and superelevation, employing theoretical equations and dimensional analysis based on experimental data collected on a physical model of a diversion tunnel. The findings reveal an exponential decrease in the bend loss coefficient with increasing Reynolds numbers and shockwaves within the bend for Froude numbers exceeding 1.945. These findings are relevant in a hydraulic tunnel design with similar features and offer insights to minimize energy losses and maintain stable flow conditions.

Pull-out behavior of cluster stud-post pouring UHPC connectors in prefabricated steel-concrete composite beam

The use of ultra-high performance concrete (UHPC) as a connection material for cluster studs of prefabricated steel-concrete composite beams can achieve higher connection strength and less space for reserved holes. However, in addition to bearing the shear force, the studs need to bear the pull-out force to counteract the vertical relative separation between the steel and concrete. The pull-out behavior for cluster stud-post pouring UHPC connectors is complex and has not been clarified completely. Thus, a total of 30 cluster stud pull-out tests in 10 groups were carried out in this study, and the interface type, length-to-diameter ratio of the stud, transverse spacing of stud group, dimensions of the reserved holes, and type of post pouring concrete were considered. The results showed that the pull-out behavior of the cluster studs was different from that of studs embedded in cast-in-place intact UHPC slabs due to the UHPC conical integrity having been reduced significantly by the old-to-new concrete interface. The rough groove interface and UHPC as a post pouring material significantly improved the pull-out capacity and stiffness of the cluster studs. The stud fracture belongs to ductile failure, whereas UHPC and normal concrete (NC) cone failures are brittle. The bearing capacity of the UHPC cone is observed to increase with the effective embedment depth of the stud, the transverse spacing, and the dimensions of the reserved holes. The angle of the UHPC conical failure surface is 70° based on 3D laser scanning. Finally, the theoretical equations for predicting the pull-out capacity of stud-post pouring UHPC connectors with a rough groove interface were proposed, and the critical length-to-diameter ratio of the stud was calculated for different combinations of stud and UHPC strength.

Trajectory optimization of B-splines interpolation based on dynamic error adjustment

In this paper, we propose a motion planning algorithm based on the five-fold B-spline curve for multi-axis motion control systems with non-smooth trajectories, acceleration, plus acceleration over the limit, etc. We construct a smooth transition model for the micro-line segment G3 of the continuous five-fold B-spline curve. A derivation of the corresponding theoretical equation is given. Using the transition model, we propose an optimization method for dynamic adjustment of motion trajectory errors based on the velocity forward planning constraints by smoothing the transition after the trajectory of the micro-line segment for the forward planning velocity. Finally, the design flow for the forward planning of the velocity is given. Finally, the above algorithm is used to perform simulation experiments for the optimization algorithm. Experimental results show that the proposed optimization improves the accuracy of fitting motion trajectories under the constraints of acceleration and deceleration addition, which validates the proposed algorithm.

First ion source at ISOL@MYRRHA with an improved thermal profile - Theoretical considerations

ISOL@MYRRHA will be a new Radioactive Ion Beam (RIB) facility in Belgium based on the Isotope Separation On-Line (ISOL) technique, and established within the framework of MYRRHA, the world’s first large-scale accelerator driven system project at power levels scalable to industrial systems. The surface ion source, or hot cavity, is chosen as initial source for its reliability and simple design. To account for the higher flux of atoms through this cavity, a theoretical study of the processes within the ion source is discussed here, based on theoretical equations and thermal-electric simulations. In the past, the temperature was clearly identified as a key element to this source, but with the assumption that it remains constant throughout the cavity. Nonetheless, more recent thermal-electric simulations have revealed that the source Ohmic heating leads to temperature gradients along the cavity tube. The temperature profile impact on ionisation in the hot cavity will be reviewed here.

Study on the Damage Mechanism of Coal under Hydraulic Load

Hydraulic fracturing is extensively utilized for the prevention and control of gas outbursts and rockbursts in the deep sections of coal mines. The determination of fracturing construction parameters based on the coal seam conditions and stress environments merits further investigation. This paper constructs a damage analysis model for coal under hydraulic loads, factoring in the influence of the intermediate principal stress, grounded in the unified strength theory analysis approach. It deduces the theoretical analytical equation for the damage distribution of a coal medium subjected to small-flow-rate hydraulic fracturing in underground coal mines. Laboratory experiments yielded the mechanical parameters of coal in the study area and facilitated the fitting of the intermediate principal stress coefficient. Leveraging these datasets, the study probes into the interaction between hydraulic loads and damage radius under assorted influence ranges, porosity, far-field crustal stresses, and brittle damage coefficients. The findings underscore that hydraulic load escalates exponentially with the damage radius. Within the variable range of geological conditions in the test area, the effects of varying influence range, porosity level, far-field stress, and brittle damage coefficient on the outcomes intensify one by one; a larger hydraulic load diminishes the impact of far-field stress variations on the damage radius, inversely to the influence range, porosity, and brittle damage. The damage radius derived through the gas pressure reduction method in field applications corroborates the theoretical calculations, affirming the precision of the theoretical model. These findings render pivotal guidance for the design and efficacy assessment of small-scale hydraulic fracturing in underground coal mines.

Review of the Quantification of Aeolian Sediment Transport in Coastal Areas

Coastal dunes, formed and shaped by aeolian sediment transport, play a crucial role in ecosystem services and act as natural flood and coastal erosion defenses. This paper delves into theoretical equations and numerical models predicting sediment transport. Numerical models like cellular automata, XBeach-DUNA, the coastal dune model, and others are analyzed for their ability to simulate dune morphology, erosion processes, and vegetation impacts accurately. Evaluated are field observation and measurement techniques, such as sand traps, impact sensors, and optical sensors, for their precision in quantifying aeolian dynamics. Further examined is the effectiveness of vegetation and fencing in dune stabilization, noting species-specific responses and the influence of fence design on sediment accumulation. These tools offer insights into optimizing aeolian sediment management for coastal protection. By conducting a systematic review and connecting theoretical, empirical, and modeling findings, this study highlights the complex challenge of measuring and managing aeolian sediment transport and proposes integrated strategies for enhancing coastal dune resilience against the backdrop of climate change and erosion. This study’s objectives to bridge gaps in current understanding are met, highlighting the need for a multidisciplinary approach to coastal dune management and conservation, especially combining wind- and wave-driven processes.

Comment on “the hydraulic investigation of harmonic plan weirs” by A. Yıldız, A. İhsan Marti, M. Göğüş

In this paper, the stage-discharge equation of a harmonic plane weir is deduced applying both the classical approach of the discharge coefficient Cd and the Π- Theorem of dimensional analysis and the self-similarity theory. At first, using the laboratory measurements carried out by Yildiz et al. (2024), a new relationship for estimating Cd is proposed. This new empirical expression of the discharge coefficient (Eq. (15)) allows for improving the performance of the stage-discharge equation (Eq. 13), which is characterized by errors in the discharge estimate E varying from – 7.7 to 7.7 % and a mean square error MSE of 0.214. Then, applying the dimensional analysis, a new stage-discharge relationship was deduced and calibrated using the same dataset. This theoretical equation is characterized by errors E ranging from – 7.1 to 7.4 %, and a MSE of 0.193. In conclusion, the stage-discharge relationship deduced by dimensional analysis is characterized by the best performances in the discharge estimate and has also the advantage of working without the need of estimating the discharge coefficient.

The effects of precursory velocity changes on earthquake nucleation and stress evolution in dynamic earthquake cycle simulations

Seismic velocity changes in earthquake cycles have been observed over a wide range of timescales and may be a good indicator of the onset of future earthquakes. Understanding the effects of precursory velocity changes right before seismic and slow-slip events could potentially elucidate the onset and timing of fault failure. We use numerical models to simulate fully dynamic earthquake cycles in 2D strike-slip fault systems with antiplane geometry, surrounded by a narrow fault-parallel damage zone. By imposing S-wave velocity changes inside fault damage zones, we investigate the effects of these precursors on multiple stages of the seismic cycle, including nucleation, coseismic, postseismic, and interseismic stages. Our modeling results show a wide spectrum of fault slip behaviors including fast earthquakes, slow-slip events, and variable creep. One primary effect of the imposed velocity precursor is on the earthquake nucleation phase, and earlier onset of precursors causes earthquakes to nucleate sooner with a smaller nucleation size that is not predicted by theoretical equations. Furthermore, such precursors affect the nucleation of dynamic earthquakes and slow-slip events. Our results highlight the importance of short- and long-term monitoring of fault zone structures for better assessment of regional seismic hazard.

Uranium concentrations and its isotopes in baby food of Iraq

Abstract This study determines uranium concentrations and isotopes (238U, 235U, and 234U) in baby food samples collected from Iraqi markets using solid-state nuclear track detector technical (CR-39). Also, some radiological hazard parameters such as annual committed effective dose (E U) and risk of an excess cancer fatality per million persons (RECFPMP) for the same study samples were calculated using theoretical equations. The samples in the present study were classified into three varieties: cereals and cereal products, vegetables and fruits, and biscuits. The results show that the average uranium concentration (mg/kg or ppm) values in cereals and cereal products, vegetables and fruits, and biscuits were 0.71 ± 0.01, 0.81 ± 0.04, and 0.72 ± 0.031, respectively. At the same time, the average values of 238U, 235U, and 234U in all samples of the present study were 9.08 ±0.17 Bq/kg, 0.42 ± 0.0081 Bq/kg, and 9.33 ± 0.18 Bq/kg, respectively. The total average of E U (mSv/y) due to all uranium isotopes (238U, 235U, and 234U) in cereals and cereal products, vegetables and fruits, and biscuits were 0.042 ± 0.0006, 0.039 ± 0.001, and 0.034 ± 0.001, respectively. Moreover, it was found that the average values of RECFPMP were 0.159 ± 0.002 in cereals and cereal products samples, 0.154 ± 0.007 in vegetables and fruits samples, and 0.130 ± 0.005 in biscuits samples. Uranium concentrations and the total annual committed effective dose in all baby food samples comply with the worldwide limits approved by UNSCEAR, which state safe limitations (1.7 mg/kg) and (0.32 mSv/y), respectively. So, one may conclude that there is no danger of uranium concentrations in the case of baby consumption.

Evaluation of Evaporation Fluxes for Pesticides and Low Volatile Hazardous Materials Based on Evaporation Kinetics of Net Liquids.

Evaporation is the phase transition process that plays a significant role in many spheres of life and science. Volatilization of hazardous materials, pesticides, petroleum spills, etc., impacts the environment and biosphere. Predicting evaporation fluxes under specific environmental conditions is challenging from theoretical and empirical points of view. A new practical method for estimating fluxes is proposed based on our experimental results and previously published data. It is demonstrated that some parameters in theoretical equations for near-equilibrium evaporation can be estimated from experiments, and these formulas can be exploited to predict steady-state evaporation fluxes in the air in a range of 8 orders of magnitude based on a single experiment carried out for nontoxic volatile compounds.

Theoretical analysis and design of inter cum intra-row wetland paddy field weeder

Most of the paddy field weeders developed belongs to inter-row types and the use of inter cum intra-row weeding in wetland paddy fields is obscure. This study aims to design and develop inter cum intra-row weeders so that weeds in both inter and intra-row zone can be eradicated in one go. From the design point of view, the power source (engine), cutting blades, rotor shaft, inter and intra-row weeding units, rectangular link, trapezoidal and lateral plates, and support frames were the important components for the functioning of the machine. The power requirement of the machine and finite element analysis (FEA) of the major components have been analyzed. The numerical values obtained from the available theoretical equations were plugged into the SolidWorks software to analyze the strength of each component. The magnitudes of every result showed superb agreement with the values obtained through analysis in the SolidWorks software. To eliminate weeds in the intra-row zone, a sinusoidal curve path was devised for the intra-row unit to move around the paddy plant. Thus, a 3-D (3-Dimensional) CAD model paddy field weeder suitable for inter cum intra-row weeding has been created and the path to be followed by the intra-row weeding unit has been traced using SolidWorks simulation.

High-performance flexible piezoelectric sensors based on honeycomb graphene macro-film exploiting auxetic mechanical property

Flexible piezoelectric sensors have received widespread attention in wearable electronics for their ability to convert mechanical energy into electrical energy, while the insufficient output power and complex preparation process have limited their application. In this work, several honeycomb structures based on graphene macro-film (GAMF) were created via laser engraving, which can utilize negative Poisson’s ratio (NPR) properties to improve the output electric performance of flexible piezoelectric sensors. The effect of different electrode materials on the piezoelectric output was investigated in the experiments and compared with the theoretical equations, indicating that the output power of the sensor could be enhanced up to 142 % by improving the materials auxetic mechanical properties. The stability tests have proven that the sensors can operate effectively for a long time under different operating conditions. Moreover, the optimized sensor shows powerful potential for monitoring human movements such as finger tapping, joint bending, and foot stepping. This work opens up a new development path for the preparation of convenient and high-performance wearable electronic devices.

Humidity-dependency of the relaxation behavior of fabric crease recovery angle

The unfolding of fabric creases induced by humidity is an issue of the capillary forces driving the deformation of materials, related to the interactions of textiles with moisture. Most are about complex moisture transport dynamics in fibrous assemblies. However, the effect of humidity on the crease recovery course of fabric with multiscale structure is not clear. Therefore, the fabric crease unfolding over time in different humidities was explored. In this study, theoretical analysis based on Burger’s viscoelasticity model and experiments on the crease recovery were conducted. Then the evaluation indices, that is, the crease recovery ratio ([Formula: see text]) and the recovery gradient ratio ([Formula: see text]), which were obtained from fitting coefficients and constructed in the form of the theoretical equation, were established. They were then combined with the fabric porosity ( P) at yarn scale, to demonstrate the capillary forces driving the deformation of materials, that is, crease unfolding humidity-induced. The results show that the higher the [Formula: see text] or [Formula: see text] value, the greater capillary forces promoting the crease to recover under the same humidity changes. The smaller the P, the more easily the contacted structures move, and the crease recovers better. In conclusion, the deformations induced by capillary forces are studied in a form of a crease unfolding at a humidity change. The results obtained in this study lay a certain foundation for further research on the mechanism and theoretical model of the moisture on fabric crease recovery.

Acoustic vibration analysis of high-temperature thin-walled structures

Advanced aerospace structures are subjected to extremely harsh working environment, including of mechanical, acoustic, thermal, and aerodynamic loads. These combined loads can make the structures exhibit complex response, which has already attracted increasing concern in the design of advanced aerospace structures. To tackle the problem, a finite element model (FEM) by discretizing the theoretical differential equation is established to calculate the dynamic response of thin-walled structures under combined thermal and acoustic loads. The numerical analysis indicates that three types of nonlinear responses of the thin plate under combined thermal-acoustic loads are obtained, and the mechanism of snap-through is revealed through two ways: thermal buckling analysis and thermal modal analysis. which can be used to explain the nonlinear response characteristics.

Determination of long-lived gamma emitters in some vegetarian products in Al-Najaf governorate using NaI(Tl)

In this study, gamma emitters including potassium-40, thorium-232, and uranium-238 were found in samples of 10 types of vegetarian products that were taken from various locations of Al-Najaf governorate. The experimental study is done by NaI(Tl) detectors that are produced by the ORTIC Analysis System. Also, some radiological risks due to these emitters as radium equivalent activity and internal hazard index were calculated using different theoretical equations. Given that all samples from Iraqi vegetarian products in the current study that tested for long-lived gamma emitters and risk factors for hazard were found to be below the global limit suggested by numerous organizations and commissions, one may conclude that there is no risk to human health from radiological hazard caused by gamma emitters.

Data-driven prediction of dimensionless quantities for semi-infinite target penetration by integrating machine-learning and feature selection methods

This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements. The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables. As a physics-based dimension reduction methodology, this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases. Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering. The results indicate that the selected critical dimensionless feature variables by this synergistic method, without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics, are in accordance with those reported in the reference. Lastly, the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case, and the reliability of regression functions is validated.

Evaluating the effects of soil grain roughness and rill cross‐section shape on flow resistance

AbstractThe knowledge of the hydraulic characteristics of rill flows is needed to improve the understanding and the accurate modelling of upland erosion processes. Flume investigations are developed to schematize conditions useful to analyze the influence of a unique variable significant for modelling rill hydraulics, while field investigations are used to simulate morphological and hydraulic conditions of natural cases. The main aim of this investigation is to compare flow resistance measurements carried out using a rectangular rill channel (flume data) and manually generated and naturally shaped rills (plot data) for the same soils and hydraulic conditions. The two data sets allowed for establishing how the soil grain roughness and rill cross‐section shape affect flow resistance using a theoretical equation deduced by applying dimensional analysis and self‐similarity theory. The analysis developed for a fixed‐bed channel with a rectangular cross‐section demonstrated that the influence of different soil roughness on the Darcy‐Weisbach friction factor is approximately equal to ±1%, while for a rill with an irregular cross‐section the same effect is almost equal to ±2%. Therefore, for an open‐channel flow on a fixed bed, the effect of the grain size roughness on the friction factor is limited. For each examined soil, the investigation also demonstrated that the rill cross‐section shape leads to a variability of the friction factor from −20% to +30%. This result highlights that, for a fixed‐bed channel, the effect of the cross‐section shape on the Darcy‐Weisbach friction factor is much greater than that due to the soil grain size roughness. The main implication of this work is that the results deduced by laboratory measurements with regular cross‐sections, thus neglecting a complex geometry, can be affected by relevant discrepancies from those obtained by the field measurements, which better simulate natural conditions.

Shear Test of Corrugated Web Girders with Concrete-Filled Compression Tubular Flanges Used in Buildings

Corrugated web girders with plate flanges have been widely applied in buildings and bridges due to the large shear capacity of the corrugated web (CW). However, experiments on corrugated web girders with tubular flanges are limited. Accordingly, this paper explores, through four full-scale small-size experimental tests used on buildings, the shear behavior of a type of girder formed with a CW, concrete-filled tubular flange, and bottom flat plate flange (CWGCFTF) with different CW thicknesses, wavelengths, and concrete strengths. Based on the imprecise results of one current test, a novel simple support device is proposed to improve the accuracy of the shear test of the CWGCFTF. The test results also show that the shear ratios of the tubular flange to the entire cross-section range from 15–18% when the loading reaches that of the corresponding shear stress to 80% of the shear yield strength of the CWs. Moreover, local buckling appears at the top surface of the steel tube with the CW shear buckling failure of the CWGCFTF under the shear tests. At the end, a theoretical equation of the shear ratio of the CW to the whole cross-section is derived, and a shear yield strength equation of the CWGCFTF is proposed and verified by comparisons with the test results.

MHD Inertial and Energy-containing Range Turbulence Anisotropy in the Young Solar Wind

We study solar wind turbulence anisotropy in the inertial and energy-containing ranges in the inbound and outbound directions during encounters 1–9 by the Parker Solar Probe (PSP) for distances between ∼21 and 65 R ⊙. Using the Adhikari et al. approach, we derive theoretical equations to calculate the ratio between the 2D and slab fluctuating magnetic energy, fluctuating kinetic energy, and the outward/inward Elsässer energy in the inertial range. For this, in the energy-containing range, we assume a wavenumber k −1 power law. In the inertial range, for the magnetic field fluctuations and the outward/inward Elsässer energy, we consider that (i) both 2D and slab fluctuations follow a power law of k −5/3, and (ii) the 2D and slab fluctuations follow the power laws with k −5/3 and k −3/2, respectively. For the velocity fluctuations, we assume that both the 2D and slab components follow a k −3/2 power law. We compare the theoretical results of the variance anisotropy in the inertial range with the derived observational values measured by PSP, and find that the energy density of 2D fluctuations is larger than that of the slab fluctuations. The theoretical variance anisotropy in the inertial range relating to the k −5/3 and k −3/2 power laws between 2D and slab turbulence exhibits a smaller value in comparison to assuming the same power law k −5/3 between 2D and slab turbulence. Finally, the observed turbulence energy measured by PSP in the energy-containing range is found to be similar to the theoretical result of a nearly incompressible/slab turbulence description.

Field Testing of Gamma-Spectroscopy Method for Soil Water Content Estimation in an Agricultural Field.

Gamma-ray spectroscopy (GRS) enables continuous estimation of soil water content (SWC) at the subfield scale with a noninvasive sensor. Hydrological applications, including hyper-resolution land surface models and precision agricultural decision making, could benefit greatly from such SWC information, but a gap exists between established theory and accurate estimation of SWC from GRS in the field. In response, we conducted a robust three-year field validation study at a well-instrumented agricultural site in Nebraska, United States. The study involved 27 gravimetric water content sampling campaigns in maize and soybean and 40K specific activity (Bq kg-1) measurements from a stationary GRS sensor. Our analysis showed that the current method for biomass water content correction is appropriate for our maize and soybean field but that the ratio of soil mass attenuation to water mass attenuation used in the theoretical equation must be adjusted to satisfactorily describe the field data. We propose a calibration equation with two free parameters: the theoretical 40K intensity in dry soil and a, which creates an "effective" mass attenuation ratio. Based on statistical analyses of our data set, we recommend calibrating the GRS sensor for SWC estimation using 10 profiles within the footprint and 5 calibration sampling campaigns to achieve a cross-validation root mean square error below 0.035 g g-1.