Radius Length Research Articles

Impact of Geometric Parameters on Spring-Back Deformation in Double-Layer Metal Sheet Bending with an L-Shaped Die

This study delves into the intricate dynamics of the return deformation process in double-layer metal sheet stamping on an L-shaped die, focusing on the pivotal influence of punch and die size parameters. The specific parameters under scrutiny include die radius, die clearance, and plate length. Employing a comprehensive methodology, this research conducts finite element simulations using Abaqus software, ensuring both data collection requirements and implementation feasibility are met. The simulation results are rigorously compared with the published data from a seminal comparative study [1], providing a critical point of reference for analysis. The findings of this investigation illuminate a profound similarity in the impact of three critical parameters, namely die radius, degree of mold opening, and plate length, on the degree of spring-back deformation in the L-bending of SPCC double-layer materials. This outcome not only substantiates and extends the existing body of knowledge but also offers novel insights into the interplay of these parameters in the double-layer metal sheet stamping process, thus contributing significantly to the field of manufacturing and process optimization.

Study on flame propagation and inherent instability of hydrogen/ammonia/air mixture

To improve the safety and reliability of hydrogen energy, this paper studied the flame propagation and instability characteristics of hydrogen/ammonia/air mixture under different hydrogen contents, equivalence ratios and initial pressures. The results show that three typical phenomena are observed in the premixed hydrogen/ammonia/air flame propagation process under different experimental conditions. In a stable flame, the roughness of the flame surface does not increase, while during unstable flame expansion, the cracking of the flame surface splits and increases. In addition, under the condition of low equivalence ratio and hydrogen content, significant flame uplift is observed. With the increase in hydrogen content, the flame thickness and critical instability radius of the hydrogen/ammonia/air mixture decrease monotonously. The increase of hydrogen content mainly strengthens the hydrodynamic instability, leading to the weakening of flame stability. With the increase of the equivalence ratio, the Markstein length and the critical instability radius increase monotonically. The minimum value of flame thickness appears at the equivalence ratio of 1.0. The Lewis number is always less than 1 for poor combustion and greater than 1 for rich combustion. An increase in the hydrogen content only moves the Lewis number further away from 1. In rich burn, the thermal-diffusion is beneficial to flame stability, and the flame thickness increases with the increasing equivalence ratio. Under the combined effect of thermal-diffusion and hydrodynamic instability, the overall stability of the hydrogen/ammonia/air flame gradually increases with the increasing equivalence ratio. With the increase of initial pressure, the flame thickness decreases gradually. The critical instability radius and Markstein length both decrease rapidly with the increase of initial pressure.

Structural evolution of bed drainage channels under the shear effect of the whole process of tailings thickening

Cemented paste backfill (CPB) technology has the advantages of safety, environmental friendliness, economics, and efficiency. This method offers assurances for practical underground mining and tailings pond management. The bed drainage channel structure and coarse particles with diameters above 45 μm were reconstructed and quantitatively characterized in 3D by computed tomography (CT) for the whole tailings thickening process. The spherical pore diameter evolution trends, stick throat channel radius and throat channel length were analyzed with and without shear using the pore network model (PNM). The functional relationship between the average spherical pore diameter and bed pressure is given, and the boundary values between the bed’ primary and secondary drainage channels are clarified. The ratio of throat length to diameter (Tw) is proposed to measure the difficulty of throat channel structure on the water discharge in the bed. The effects of the volume and number of coarse particles with diameters above 45 μm on the bed porosity and pore connectivity were analyzed. The range of particle diameters that significantly affect the bed porosity and pore connectivity was clarified. The results show that the spherical pore diameter, throat channel radius, and throat channel length decrease with increasing bed pressure with and without shear. Moreover, the average spherical pore diameter in the bed has a power-law relationship with the bed pressure. The spherical pore diameter, throat channel radius, and throat channel length with shear were lower than without shear, and the slurry concentration was higher than without shear. The main drainage channels of the bed with and without shear consisted of large pore structures with diameters of not less than 433.3 μm and 329.8 μm, respectively. The throat channel structure parameter Tw increases with the increase of bed pressure. When Tw is higher than 8.7, the discharge of water in the bed is hindered, making it challenging to improve the slurry concentration. The porosity and pore connectivity of the bed decreases with increasing volume and number of coarse particles. Among them, coarse particles in the diameter 150–300 μm range significantly reduce the bed porosity and pore connectivity. This study guides the preparation of high-concentration paste filling slurry, which is helpful to improve the efficient mining capacity of mines and have fewer tailings ponds.

Numerical investigation of entropy generation of turbulent flow in twisted tri-lobed tubes

Twisted tri-lobed tubes have garnered attention due to their exceptional heat transfer efficiency and straightforward fabrication. Existing literature lacks comprehensive assessments of the overall heat transfer performance of twisted tri-lobed tubes from the perspective of energy loss and irreversibility. This research aims to investigate entropy generation during turbulent water flow within twisted tri-lobed tubes, examining the influence of geometric parameters on local and average entropy production. Findings indicate that larger small circle radius (r) and straight lengths (l), coupled with smaller transition circle radius (R) and twist pitch lengths (p), result in diminished local and average heat transfer entropy production while enhancing local and average frictional entropy production, with heat transfer entropy generation dominating the overall entropy production. Additionally, with increasing Reynolds numbers, all twisted tubes demonstrate an increasing trend in average frictional entropy production, except for some cases (Case 1-Case 4) that exhibit an initial rise followed by a decline in average heat transfer entropy generation. Among the examined Reynolds range, Case 4 displays lower overall irreversibility compared to a plain tube. Following the second law of thermodynamics, Case 4 is preferred. The findings and methodology contribute to enhancing the thermodynamic evaluation of convective heat transfer in twisted tri-lobed tubes.

Effect of capillary pressure on the CO2 flux in the pores of membrane contactor: Theory and simulation results

A simulation model was made to evaluate the effect of the capillary pressure on the CO2 capture by membrane absorption. More specifically, the model calculated the changes in the interfacial pressure and CO2 flux as the interface of gas and liquid moves through the pore opening to its exit. Two cases were considered; hydrophilic or hydrophobic membrane materials with a respective contact angle of less or more than 90°. It was revealed that CO2 flux is about 70% higher for the hydrophilic membrane of 10−6 m radius and 50 × 10−6 m length than the hydrophobic membrane of equal pore radius and pore length, when nearly equal to 1.72 × 105 Pa is applied either on the feed side (hydrophilic membrane) or on the permeate side (hydrophobic membrane) to keep the membrane pore dry without gas bubble formation. It should be noted that CO2 flux is higher when a hydrophilic membrane is used, which is against the common belief that a hydrophobic membrane is preferable for membrane absorption. Also, the duration for the interface to get to the pore exit was determined. The effect of capillary pressure increases as the membrane pores become smaller, which turns into an increase in CO2 flux when the porosity and the pore length are maintained constant. It was also revealed that the CO2 flux can be significantly increased when water absorbent is replaced by 1 M monoethanolamine solution due to increased CO2 solubility. Thus, this work is the first attempt to study the effect of capillary pressure on the flux of membrane contactors. It is recommended to collect more data on membrane contactors by the hydrophilic membrane. Electronic structure calculations were also performed to investigate the reaction mechanism between CO2 and MEA, with a focus on non-conventional interactions such as hydrogen bonding and van der Waals interactions. This is to know the details of the reaction occurring between CO2 and MEA.

A three-dimensional compression-torsion metamaterial based on the three-period minimum surface theory

This paper proposes a novel design for a three-dimensional compression-torsion mechanical metamaterial based on the three-period minimal surface (TPMS) theory. Unlike the conventional approach of utilizing chiral or diagonal rod structures to achieve compressive-torsional properties in metamaterials, this paper employs a two-dimensional level of TPMS theory and the synergistic effect of a re-entrant structure to achieve compressive-torsional properties. Theoretical, experimental, and numerical methods were employed to investigate the deformation characteristics and mechanical properties of the proposed structure. The paper investigates the impact of the periodic value of the TPMS on the torsion direction, as well as the influence of unit cell radius r on the deformation characteristics, torsion angle, and Poisson's ratio of the lattice structure. The length of radius r can be appropriately selected to control the torsion angle and negative Poisson's ratio (NPR) effect of the structure. Furthermore, by adjusting the period values of the TPMS, the torsion direction of the structure can be controlled. Finally, the torsion angle, Poisson's ratio, stiffness and specific energy absorption (SEA) were compared with the structure with a diagonal rod microstructure (SDRM). The findings indicate that the proposed structure exhibits superior torsion performance and NPR effect compared to the previously proposed three-dimensional compression-torsion material. This design concept has significant implications for the development of smart devices, aerospace engineering, and conservation engineering applications.

МОДЕЛЮВАННЯ ПЛАЗМОННИХ ВЛАСТИВОСТЕЙ ЧАСТИНОК МОНОСУЛЬФІДУ МІДІ В БЛИЖНЬОМУ ІЧ ДІАПАЗОНІ

This paper is devoted to the theoretical study of the extinction spectra of copper monosulfide particles under conditions of localized surface plasmon resonance. The study was conducted for plasmonic copper monosulfide particles of spherical and ellipsoidal shapes of variable size in media with different values of the refractive index. The simulation results reveal that increasing the radius of CuS nanoparticles leads to a significant enhancement in the amplitude of the plasmon peak and a shift of the peak towards longer wavelengths. It was investigated how the positions of the extinction peaks on the spectral scale and their amplitudes change when the particles deviate from the spherical shape. Simulations were performed for spherical and elongated ellipsoidal particles with fixed cross-sectional radius and variable length. Specifically, we varied the length of the major axis while keeping the lengths of the minor axes constant. It is shown that the deviation from the sphericity of the particles will affect both the position of the extinction maximum on the spectral scale and the shape of the spectral curve. An increase in the ratio of the ellipsoid semi-axes lengths leads to a significant increase in the amplitude of the extinction peak and its shift to the long-wavelength region. Besides, the position of the plasmonic peak on the spectral scale is influenced not only by the geometric parameters of the particles such as size and shape but also by the dielectric properties of the surrounding medium, including its refractive index. We assess the impact of changing the refractive index of the surrounding medium on the shape, amplitude, and position of the extinction maxima of CuS nanoparticles. It is showed that increasing the refractive index of the surrounding medium leads to a significant shift of the plasmon resonance peak into the long-wavelength region of the spectrum an increase in the peak width, and a decrease in its amplitude. Thus, ellipsoid copper monosulfide particles show improved surface plasmon characteristics compared to spherical ones and can be effectively used in the near-infrared spectral region.

Investigation of Trap Density Effect in Gate-All-Around Field Effect Transistors Using the Finite Element Method

Trap density refers to the density of electronic trap states within dielectric materials that can capture and release charge carriers (electrons or holes) in a semiconductor channel, affecting the transistor’s performance. This study aims to investigate the influence of trap density on the electrothermal behavior of nanowire gate-all-around GAAFET devices. The numerical solution of Poisson’s equations and continuity equations, coupled with the heat conduction model, has been used to predict the temperature inside the GAAFET device. The finite element method has been used to discretize the semiconductor equations. Investigations have been carried out on a number of physical and geometric parameters, such as oxide thickness, nanowire radius, and gate length. Their effects on output characteristics and device temperature have been discussed. A thinner oxide thickness, lower device radius, and longer channel length led to a higher current flow. Results also reveal that high trap densities can have significant impacts on the degradation of electronic devices, particularly in the context of semiconductor devices like transistors.

Exploring the geometry of miniaturized Archimedean SPIRAL Antennas for small and portable multitask devices

The focus of miniaturization is the production of small and portable devices that can be carried in the pocket anywhere and anytime. Small and portable devices that perform multitask such the smartphone requires a portable and efficient antenna that operates in many frequency bands. A single planar miniaturized Archimedean spiral antenna, which operates in a frequency range that is determined by its inner and outer radii of its arc, has been adjourned to be a better candidate for these multiple tasks. This study examined the geometry of a miniaturized Archimedean spiral antenna of varying turns. An inner radius of 4.90 mm and a thickness of 0.0356 mm suitable for the printed antenna were previously chosen for the study. The length of the arc and the outer radius were determined for spiral turns ranging from 0.5 to 100 with an incremental step of 0.5. Results revealed the radial distance generating the spiral, the length of its arc, the outer radius, and the surface area were 4.97 mm, 2 15.51 mm, 4.97 mm and 77.16 mm for 0.5 spiral turns, and 19.12 mm, 7,546.80 mm, 2,849.33 mm and 1,148.64 2 mm for 100 spiral turns. Based on the outer radii, the frequency range of operation will be between 16.76 MHz and 9.60 GHz. The mathematical functions formulated through curve fitting described the relationship between the outer radius and arc length with a power function and the number of turns and frequency with an exponential function, while arc length and radial distance, area and number of turns, and area and pitch angle are described by polynomial functions. It is recommended that further analysis on the geometry of the minimized Archimedean spiral antenna be conducted.

Simulation analyses and configuration optimizations of an LD pumped 3.1 µm Co/Er:PbF2 MIR laser

The demand for mid-infrared physics technology is increasing, and it is still a difficult process from growing excellent laser crystals to performing laser experiments. In this paper, we consider the energy transfer process between Co2+ and Er3+, and present the theoretical simulation results of the output power of the 3.1 µm Co/Er:PbF2 MIR laser. Based on the setup of a LD pulse pumped laser system, the effects of beam waist radius, resonator parameters and crystal length on the output are discussed in detail. The calculation results show that under good cavity mirror conditions, we can obtain a 3.1 µm laser with an output slope efficiency of 43.4%, whose output energy reaches 2.19 mJ at an input of 5 mJ. This provides guidance include the cavity mirror parameters and crystal parameters for laser experiments.

Cutoff values of axial length/corneal radius ratio for determining myopia vary with age among 3-18 years old children and adolescents.

To investigate the effectiveness and cutoffs of axial length/corneal radius (AL/CR) ratio for myopia detection in children by age. Totally, 21 kindergartens and schools were enrolled. Non-cycloplegic autorefraction (NCAR), axial length (AL), horizontal and vertical meridian of corneal radius (CR1, CR2), and cycloplegic autorefraction were measured. Receiver operating characteristic (ROC) curve was used to obtain the effectiveness and cutoff for myopia detection. Finally, 7803 participants aged 3-18years with mean AL/CR ratio of 2.99 ± 0.16 were included. Area under the ROC curve (AUC) of AL/CR ratio for myopia detection (0.958 for AL/CR1, 0.956 for AL/CR2, 0.961 for AL/CR) was significantly larger than that of AL (0.919, all P < 0.001), while AUCs of the three were similar with different cutoffs (> 2.98, > 3.05, and > 3.02). When divided by age, the ROC curves of AL/CR ratio in 3- to 5-year-olds showed no significance or low accuracy (AUCs ≤ 0.823) in both genders. In ≥ 6-year-olds, the accuracies were promising (AUCs ≥ 0.883, all P < 0.001), the cutoffs basically increased with age (from > 2.93 in 6-year-olds to > 3.07 in 18-year-olds among girls, and from > 2.96 in 6-year-olds to > 3.07 in 18-year-olds among boys). In addition, boys presented slightly larger cutoffs than girls in all ages except for 16 and 18years old. For children aged 3-5years, AL/CR ratio or AL combined with NCAR increased AUC to > 0.900. AL/CR ratio provided the best prediction of myopia with age-dependent cutoff values for all but preschool children, and the cutoffs of boys were slightly larger than those of girls. For preschool children, AL/CR ratio or AL combined with NCAR is recommended to achieve satisfactory accuracy. AL/CR ratio calculated by two meridians showed similar predictive power but with different cutoffs.

Serial ultrasonographic measurements of fetal parameters over three successive pregnancies in a captive Eastern black-and-white colobus monkey (Colobus guereza).

This study provides ultrasonographic fetal growth charts for the Eastern black-and-white colobus monkey (Colobus guereza). Throughout three consecutive gestations (-162 to -2 days to parturition) in a single dam, we opportunistically obtained ultrasonographic measurements for the following parameters: biparietal diameter, head circumference, humerus length, femur length, tibia length, radius length, thoracic width, kidney length, and crown-rump length. Biparietal diameter was the most consistently measured parameter. First detection of fetuses occurred between 96 and 162 days before parturition. This report demonstrates that voluntary transabdominal ultrasound can be well-tolerated in the colobus monkey using operant conditioning. These findings may be useful to assess fetal development and predict parturition dates in the absence of a known conception date in this species.

Investigation of molecular details of a bacterial cationic amino acid transporter (GkApcT) during arginine transportation using molecular dynamics simulation and umbrella sampling techniques.

Cationic amino acid transporters (CATs) facilitate arginine transport across membranes and maintain its levels in various tissues and organs, but their overexpression has been associated with severe cancers. A recent study identified the alternating access mechanism and critical residues involved in arginine transportation in a cationic amino acid transporter from Geobacillus kaustophilus (GkApcT). Here, we used molecular dynamics (MD) simulation methods to investigate the transportation mechanism of arginine (Arg) through GkApcT. The results revealed that arginine strongly interacts with specific binding site residues (Thr43, Asp111, Glu115, Lys191, Phe231, Ile234, and Asp237). Based on the umbrella sampling, the main driving force for arginine transport is the polar interactions of the arginine with channel-lining residues. An in-depth description of the dissociation mechanism and binding energy analysis brings valuable insight into the interactions between arginine and transporter residues, facilitating the design of effective CAT inhibitors in cancer cells. The membrane-protein system was constructed by uploading the prokaryotic CAT (PDB ID: 6F34) to the CHARMM-GUI web server. Molecular dynamics simulations were done using the GROMACS package, version 5.1.4, with the CHARMM36 force field and TIP3P water model. The MM-PBSA approach was performed for determining the arginine binding free energy. Furthermore, the hotspot residues were identified through per-residue decomposition analysis. The characteristics of the channel such as bottleneck radius and channel length were analyzed using the CaverWeb 1.1 web server. The proton wire inside the transporter was investigated based on the classic Grotthuss mechanism. We also investigated the atomistic details of arginine transportation using the path-based free energy umbrella sampling technique (US).

Bandgap mechanisms and wave characteristics analysis of a three-dimensional elastic metastructure

PurposeIn order to investigate the vibration reduction properties of a three-dimensional elastic metastructure with spherical cavities at low frequencies.Design/methodology/approachThe bandgap characteristics of a three-dimensional elastic metastructure with spherical cavities are studied based on analytical and numerical approaches.FindingsThe results of both method revealed that the vibration of the vertexes masses is important for opening bandgaps. The fact that the big sphere cavity radius or short side length of the cube unit leads to a wider bandgap, is noteworthy.Originality/valueThis research provides theoretical guidance for realizing the vibration attenuation application of EMs in practical engineering.

Multi-field coupled dynamics for a movable tooth drive system integrated with shape memory alloys

The harmonic movable tooth drive system integrated with shape memory alloys has a small size and a large output torque. Its dynamics performance is the key factor for evaluating the drive system. Here, for the drive system, based on its structure and working principle, the coupled dynamics equations are deduced. Using the equations, changes of the natural frequencies of the drive system during the operation are investigated. Effects of the system parameters and SMA wires phase change process on the natural frequencies are analyzed. The nonlinear resonant frequencies of the drive system and its amplitude-frequency relationship are studied. Results show that natural frequencies of the drive system change periodically which is caused by SMA phase transformation during operation. The eccentricity, movable tooth radius, the wave generator radius and SMA wire length have also important effects on the natural frequencies of the drive system. The nonlinear resonant frequencies are smaller than linear resonant frequencies. In the design of the drive system, the coupled nonlinear effects of the temperature, phase change, stress and strain of the SMA wires, and the system parameters of the movable tooth drive system should be considered. In this paper, the coupled nonlinear dynamics model of the harmonic movable tooth drive system integrated with shape memory alloys is proposed in which the coupled effects of the temperature, phase change, stress and strain of the SMA, and the system parameters of the movable tooth drive system are considered.

Pore Structure and Permeability Characterization of Tight Sandstone Reservoirs: From a Multiscale Perspective

Due to the influence of a sedimentary environment, sandstone characteristics, diagenesis, and geological structure, the complexity and heterogeneity of the pore structure in tight sandstone reservoirs act as key barriers for accurate characterization of the influence of different pore microparameters on reservoir physical properties. This paper obtained different scale microscopic pore–throat parameters through mercury intrusion porosimetry (MIP) and digital core reconstruction models. According to the connectivity of different scale pores, connected pore structure parameters, and pore fractal dimension, the pore structure characteristics of tight sandstone reservoirs were evaluated. Subsequently, through partial correlation analysis, the contribution rate of different scale connected pore parameters to permeability and porosity was clarified. Then, a multiparameter fitting equation for the absolute permeability and porosity of the rock was obtained through multiple regression analysis. The analysis results show that (1) the connected pores of tight sandstone reservoirs are mainly mesopores, with the pore radius distribution between 1 and 3 μm, and throat radius distribution between 0 and 2 μm. (2) The complexity of the pore structure in tight sandstone reservoirs is most strongly correlated with the fractal dimension of the pore structure at the mesoporous scale. (3) The pore radius and throat length at the mesoporous scale have the strongest correlation with the absolute permeability of the rock, and the pore radius at the mesoporous scale has the strongest correlation with the porosity of the rock. (4) The multiparameter fitting equation established by multiple regression analysis quantitatively and qualitatively analyzed the impact of microscopic parameters of the pore–throat structure at different scales on reservoir properties, achieving the purpose of predicting the absolute permeability and porosity of the tight sandstone reservoir. It provides guidance for the study of the pore structure and permeability characteristics of tight sandstones.

Anatomical depth parameters of pronator quadratus: a cadaveric study.

There is a paucity of literature documenting the cadaveric muscle thickness of pronator quadratus. We measured the width and depth of this muscle bilaterally in 15 cadavers. There was a significant difference in thickness between male and female cadavers, but the width was proportional to radius length.

A dual paths magnetorheological damper with small field-off force and large dynamic range

Magnetorheological (MR) dampers are widely used for vibration isolation and the dynamic range is a key index to evaluate its performance. According to the vibration isolation theory, it is essential for the damper to maximize the damping force in resonance region and minimize the damping force in high-frequency excitation. However, for single-path MR dampers, achieving the goals of low field-off force and large dynamic range has conflicting requirements on the structural parameters. In this research, a dual paths MR damper has been proposed to overcome this problem. The proposed MR damper has two coaxial paths and the magnetic field strength in each path can be controlled separately. According to the flow state of the MR fluid, the working modes of the proposed MR damper are divided into three kinds and the corresponding mathematical models are driven. Based on the mathematical models, the effect of structural parameters on the dynamic range, maximum and minimum damping force is investigated. It is concluded that increasing the piston rod radius and piston length is an effective method to expand the dynamic range while maintain a small field-off damping force. The experimental results show that the proposed MR damper working mode can be controlled by the applied currents, the minimum force is obtained in the dual paths flow state while the maximum force is obtained in the inner path flow state. In particular, the dynamic range of the proposed MR damper is significantly improved to 93.3 and the filed-off damping force remains small compared to the previously reported MR damper.

Numerical study on convective heat transfer and flow characteristics in twisted tri-lobed tubes

ABSTRACT The convective heat transfer and flow resistance properties of water flowing through a twisted trilobed tube (TTT) with Reynolds numbers that ranged from 10,000 to 40,000 were examined in this work. Specifically, we examined how the tip circle radius (r), straight length (l), transition radius (R), and twist pitch (S) influenced the heat transfer and flow resistance in the tube. Our results showed that the TTT had an average Nusselt number (Nu) that was 30% higher than that of a plain tube, while the friction coefficient (f) increased by 39%. We also presented temperature and velocity field distributions and explained the enhanced heat transfer process using the field synergy principle. Furthermore, we found that a larger tip circle radius (r) and straight length (l), as well as a smaller transition radius (R) and twist pitch (S), led to better overall heat transfer performance of the TTT. Among the different cases evaluated, Case 7 had the highest overall heat transfer performance with a PEC of 1.37. The unusual structure of the TTT caused a rotating motion, which resulted in secondary and spiral flows that increased the synergy through the velocity and temperature fields. Finally, our research found a correlation with the Nusselt number (Nu) as well as the friction coefficient (f).

Investigation of the geometry effect on air-demand ratio in conduits with a sluice gate

Gated conduits involve high-velocity air–water flow. When studies on gated conduits are examined, it is determined that the air-demand ratio changes according to the hydraulic and geometric parameters. However, no study has investigated the effect of the cross-sectional geometry of high-head conduits with a sluice gate on the air-demand ratio. In this study, the effect of conduit cross-sectional geometry on the air-demand ratio is examined. Results indicate that a conduit's cross-sectional geometry has an important effect on the air-demand ratio, especially at 10% and 15% gate opening rates. It is seen that the effect of the conduit geometry on the air-demand ratio decreases at 20%, and for greater gate opening rates. Moreover, a formula for estimated the air-demand ratio is presented, relating the air-demand ratio to the gate opening rate, Froude number, hydraulic radius and conduit length.