Formula For Velocity Research Articles

The rate of constrained particles deposition in a wide range of suspension densities in the laminar-turbulent operating modes

The rate of constrained fall of mineral particles in suspensions of different densities is necessary for calculating the design and operating modes of gravity concentrating equipment. During hydraulic classification and separation, a mixed, laminar-turbulent, flow regime is observed in real pulps. There are no theoretical velocity formulas for such a regime, and most of the known semi-experimental and experimental formulas have limited application. This article proposes a new method for comparing different formulas with each other in a wide range of suspension densities. The method uses an analytical calculation of the hydraulic characteristics of the medium - porosity, concentration and viscosity. What is new is that all these characteristics depend on only one indicator - the density of the suspension, which is easily determined in practice by weighing a pulp sample. In these calculations, the weighted average density of heterogeneous particles in suspension is used. A feature of the method is the approximation of the analyzed calculation formulas to the conditions of free fall in order to obtain only one control point and compare it with known experimental data. This method allows to set the limits of the application of formulas depending on the density of the suspension. The choice of a more precise formula is necessary for the design hydraulic devices for the classification and separation of mineral suspensions and finely ground composite raw materials. The application of this method for the most common formulas of Ergan and Todes-Rosenbaum is shown. It was found that the latter formula іs actually not suitable for dilute suspensions with a density below 1.65 g/cm3. A new linear equation for calculating the rate of constrained particles deposition is proposed, which provides high accuracy in a wide range of suspension densities. The resulting equation has a simple form and, together with an analytical calculation of the characteristics of the medium, forms a system of linear equations for calculating the rate of constrained particles deposition of any size and density in mineral pulps of different densities. The calculation of the velocity of constrained settling and the ascent of particles is the basis for the design of hydraulic classifiers and separators for mineral dressing. Such calculations are necessary for determining of hydraulic devices optimal modes and monitoring indicators during their operation.

Characteristics of the elevation amplification effect of vibration velocity in rock surrounding underground cavities under different stress conditions

Side walls of deep underground cavities are commonly subject to dynamic disturbance of blasting excavation. To study the distribution of blasting vibration velocity in the side walls of underground cavities, the side walls were simplified as a mechanical model of simply supported slabs. Based on the field blasting vibration tests in the Taohuazui mining area in Hubei Province, China, a predictive formula for the peak particle velocity (PPV) in rock surrounding of cavities considering the geostress was deduced combining with dimensional analysis. The PPV in side walls of underground cavities under different geostress conditions was simulated using the LS-DYNA dynamic finite element software. The results show that the mechanical model of simply supported slabs is analogous to the vibration mode of side walls of underground cavities in the Taohuazui mining area: both show the amplification effect of PPV in the middle of the side walls. In addition, the prediction formula is highly consistent with the field measurements and numerical simulation results. With the increases in the geostress and the lateral pressure coefficient (σH/σV), the PPV on side walls always increases, while the overall trend remains unchanged.

Field-driven domain wall motion in ferrimagnetic nanowires

The fascinating high-speed field-driven domain wall (DW) motion along ferrimagnetic nanowires near the angular momentum compensation point (AMCP) is solved based on the generic ferrimagnetic dynamics. The physics of the absences of precessional torque and infinite high Walker breakdown field at the AMCP is proved under general conditions. Based on the energy conservation principle, an almost exact DW velocity formula, valid beyond the Walker breakdown field, is obtained. Our results agree with all existing experiments and simulations. This theory provides useful guidances to DW manipulation.

Simplified analytical procedure to calculate the impact behaviour of steel parking-structure columns

The steel supporting frame of automatic mechanical garages is called a parking structure. Presently, for these novel structures, the design codes are without giving detailed guidelines to predict the response of their impacted column. Thus, this paper presents a simplified analytical procedure to calculate the impact behaviour of the column. The proposed method is based on the co-rotational rigid body model and follows the energy-balance principle. Compared with the previous analytical method, it specially targets the parking-structure column and can be used to conveniently and quickly calculate the column transverse displacement with considering the effects of the surrounding structural members and axial loads on the column. The research covers the situation where the column is subjected to the impacts at a low velocity, critical velocity, and overcritical velocity. Primarily, an approach is developed to simplify the overall parking structures. On that basis, the calculation formula for the critical impact velocity, i.e. the velocity that results in the formation of plastic hinges in the column, is derived. To predict the behaviour of the column under the impact beyond the critical impact velocity, the simplified analytical procedure is provided and then its accuracy is examined by validated numerical models. Eventually, according to the procedure, some suggestions are given to improve the design of the column after parametric analyses. It is recommended that control the axial-load levels of the column, particularly the column with a small section area, as well as set stiffeners on the column within the height of 1000 – 1500 mm.

Significance of Brinkman and Stokes system conjuncture in human knee joint

Stokes’s equation in the fluid domain and Brinkman’s equation in the porous media are combined in the current study which is designated by the Stokes-Brinkman coupling. The current paper gives a theoretical analysis of the Stokes-Brinkman coupling. It has been shown that such a model is a good match for the knee joint. A flow model has been investigated in order to get a better understanding of the convective diffusion of the viscous flow along the articular surfaces between the joints. The Beavers and Joseph slip conditions which are a specific boundary condition for the synovial fluid are used to solve the governing system of partial differential equations for the synovial fluid and the results are provided here. We develop formulas for the interfacial velocity for both flow through special slip condition and analyse the link between the slip parameters alpha and beta . Thus, the damping force due to the porous medium naturally when we non-dimensionalize, some parameter which are controlling the structure like, beta and alpha . Through the development of an analytical solution and numerical simulation (using the finite volume approach) it is hoped that the mechanisms of nutritional transport into the synovial joint will be better understood. According to the data the average concentration has a negative connection with both the axial distance and the duration spent in the experiment. Many graphs have been utilized to gain understanding into the problem’s various characteristics including velocity and concentration, among others. Hyaluronate (HA) is considered to be present in porous cartilage surfaces and the viscosity of synovial fluid fluctuates in response to the amount of HA present.

A time-varying distributed unit hydrograph method considering soil moisture

Abstract. The distributed unit hydrograph (DUH) method has been widely used for flow routing in a watershed because it adequately characterizes the underlying surface characteristics and varying rainfall intensity. Fundamental to the calculation of DUH is flow velocity. However, the currently used velocity formula assumes a global equilibrium of the watershed and ignores the impact of time-varying soil moisture content on flow velocity, which thus leads to a larger flow velocity. The objective of this study was to identify a soil moisture content factor, which, based on the tension water storage capacity curve, was derived to investigate the response of DUH to soil moisture content in unsaturated areas. Thus, an improved distributed unit hydrograph, based on time-varying soil moisture content, was obtained. The proposed DUH considered the impact of both time-varying rainfall intensity and soil moisture content on flow velocity, assuming the watershed to be not in equilibrium but varying with soil moisture. The Qin River basin and Longhu River basin were selected as two case studies, and the synthetic unit hydrograph (SUH), the time-varying distributed unit hydrograph (TDUH) and the current DUH methods were compared with the proposed method. Then, the influence of time-varying soil moisture content on flow velocity and flow routing was evaluated, and results showed that the proposed method performed the best among the four methods. The shape and duration of the unit hydrograph (UH) were mainly related to the soil moisture content at the initial stage of a rainstorm, and when the watershed was approximately saturated, the grid flow velocity was mainly dominated by excess rainfall. The proposed method can be used for the watersheds with sparse gauging stations and limited observed rainfall and runoff data.

Multi-scale characterization and in-plane crushing behavior of the elliptical anti-chiral honeycomb

Honeycombs with anti-chiral (AC) unit cells are found to have auxetic properties and enhanced energy absorption capacities than regular hexagonal honeycombs. To further improve the energy absorption capacity, by replacing the straight cell walls of the criss-cross anti-chiral (CAC) honeycomb with elliptical cell walls, a novel elliptical anti-chiral (EAC) honeycomb is proposed in this paper. The in-plane crushing response of the EAC honeycomb is investigated numerically under different impact velocities. The numerical modeling method in ABAQUS software is validated by the compression test data of 3D-printed EAC honeycomb specimens. Both experimental and numerical results reveal that the EAC honeycomb has a plateau stage and an enhancement stage in the stress–strain curve. The empirical formulas of critical impact velocity and plateau stress are further derived, which is in good agreement with the numerical simulation results. The parameter analysis further shows that the microstructural parameters have a great influence on the crushing strength of the EAC honeycomb. Under the same impact velocity, larger semi-axis length ratio results in larger plateau stress and densification strain, while smaller semi-axis length ratio means larger initial peak stress and plateau strain.

Study on the Calculation Method of Water Inflow Velocity of Loose Rock Landslide

Landslide surges pose a serious threat to the ecological environment and human life safety. Based on rock structure mechanics and water sediment dynamics, considering the additional resistance caused by the interference of loose landslide particles on flow structure, this paper deduces the resistance calculation formula of loose-rock landslide particles when entering water. It modifies the landslide velocity formula (ASCE) recommended by the American Society of Civil Engineers. The acceleration calculation formula and velocity calculation formula of bulk-rock landslides entering water are obtained, and the determination method of the main parameters in the formula is given. Based on the data of the Xintan Landslide into the Yangtze River, the rationality of the calculation results of this formula and the ASCE formula are compared and analyzed. It shows that the ASCE formula calculates the average velocity of landslide movement on land, and there will be a noticeable deviation from the actual situation when it is used to calculate the water entry velocity of a loose-rock landslide. The formula given in this paper is more practical and can be used to calculate the velocity of loose-rock landslides entering water.

Simulation of suspended sediment transport in a floating canopy channel based on random displacement model.

In conventional research, the suspended sediment distribution in a channel under the action of floating canopy has been rarely studied. In this study, experiments on sediment transport in flume with fixed suspended vegetation were carried out under different velocity conditions. It was performed to examine the suspended sediment transport and distribution law as impacted by the floating canopy. The vertical distribution formula of velocity impacted by the floating canopy was derived based on improved two-layer theory. Combined with the random displacement model (RDM), a Lagrangian method was developed to simulate the suspended sediment transport under the action of the floating canopy. Compared with the experimental data, the R2 of vertical velocity simulation was higher than 0.96, and the vertical distribution of suspended sediment concentration varied significantly (4.64 to 19.83 g/L) following the vertical coordinate. Subsequently, the numerical model of sandy flow with the floating canopy was established by complying with the stratified sediment turbulence diffusion coefficient to predict the suspended sediment transport. Besides, the established numerical model can lay a theory basis for sediment transport in such channels (floating canopy channels).

Stock Prediction Model Based on Mixed Fractional Brownian Motion and Improved Fractional-Order Particle Swarm Optimization Algorithm

As one of the main areas of value investing, the stock market attracts the attention of many investors. Among investors, market index movements are a focus of attention. In this paper, combining the efficient market hypothesis and the fractal market hypothesis, a stock prediction model based on mixed fractional Brownian motion (MFBM) and an improved fractional-order particle swarm optimization algorithm is proposed. First, the MFBM model is constructed by adjusting the parameters to mix geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM). After that, an improved fractional-order particle swarm optimization algorithm is proposed. The position and velocity formulas of the fractional-order particle swarm optimization algorithm are improved using new fractional-order update formulas. The inertia weight in the update formula is set to be linearly decreasing. The improved fractional-order particle swarm optimization algorithm is used to optimize the coefficients of the MFBM model. Through experiments, the accuracy and validity of the prediction model are proven by combining the error analysis. The model with the improved fractional-order particle swarm optimization algorithm and MFBM is superior to GBM, GFBM, and MFBM models in stock price prediction.

A multi-dimensional two-phase mixture model for intense sediment transport in sheet flow and around pipeline

A two-phase mixture model is developed to simulate intense sediment transport covering the bed-load layer and suspended load layer. The proposed model maintains high accuracy as an Eulerian two-phase model but requires low computational cost. The proposed model applies an analytical formula for relative velocity between phases. The dense granular flow rheology is employed to close particle stress economically. The closure of Reynolds stress considers turbulence damping and small-scale fluctuation of fluid–particle interaction and particle collision. A damping function is adopted in eddy viscosity for extra turbulence damping from inter-particle interaction. The optimal exponent of the damping function refers to sediment shape and size. The sediment diffusion includes turbulence diffusion and shear-induced self-diffusion originating from dense sediment. The proposed model is validated by several sets of sheet flow cases (Shields number Θ = 0.44–2.20 and particle Reynolds number Res = 1.6–603.0) and shows a wide applicable range and good accuracy. The small-scale fluctuation and shear-induced self-diffusion improve the computation in the lower sheet flow layer where volumetric sediment concentration is larger than 0.2. Furthermore, the proposed model shows reasonable applicability on the multi-dimensional pipeline scour development. The scour profiles are well predicted and the Brier Skill Score = 0.809. However, the proposed model does not perform the wake characteristic around the pipeline sufficiently, and slight scour difference exists between the simulation and experiment.

Experimental investigation of the effects of shrub filter strips on debris flow trapping and interception

Ecological engineering plays an increasingly significant role in mountain hazard control, but the effect of species selection and arrangement (e.g., row spacing and stem spacing) on debris flow suppression is still unclear. To further understand the interception efficiency of shrub arrangement parameters on debris flow and explore the difference with slow hydraulic erosion, sixteen sets of small-scale flume experiments with different stem and row spacings were done to study the effects of shrubs on debris flow severity, flow rate, velocity, and particle size. The results suggest that, for a dilute debris flow, sediment interception effectiveness (27.4%–60.9%) decreases gradually as stem spacing increases. Moreover, as row spacing increases, flow velocity reduction (34.4%–44.9%) and flow reduction (18.5%–47.4%) gradually decrease; and the bulk density reduction (0.5%–5.3%) and sediment interception increase initially and then decrease. In contrast, for a viscous debris flow, the flow reduction, flow velocity reduction, and sedimentation interception decrease gradually as the stem spacing increases. As row spacing increases, the flow velocity reduction, flow reduction, and sediment interception all increase initially and then decrease. A formula for the flow velocity of dilute debris flow after the filter strip was derived based on the energy conservation law and Bernoulli's equation, confirming that debris flow movement is closely related to the degree of vegetation cover. This research strengthens the current understanding of the effectiveness of vegetation in debris flow disaster prevention and control and can guide practical applications.

Study on the Measurement Method of Shot Velocity and Mechanical Properties Based on Conventional Shot Peening.

Shot velocity is a crucial control parameter that is closely related to the shot peening effect. However, the traditional measurement method of shot velocity corresponding to air pressure is complicated and cannot reflect shot peening parameters (impingement angle, etc.). This study proposes a robust method to measure shot velocity by coupling simulations and experiments. By developing the measurement method presented in this paper, we can quickly and easily derive the linear shot velocity formulas corresponding to a series of impingement angles. The validity is verified and characterized by the arc height, surface roughness, residual stresses, and existing literature. The measured shot velocity can be applied to predict the effect of shot peening by the simulation method in aerospace and automotive industries. In addition, optimization of process parameters in terms of microstructure, microhardness, and mechanical properties is discussed in the context of experiments. This study shows that shot velocity is linearly related to shot peening pressure and is affected by impingement angles. The air pressure and exposure time should not be too large, and no microcracks should be created. The ultimate strength reaches the maximum, and the yield strength is significantly improved.

Numerical study on the dynamic fracture of explosively driven cylindrical shells

Research on the expansion and fracture of explosively driven metal shells has been a key issue in weapon development and structural protection. It is important to study and predict the failure mode, fracture mechanism, and fragment distribution characteristics of explosively driven metal shells. In this study, we used the finite element-smoothed particle hydrodynamics (FE-SPH) adaptive method and the fluid–structure interaction method to perform a three-dimensional numerical simulation of the expansion and fracture of a metal cylindrical shell. Our method combined the advantages of the FEM and SPH, avoiding system mass loss, energy loss, and element distortion; in addition, the proposed method had a good simulation effect on the interaction between detonation waves and the cylindrical shell. The simulated detonation wave propagation, shell damage morphology, and fragment velocity distribution were in good agreement with theoretical and experimental results. We divided the fragments into three regions based on their shape characteristics. We analyzed the failure mode and formation process of fragments in different regions. The numerical results reproduced the phenomenon in which cracks initiated from the inner surface and extended to the outer surface of the cylindrical shell along the 45° or 135° shear direction. In addition, fragments composed of elements are identified, and the mass and characteristic lengths of typical fragments at a stable time are provided. Furthermore, the mass and size distribution characteristics of the fragments were explored, and the variation in the fitting results of the classical distribution function under different explosion pressures was examined. Finally, based on mathematical derivation, the distribution formula of fragment velocity was improved. The improved formula provided higher accuracy and could be used to analyze any metal cylindrical shells with different length-to-diameter ratios.

Study on the Influence of the Blasting of Preceding Tunnel on the Pre-Penetration Surrounding Rock in Succeeding Tunnel with Small Clear Distance

To study the influence of the preceding tunnel blasting on the surrounding rock in the pre-penetration area of the succeeding tunnel, combined with the actual monitoring of the Kaifeng Mountain small clear distance tunnel, the relationship between the vibration velocity and the blasting center distance was derived according to the energy attenuation law, predicted the peak velocity of particle vibration on the pre-penetration surrounding rock, came up with the conception of surrounding rock seismic wave vibration velocity ratio, obtained its change situation, and then established a numerical model to further analyze the changes in vibration velocity, plastic strain, and stress. The results show the prediction formula of peak vibration velocity obtained from theoretical analysis of vibration velocity, which can well calculate the peak vibration velocity of some unmeasurable points in tunnel engineering and provide theoretical support for actual tunnel blasting engineering. Under the same clear distance conditions, the front blasting side of surrounding rock in the pre-penetration area of the succeeding tunnel is affected by blasting vibration more than the back blasting side, and the vibration velocity decreases gradually from the arch waist⟶arch shoulder⟶arch foot⟶vault (arch bottom), and the most unfavorable section is that the blasting surface is parallel to the surrounding rock section in the pre-penetration area of the preceding tunnel. The excavation of the lower step has greater destructive force than that of the upper step; with the clear distance that gradually increases, the impact of the preceding tunnel blasting on the surrounding rock in the pre-penetration area of the succeeding tunnel becomes smaller, and D (D is the tunnel span) is the minimum safe clear distance.

Thin-shell effects on nonlinear bubble evolution in the ablative Rayleigh–Taylor instability

The influence of thin-shell effects on the nonlinear evolution of two-dimensional single-mode ablative Rayleigh–Taylor instability (ARTI) is studied in the parameter range of inertial confinement fusion implosions. A new phase of unsaturated nonlinear bubble evolution caused by thin-shell effects is found. This is different from the traditional opinion that the bubble velocity becomes saturated after the ARTI evolution enters a highly nonlinear regime. A modified bubble velocity formula is proposed, based on the Betti–Sanz model [Betti and Sanz, Phys. Rev. Lett. 97, 205002 (2006)], considering the thin-shell effects. It is shown that the bubble velocity becomes saturated in the thick-target case after the ARTI evolution enters a highly nonlinear regime. In this case, the Betti–Sanz bubble dynamics model can predict the evolution of bubble velocity. However, when the thin-shell effects become significant in the case of kD0 < 100, where D0 is the initial thickness of the target and k is the perturbation wavenumber, the difference of the average acceleration between the bubble vertex and the spike tip can be much more significant than that of the thick-target case. In this situation, the nonlinear evolution of the ARTI bubbles will accelerate without saturation until the target breakup, which cannot be depicted by the Betti–Sanz model while the improved theory formula is applicative. The Betti–Sanz model and the improved theory formula are independent of the initial perturbation amplitude.

Measuring the Water Surface Speed of the Cikidang River as a Supporting Facility for the Development of Ecotourism Areas

Pangandaran Regency is famous for its natural beauty, especially the beauty of its beaches. In this district there are many famous beaches. Besides the beach, there are also rivers that offer beautiful views. However, not many tourists have made the rivers in Pangandaran as tourist destinations, especially the Cikidang River. Cikidang River has the potential to be used as ecotourism. In building an ecotourism area on the banks of a river, it is necessary to carry out an in-depth analysis of the damage that might occur due to erosion. One of the factors that can increase erosion is the speed of water on the surface. Therefore, in this paper, measurement of river surface velocity is carried out in a simple way and analyzed using the velocity formula. From the results of this measurement, a recommendation was made to direct all parties involved in measuring the surface velocity of the Cikidang River as a means of supporting the development of ecotourism areas.

Numerical study on the ballistic performance of prestressed concrete slabs subjected to hard missile impact

Prestressed concrete (PC) structure has been extensively used in civil engineering like nuclear and protective structures. But systematic studies on its ballistic performance are still inadequate, hindering its ballistic design and applications. In this paper, the ballistic performance of PC slabs subjected to hard missile impact is numerically investigated through finite element (FE) modeling. The method to introduce prestressing force is specially investigated and the feasibility of the established models is verified against existing experimental results. The models are then employed to conduct a comparative study between PC and reinforced concrete (RC) slabs, in which the influences of the prestress and prestressing bars are decoupled. The variations of concrete tensile strain and energy dissipation capacities of PC slabs with different failure modes are analyzed to understand the mechanism of the ballistic resistance. It is revealed that the prestress is the main reason for the enhancement of ballistic resistance of PC slabs, while the increase of reinforcement ratio due to prestressing bars is the secondary reason. It is also proved that the confinement effect applied to the concrete is the major reason for the increase in ballistic resistance. Based on the mechanism, by using mechanical and regression analysis, a semi-empirical formula for the critical perforation velocity of the PC slabs is proposed, which gives better predictions compared to existing formulas. The proposed formula also allows a straightforward parametric study, the results of which could be used for simplified estimations in the ballistic design of PC slabs.

Discrete particle swarm algorithm with Q-Learning for solving flexible job shop scheduling problem with parallel batch processing machine

For the flexible job shop scheduling problem with parallel batch processing machines (FJSP-PBPM), the mathematical model of the problem is defined, and an improved enhanced discrete particle swarm algorithm is proposed to solve this problem. In terms of global search, an improved discrete particle swarm algorithm is adopted, and effective particle velocity and position update formulas are designed; in the local search, in order to speed up the convergence speed and avoid local convergence, it is integrated into the q-learning method in reinforcement learning. The state space, action space, reward function, and Q-table update methods that meet the scheduling problem are designed, and the proposed hybrid algorithm achieves an effective balance between global search and local search capabilities. At the same time, according to the characteristics of FJSP-PBPM, effective process sequence scheduling rules and batch machine selection rules are designed respectively to improve the search ability of the algorithm. Through the standard FJSP benchmark problem and the production data of a transformer manufacturer that meets the characteristics of the FJSP-PBPM problem, the validity and feasibility of the proposed algorithm are verified.

Estimation of changes in the length of a moving conical domain wall in bistable microwire

The single domain wall process of magnetization reversal in a bi-stable microwire is studied. Models for static planar and folded planar domain walls are analyzed. The results obtained show that a folded domain wall can have lower total energy. Based on this finding, the dynamic properties of the more probable conical shape of a moving domain wall were studied. Using a simple model of the folded conical domain wall, the formulas for length, velocity, and mobility of the domain wall as a function of the applied magnetic field were derived. The main result of the proposed model is that it predicts domain wall shortening with an increasing applied magnetic field. Fitting the model function to the experimental data made it possible to estimate the characteristic length of the domain wall and changes in its shape in the magnetic field applied. Comparison of the model and experimental data indicates that there is a difference in eddy current damping for fast and slow domain walls, which may be responsible for the unidirectional effect in domain wall propagation.