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Determination of the loss coefficient of elbows in the flow of low-density spherical capsule train
Abstract
Design parameters of a pipelines capsule flow can be calculated if dependence of pressure drops on flow velocity and capsule concentration of such pipelines are known. For this purpose, loss coefficients of elbows were studied experimentally in pipeline loop of I.D. 0.1 m. Elbows with central angles of 90 and 45 made of PVC were used for low-density spherical capsule train flow. The outer diameter and relative density of the capsules were 0.08 m and 0.87, respectively; the pressure drops were measured at Reynolds number range 2 x 10â´ < Re < 1 x 10âµ and for a transport concentration from 5% to 25%. Increments of the pressure gradient become larger at higher velocities and solid phase concentrations. The pressure gradients that occurred at the 90 elbow were higher than that occurred at the 45 elbow. Loss coefficient of the 90 elbow for the same flow velocity and capsule concentration in the capsules-water mixture flow is from 3 to 2 times higher than the loss coefficient at the 45 elbow. (author)
... Mathur et al. (1989), Agarwal et al. (2001) and Mishra et al. (1992); Mishra and Agarwal, (1998) conducted experimental investigations on the flow of capsules of shape factor (ψ) of 1 in HCPs, focusing on developing relationships for capsules' velocity. Ulusarslan and Teke, (2005a) ;Ulusarslan, (2007Ulusarslan, ( , 2010aUlusarslan, ( , 2010bUlusarslan, ( , 2013; Ulusarslan and Teke, (2005b) ;Uluasarslan, (2008); Uluasarslan andTeke, (2008, 2009) have carried out extensive experimental instigations on the transport of capsules of ψ ¼ 1 in HCPs for on-shore applications (i.e. horizontal pipelines), developing expressions for capsules' velocity and pressure drop within the HCP. ...
... A 1 m long outlet pipe has been used to minimise the effects of the outlet boundary condition in the test section of the pipeline. The test section is similar to that of (Ulusarslan and Teke, 2005a;Ulusarslan, 2007Ulusarslan, , 2010aUlusarslan, , 2010bUlusarslan, , 2013Ulusarslan and Teke, 2005b;Uluasarslan, 2008;Uluasarslan andTeke, 2008, 2009;Asim, 2013;Asim andMishra, 2016a, 2016b; with a 100 mm internal diameter. The pipe surface has been considered to be hydrodynamically smooth, with an absolute roughness constant (ε) of zero. ...
... The inlet boundary of the flow domain has been modelled as a velocity inlet, where the inlet flow velocity can vary from 1 to 4 m/sec, depending on the operating conditions considered, as considered by many other researchers (Ulusarslan and Teke, 2005a;Ulusarslan, 2007Ulusarslan, , 2010aUlusarslan, , 2010bUlusarslan, , 2013Ulusarslan and Teke, 2005b;Uluasarslan, 2008;Uluasarslan andTeke, 2008, 2009;Asim, 2013;Asim andMishra, 2016a, 2016b;. The outlet boundary of the flow domain has been modelled as a pressure outlet at atmospheric conditions (see Table 3). ...
... After that, many relevant scholars have also analyzed and optimized the power device and capsule fabrication process in the capsule transportation system, further improving the technology [15]. Ulusarslan [16] studied the effects of the size and arrangement of the capsule on its movement speed. Kollár et al. [17] studied the relationship between the movement velocity of the capsule and its geometric parameters and Reynolds number and obtained the optimal diameter of the capsule based on the minimum energy consumption. ...
... Li et al. [21][22][23] studied the movement characteristics of the capsule under different length-diameter ratios, flow discharges, and transporting load conditions, established a movement model of the capsule under various influencing factors, and analyzed the energy consumption of the capsule in the process of transporting materials. Ulusarslan and Teke [24,25], as well as Ulusarslan [16], studied the pressure drop of flow during the movement of a low-density spherical capsule and analyzed the relationship between the pressure drop of flow and the density of the capsule. Ginevskii et al. [26] analyzed the relationship between the flow pattern and the movement velocity of the capsule and concluded that when the flow pattern was turbulent, the velocity of the capsule was greater than the average velocity of the carrier. ...
Capsule hydraulic transportation is a kind of low-carbon and environmentally friendly pipeline transportation technique. In this study, the flow velocity characteristics in the pipeline when the capsule is transported in a straight pipe section were simulated by adopting the RNG (Renormalization Group) k–ε turbulence model based on Fluent software and experimentally verified. The results showed that the simulated value of flow velocity in the pipeline was basically consistent with the experimental value during transportation of the material by the capsule, and the maximum relative error was no more than 6.7%, proving that it is feasible to use Fluent software to simulate the flow velocity characteristics in the pipeline when the capsule is transported in a straight pipe section. In the process of material transportation, the flow velocity distribution of the cross-section near the upstream and downstream sections of the capsule was basically the same, which increased with the increased length–diameter ratio of the capsule. The axial flow velocity was smaller in the middle of the pipe and larger near the inner wall of the pipe. From the inner wall to the center of the pipe, the radial flow velocity first increased and then decreased. The circumferential flow velocity was distributed in the vicinity of the support body of the capsule. The axial flow velocity of the annular gap section around the capsule first increased and then decreased from the inner wall of the pipe to the outer wall of the capsule. In the process of transporting materials, the influence of the capsule on the flow of its downstream section was greater than that of its upstream section. These results could provide a theoretical basis for optimizing the technical parameters of capsule hydraulic transportation.
... Taimoor et al. [17][18][19] studied the movement velocity of rectangular, cylindrical, and spherical capsules, analyzed the relationship between the geometry of the capsule and the flow pressure in the pipeline, and derived the semiempirical formula for calculating the flow pressure drop in the pipeline when the capsule moved in the pressurized pipe. Deniz et al. [20] studied the pressure distribution of flow in the pipeline when the capsule moved under the conditions of different flow discharges, different density of the capsule, and different elbow angle and determined the pressure gradient of flow in the pipeline gradually increased with the increase of flow discharge, density of the capsule, and elbow angle. Li et al. [21][22][23] studied the movement characteristics of the capsule under different length diameter ratio, flow discharge, and transporting load conditions, established the movement model of the capsule under various influencing factors, and analyzed the transporting energy consumption of the capsule in the process of transporting materials. ...
As a clean, low-carbon, and green hydraulic transportation technology, wheeled capsule pipeline hydraulic transportation is a transportation mode conducive to the sustainable development of the social economy. Based on the method of a physical model experiment and hydraulic theory, the flow velocity characteristics in the pipeline when the wheeled capsule with a length–diameter ratio of 2.5 and 2.14, respectively, was transported in the straight pipe section with an inner diameter of 100 mm were studied in this paper. The results show that in the process of transporting materials, the flow velocity distribution of the cross section near the upstream and downstream section of the capsule was basically the same, and the axial velocity was smaller in the middle of the pipe and larger near the inner wall of the pipe. The radial velocity distribution was more thinly spread near the pipe wall and denser near the center of the pipe. The circumferential flow velocity was distributed in the vicinity of the support body of the wheeled capsule. For any annular gap section around the wheeled capsule, the radial velocity of annular gap flow was very small, and the average radial velocity of annular gap flow was about 1/30 of the average axial velocity of annular gap flow and about 0.7 of the average circumferential velocity of annular gap flow. The axial, circumferential, and radial flow velocities on the same radius measuring ring changed with the polar axis in a wave pattern of alternating peaks and troughs. These results can provide the theoretical basis for optimizing structural parameters of the wheeled capsule.
... Consequently, head loss occurs mostly in piping fittings such as reducers, expansions, elbows, tees (a 3-way connector) and 4-way connectors. There are a number of different methods for obtaining head loss coefficients in pipeline fittings [74]- [77]. Analytical methods are generally based on the Herschel-Bulkley model [78]. ...
Dynamic thermal-hydraulic simulation models have been extensively used by process industry for decision support in sectors such as power generation, mineral processing, pulp and paper, and oil and gas. Ever-growing competitiveness in the process industry forces experts to rely even more on dynamic simulation results to take decisions across the process plant lifecycle. However, time-consuming development of simulation models increases model generation costs, limiting their use in a wider number of applications. Detailed 3D plant models, developed during early plant engineering for process design, could potentially be used as a source of information to enable rapid development of high-fidelity simulation models. This paper presents a method for automatic generation of a thermal-hydraulic process simulation model from a 3D plant model. Process structure, dimensioning and component connection information included in the 3D plant model is extracted from the machine-readable export of the 3D design tool and used to automatically generate and configure a dynamic thermal-hydraulic simulation model. In particular, information about the piping dimensions and elevations is retrieved from the 3D plant model and used to calculate head loss coefficients of the pipelines and to configure the piping network model. This step, not considered in previous studies, is crucial for obtaining high-fidelity industrial process models. The proposed method is tested using a laboratory process and the results of the automatically generated model are compared with experimental data from the physical system as well as with a simulation model developed using design data utilized by existing methods on the state-of-the-art. Results show that the proposed method is able to generate high-fidelity models which are able to accurately predict the targeted system, even during operational transients.
... The cost of pipe per unit weight of the pipe material is given by Ref. [54]: (19) where t is the thickness of the pipe wall, g p is the specific weight of the pipe material and c 2 is the cost of the pipe per unit weight of the piping material. According to Davis and Sorenson [55], and Russel [56], the pipe wall thickness can be expressed as: ...
The scarcity of fossil fuels is affecting the efficiency of established modes of cargo transport within the transportation industry. Efforts have been made to develop innovative modes of transport that can be adopted for economic and environmental friendly operating systems. Solid material, for instance, can be packed in rectangular containers (commonly known as capsules), which can then be transported in different concentrations very effectively using the fluid energy in pipelines. For economical and efficient design of such systems, both the local flow characteristics and the global performance parameters need to be carefully investigated. Published literature is severely limited in establishing the effects of local flow features on system characteristics of Hydraulic Capsule Pipelines (HCPs). The present study focuses on using a well validated Computational Fluid Dynamics (CFD) tool to numerically simulate the solid-liquid mixture flow in both on-shore and off-shore HCPs applications including bends. Discrete Phase Modelling (DPM) has been employed to calculate the velocity of the rectangular capsules. Numerical predictions have been used to develop novel semi-empirical prediction models for pressure drop in HCPs, which have then been embedded into a robust and user-friendly pipeline optimisation methodology based on Least-Cost Principle.
The scarcity of fossil fuels affects the efficiency of established modes of cargo transport within the transportation industry. Extensive research is being carried out on improving the efficiency of existing modes of cargo transport, as well as developing alternative means of transporting goods. One such alternative method is using energy contained within fluid flowing in pipelines to transfer goods from one place to another. The present study focuses on the use of advanced numerical modelling tools to simulate the flow within hydraulic capsule pipelines (HCPs) transporting spherical capsules with an aim of developing design equations. Hydraulic capsule pipeline refers to the transport of goods in hollow containers (“capsules”), typically spherical or cylindrical in shape, which are carried along the pipeline by water. HCPs are used in mineral industries and have potential for use in oil and gas sector. A novel modelling technique was employed to carry investigate various geometric and flow conditions within HCPs. Both qualitative and quantitative flow analysis was carried out on the flow of spherical capsules in an HCP for both on-shore and off-shore applications. Furthermore, based on the least-cost principle, an optimization methodology was developed for the design of single stage HCPs. The input to the optimization model is the solid throughput required from the system, and the outputs are the optimal diameter of the HCPs and the pumping requirements for the capsule transporting system. This article is protected by copyright. All rights reserved
To explore pressure drop in a hydraulic capsule transportation pipeline and pressure between two moving capsules extensively, the pressure distribution in the annular gap between a capsule and the pipe, the pressure distribution between two capsules as well as the pressure drop across capsules were measured and analyzed by using two capsules (length-100 mm, diameter-60 mm, weight-750 g) in 10 cm apart at 30, 40, 50, 60 and 70 m3/h flow rates. It is shown that the pressure in each test section increases with increasing flow rate. At a certain flow rate, the pressure on the capsule body presents a minimum. The pressure drop across the second capsule is substantially higher than that across the first one. In the annular gap, the pressure is low on the pipe wall and capsule body, but is the highest in the middle of the gap. The pressure shows a decline downstream in the gap of the first capsule, further the pressure gradient in the gap of the second capsule is higher than that in the first one. Under various flow conditions, the pressure distribution between two capsules is uneven in some degree, but the maximum pressure is achieved on the pipe wall and the minimum one is nearly at the pipe centre. The pressure gradient between two capsules increases with flow rate.
This study proposes a numerical simulation of the unsteady turbulent flow of a single coal log in a pipe using a dynamic mesh method. An eccentric two-dimensional dynamic model is developed in FLUENT 6.2. The model contains a straight section and a bent section. Comparisons of the coal log velocity and the pressure distributions of the pipe and the coal log surface are made between the calculated results and the experimental data. The shear force and the friction coefficient are also calculated to verify changes of the influence of water on the coal log. The results of this simulation display the dynamic motion of the coal log for startup and turning. Water drag force moves the coal log making the coal log velocity greater than the water velocity. The lifting force lifts the coal log and moves its tail slightly upward. The pressure drop of the whole pipe is respectively larger in the presence of the coal log. The pressure along the coal log surface slowly declines. The appearance of a bend impedes the motion of the coal log and enhances abrasion. The coal log has difficulty being suspended due to decreased lifting force and increased friction. The pressure on the coal log surface rises. This article is protected by copyright. All rights reserved
One of the most important parameters in designing a capsule transporting pipeline is the pressure drop in the pipes carrying capsules and associated pipe fittings such as bends etc. Capsules are hollow containers with typically cylindrical or spherical shapes flowing in the pipeline along with the carrier fluid. The dynamic behavior of a long train of capsules depends on the behavior of each capsule in the train and the hydrodynamic influence of one capsule on another. Researchers so far have used rather simplified empirical and semi-empirical correlations for pressure drop calculations, the range and application of which are fairly limited. Computational Fluid Dynamics (CFD) based techniques have been used to analyze the effect of the presence of solid phase in hydraulic bends. A steady state numerical solution has been obtained from the equations governing turbulent flow in pipe bends carrying spherical capsule train consisting of one to four capsules. The bends under consideration are of 45° and 90° with an inner diameter of 0.1m. The investigation was carried out in the practical range of 0.2 ≤Vb≥ 1.6 m/sec. The computationally obtained data set over a wide range of flow conditions has been used to develop a rigorous model for pressure drop calculations. The pressure drop along the pipe bends, in combination with the pressure drop along the pipes, can be used to calculate the pumping requirements and hence design of the system.
Design parameters of pipelines for capsule flow (i.e., power of pumps, number of pumps, diameters of capsules, diameter of pipe, etc.) can be calculated if pressure drops of such pipelines are estimated. All major and minor losses that incur at various levels depending on the diameter and type of pipeline selected for hydraulic transportation of capsule trains must be compensated for by the pump. For this purpose, the effect of the different diameter ratios (0.8 and 0.72) on the loss coefficient of elbows (at angles of 90°) in the flow of low-density spherical capsule train was studied experimentally. Relative density of the capsules was 0.87 and their pressure drops were measured at a range of 1.2 × 104 < Re < 1.5 × 105 and for transportation concentrations from 5 to 15%. Results of this experiment indicate that the higher the concentration, the higher the loss coefficient of the elbow. The increment of the elbow loss coefficient is nearly negligible with increasing the bulk velocity for capsule concentrations up to 10%, but is significantly influenced by the capsule concentration. The effect of the different diameter ratios on the loss coefficient of the elbow is negligible for low capsule concentration.
Critical Reynolds numbers were revealed by the study at which the velocity ratio curves typically achieved minimum or maximum values. The pronounced critical condition at Reynolds number about 1,000 is of particular interest, falling as it does in the middle of the Reynolds number range widely regarded as yielding laminar flow in a long circular pipe, but coinciding with the first manifestations of turbulence reported in previous studies. Velocity ratios for both spherical and cylindrical capsules were found to vary from about 1.10 to 1.75 in the laminar flow regime, and from 1.10 to 1.30 at the highest Reynolds numbers.
The paper presents the result of experimental investigation of the effect of mean carrier liquid velocity U SUB o, capsule velocity U SUB k, volumetric concentration C SUB v, capsule/pipe diameter ratio d/D and capsule shape B 1 on the capsule/liquid velocity ratio U SUB k/U SUB o and pressure gradient i SUB k of the system when the rigid heavy capsule trains are conveyed by turbulent stream of water in curved (a quadrantal bend) horizontal pipe of inner diameter (-0.05 m. Pressure gradient in the bend was observed to be substantially higher than in the straight pipe - about 25% for castor mounted capsules, 42% for flat ended and over 50% for ellipsoidal/flat ended capsules. The increment of pressure gradient depends first of all on the shape of the capsule. (English abstract)
New layered bismuth oxides Bi2(BiCaNa)m−1NbmO3m+3(m=2-4) with the Aurivillius type phase were successfully synthesized. The structures of the compounds have been studied by X-ray powder diffraction and refined by the Rietveld method. Bi2.25Ca0.5Na0.25Nb2O9(m=2) has an orthorhombic crystal structure with lattice constants a=5.4478(1) Å;b=5.4770(2) Å;c=24.883(8) Å, space group A21am (No. 36). Bi2CaNaNb3O12 and Bi2.25Ca0.5Na1.25Nb3O12(m=3) are orthorhombic with Fmmm(No. 69) space group and the unit-cell parameters a=5.4473(7) Å, b=5.4770(3) Å, c=32.722(6) Å and a=5.4574(7) Å, b=5.4884 (3) Å, c=32.711(6) Å, respectively. The structure of Bi2CaNa2Nb4O15(m=4) was found to be orthorhombic with parameters a=5.4584(8) Å, b=5.4833(3) Å, c=40.534(1) Å and was refined in the space group A21am (No. 36).
Hydraulic capsule pipelining is defined as the transport of commodities encapsulated in containers conveyed by carrier liquid in pipe. Since the first introduction of this concept in 1958, great progress has been made in understanding the hydrodynamics of capsule-liquid flow in pipe and also in development of hardware components and assessment of the economics of potential applications of capsules pipelining. This chapter presents the results of an experimental investigation of capsules conveyed by water in horizontal bend and straight inclined pipes. The effect of pipe curvature and inclination and geometrical and physical parameters of capsules on capsule threshold velocity, capsule/liquid velocity ratio, and hydraulic gradient of the system was evaluated. It was found that the capsule/liquid velocity ratio is not significantly influenced by pipe curvature. In an ascending pipe a decrease of the velocity ratio depends on length, angle of inclination and capsule/liquid density ratio; in a descending section of pipe the opposite is valid. The pressure gradient in the bends is substantially higher in comparison to the straight pipe sections. For inclined pipe the pressure gradient increment/decrement depends on the angle of inclination, density ratio, and capsule concentration.
An experimental investigation was carried out to determine pressure drops of the flow of a two-phase mixture of spherical ice capsules and water inside the pipelines of cooling systems. Instead of ice capsules, spherical capsules made of polypropylene material whose density (870kg/m3) is similar to that of ice were used in the experiments. Flow behavior of the said spherical capsules, 0.08m outer diameter, was observed in the measuring section inside plexiglass pipes, 0.1m inner diameter and 6m in length; pressure drops were measured on the 4m section. The investigation was carried out in the 1.2×104
This paper deals with the effect of bulk fluid velocity, diameter and length ratios, apparent density and volumetric concentration on the capsule/liquid velocity ratio, pressure gradient of the capsule flow in the pipe and on the position of capsules. The position and shape deformation of semi-rigid capsules contributed to the explanation of the effect and distribution of the transversal hydrodynamic forces, acting on a capsule. Measurements were carried out in a horizontal straight plexiglass pipe of inner diameter 0.05 m and water was used as a carrier liquid. It was found that the semi-rigid capsule trains reached lower velocities than the rigid ones for the regime given by Reynolds number (Re) lower than 5×104, whereas the opposite holds for the region where the Re exceeds 105. The semi-rigid capsule trains have about 20% lower pressure gradient than trains consisted of identical solid cylindrical capsules for the regime given by Re lower than 5×104, for the higher flow velocity this effect gradually disappears.
In the present paper, the flow behavior of single capsules of regular shape transported by two mineral oils of kinematic viscosities 45 and 7 centistokes respectively, in a 1 1/4-inch diameter pipeline, are reported. In terms of pipe Reynolds number this means that the data for the more viscous oil were obtained for the laminar flow regime and the data for the less viscous oil were obtained, for the most part, for turbulent flow. A specific gravity range of 1.19-7.86, a capsule diameter/pipe diameter ratio range of 0.39 (0.40)-0.89 (0.90) and in the case of cylinders, lengths of 2-in., 4-in., and 7-in. were investigated.
On rapporte, dans le present article, le comportement de capsules de forme régulière dans deux huiles minérales, dont les viscosités cinématiques sont de 45 et 7 centistokes, s'écoulant dans un conduite de 1 1/4 pouce de diamètre. Si l'on considère le nombre de Reynolds par rapport au tuyau les données ont été obtenues en régime laminaire pour la première huile et principalement en régime turbulent pour la seconde. Les régions suivantes ont été étudiées: densite 1.19 à 7.86; diamétre de capsule/diamètre du tuyau 0.39 (0.40) à 0.89 (0.90); longueur des cylindres 2″, 4″ et 7″.
The pressure gradients due to cylindrical capsules were reduced by up to 80% by providing them with plastic instead of steel surfaces or by fitting them with collars. The power requirements of a capsule pipeline depend greatly on the capsule density, and if the capsules were constructed so that a third of the volume consisted of voids, the power needed to transport two teragrammes (2 million tons)/year of solid with a density of 1500 kg.m−3 (S.G. = 1.50) in a 254 mm (10 in.) pipeline would be reduced by over 90%. The pressure gradients and power required to transport spherical capsules were generally much smaller than those required for even the smoothest cylinders of the same specific gravity.On a réduit de pourcentages allant jusqu'à 80% les gradients de pression causés par des capsules cylindriques; on y a réussi en remplaçant l'acier de leurs surfaces par du plastique ou en munissant les capsules de colliers. Les exigences en énergie d'un pipe-line servant à transporter des capsules dépendent beaucoup de la densité de celles-ci; si on les construisait de manière qu'un tiers de leur volume soit formé d'espace vide, l'énergie requise pour transporter, par année, 2 millions de tonnes de matiéres solides d'une densité de 1500 kg/m−3 (poids spécifique 1.50) dans un pipe-line de 254 millimètres (10 pouces) serait réduite de 90%. Les gradients de pression et l'énergie nécessaires pour transporter des capsules sphériques se sont avérés bien plus faibles que ceux qui étaient requis, même dans le cas des cylindres dont la surface était la plus lisse et qui possédaient le même poids spécifique.
Single plastic and aluminum spheres of five different diameters transported by water in a laboratory pipeline travelled at velocities from 4% to 8% greater than the average water velocity when the latter was more than 2 ft./sec. and the diameter of the spheres was over half the pipe diameter.
A short high-speed photographic investigation showed that the percentage of sliding experienced by the spheres of both materials increased both with increase of water velocity and decrease of sphere diameter, and that it was considerably greater for the plastic spheres. However, motion was predominantly by rolling.
Des sphères de plastiques et d'aluminium de 5 diamètres différents sont placées individuellement dans une conduite dans laquelle L'eau circule à une vitesse supérieure à 2 pi/sec. On a noté que les sphères, ayant un diamètre supérieur à la moitié du diamètre de la conduite, s'écoulent à une vitesse de 4 à 8% supérieure à la vitesse moyenne de L'eau.
Des photographies à grande vitesse montrent que le glissement des sphères augmente avec une augmentation de la vitesse de L'eau et une diminution du diamètre. Les sphères de plastique exhibent un glissement supérieur. Cependant, le déplacement se fait principalement par mouvement de rotation.
Critical Reynolds numbers were revealed by the study at which the velocity ratio curves typically achieved minimum or maximum values. The pronounced critical condition at Reynolds number about 1,000 is of particular interest, falling as it does in the middle of the Reynolds number range widely regarded as yielding laminar flow in a long circular pipe, but coinciding with the first manifestations of turbulence reported in previous studies.
Velocity ratios for both spherical and cylindrical capsules were found to vary from about 1.10 to 1.75 in the laminar flow regime, and from 1.10 to 1.30 at the highest Reynolds numbers.
L'étude des valeurs minimum et maximum des courbes du rapport des vitesses capsule/fluide a révélé des nombres de Reynolds critiques. La condition critique qui se produit pour un Re d'environ 1000 est d'intérět particulier car on y trouve la première manifestation de turbulence bien que ce nombre de Reynolds soit au centre d'une région considérée laminaire pour L'écoulement dans un tuyau.
Le rapport des vitesses varie de 1.10 à 1.75 pour le régime laminaire et de 1.10 à 1.30 pour les nombres de Reynolds les plus élevés et ce, pour les capsules cylindriques et sphériques.
With water as the conveying liquid the pressure gradient of a train of spheres is comprised of a basic pressure gradient due to shear of the surrounding liquid, to which has to be added a very small density‐dependent increment due to solid friction, and a further increment due to any irregularity of the spheres. With viscous liquids the pressure gradient generally rises rapidly with specific gravity and with increase of viscosity.
Even at the low specific gravity of 1.25 the power require‐nients of cast spheres conveyed by water are generally lower than those of smooth cylinders, and the advantage increases with increase of specific gravity. However, the lower power require‐uient has to be weighed against the possibly greater cost of forming spheres, and the cost of larger pipe that would be neces‐sary to secure a given throughput, particularly if the spheres were run at low velocities to secure very low pressure gradients.
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The pipeline flow of heavy solid capsules
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The pipeline flow of capsules – Part 3 – an experimental investigation of the transport by water of single cylindrical and spherical capsules with density equal to that of the water
- Ellis