Showing papers in "Flow Turbulence and Combustion in 1949"
TL;DR: In this paper, the viscous force exerted by a flowing fluid on a dense swarm of particles is described by a modification of Darcy's equation, which was necessary in order to obtain consistent boundary conditions.
Abstract: A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed by a modification of Darcy's equation. Such a modification was necessary in order to obtain consistent boundary conditions. A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation due to Carman.
2,519 citations
TL;DR: In this article, an approximate model for the fluctuations of the mean density of the particles surrounding a central one was introduced and adjusted so as to represent the experimental results. But the model was not extended to the case of catalytic particles.
Abstract: A previous calculation of the permeability of a swarm of particles is extended to closely packed particles. An approximate model is introduced for the fluctuations of the mean density of the particles surrounding a central one and adjusted so as to represent the experimental results. This refined model serves as a basis for an extension of the calculation to particles which themselves are permeable such as occur in catalyst pellets.
427 citations
TL;DR: In this paper, the radial and axial distribution of time-mean values of velocity, temperature, and gas concentration in a turbulent jet issuing from a round orifice into quiescent ambient air is described.
Abstract: This paper describes results of measurements concerning the radial and axial distribution of time-mean values of velocity, temperature, and gas concentration in a turbulent jet issuing from a round orifice into quiescent ambient air. The results show that the rates of spreading of heat and matter are mutually equal but greater than that of velocity. A constant ratio between the coefficient of transfer of heat or matter and the coefficient of shearing stress does not seem to exist. The results have been subjected to a theoretical analysis. The theory based on a constant coefficient of shearing stress across the jet gives the best agreement with measured radial velocity-distribution in a central zone of the jet. The theory based on a constant coefficient of transfer of heat or matter gives results that cover the experimental results reasonably well, again for the central zone. A better agreement, however, is obtained if the coefficient of transfer of heat or matter is assumed to contain not only a constant part but also a part proportional to the local velocity. This assumption is in agreement with the variable ratio between this coefficient and that of shearing stress.
136 citations
TL;DR: In this article, it was shown that the critical value of Weber's number for falling drops is different from the one for drops suddenly exposed to a constant air flow, which latter case occurs, for instance, during disintegration processes of liquid jets.
Abstract: A liquid globule that has a translatory motion relative to air, is split up if the speed exceeds a critical value or, inversely, if at a given speed the size of the globule is greater than a critical value. The criterion for determining whether or not the antagonism between air forces and surface tension will lead to splitting-up, is the relevant value of Weber's number. It is shown that the critical value of Weber's number for falling drops is different from the one for drops suddenly exposed to a constant air flow, which latter case occurs, for instance, during disintegration processes of liquid jets. Moreover, the critical value depends on the effect of viscosity on the deformation of the globule. The cases of a slight and of a great viscosity effect have been considered. The theory has been applied to experimental results on falling drops. The consequences for disintegration processes have been discussed.
95 citations
TL;DR: In this article, the authors deal with the behavior of the cross-spring pivot, a flexible element connecting two members of a construction and consisting of two flat springs that cross each other at an angle of, for instance, 90 degrees.
Abstract: This paper deals with the behaviour of the so-called cross-spring pivot, a flexible element connecting two members of a construction and consisting of two flat springs that cross each other at an angle of, for instance, 90 degrees To a first approximation the pivot point coincides with the point of “intersection” of the two springs By an elementary calculation we find the rigidity of the cross-spring pivot to depend to a large extent upon the size and the direction of the force to be transmitted A second calculation gives us the shift of the pivot point occurring for large angles of deflection, though for a pure bending moment only A survey of the results is given at the end of the paper
94 citations
39 citations
TL;DR: In this paper, an X-ray method, in some respects differing from Field's, was developed, the results of which diverged considerably from the figures reported by Field, and the description of the method was given.
Abstract: There are indications that the degree of crystallization in highpolymeric substances is of importance for the study of the mechanical properties. With regard to the crystallization of rubber up to now only few measurements have been made, mainly bij Field. The results, however, are in contradiction with some estimates of earlier date and therefore the necessity was felt to have them checked. An X-ray method, in some respects differing from Field's, was developed, the results of which diverged considerably from the figures reported by Field. The present article deals with the description of the method.
34 citations
TL;DR: In this article, a new electrical characteristic number is introduced which makes it possible to represent the measurements of Senftleben and Braun in a single graph, and from this graph the extra heat loss caused by an electric field of cylindrical symmetry around any horizontal wire in an arbitrary gas can be read off directly.
Abstract: If an electric field is applied between a horizontal heated wire and a concentric cylinder filled with gas, then, as first shown experimentally by Senftleben and Braun, the heat transfer from the wire is increased due to the electrostrictive forces which modify the circulation current of free convection. In analogy with the characteristic number of Grashof a new electrical characteristic number is introduced which makes it possible to represent the measurements of Senftleben and Braun in a single graph. From this graph the extra heat loss caused by an electric field of cylindrical symmetry around any horizontal wire in an arbitrary gas can be read off directly.
33 citations
TL;DR: The mathematical expressions for the stress strain relations of metals in uniaxial loading, which have been proposed by Ludwik and Hollomon and find a more general application now, are discussed in this article.
Abstract: The mathematical expressions for the stress strain relations of metals in uniaxial loading, which have been proposed by Ludwik and Hollomon and find a more general application now, are discussed. It is elucidated that these empirical formulae cannot agree with the essential behaviour of a metal during uniform straining.
29 citations
TL;DR: In this paper, it was shown that L a m b's formula for the coefficient of damping, derived for the case of a slight viscosity effect, cannot be correct.
Abstract: Solutions of the linerized hydrodynamical equations, consistent with slight deformations of the globule, are obtained in the cases of very slight and very great viscosity effect Formulae for the forced deformations are given for these cases It is shown that L a m b's formula for the coefficient of damping, derived for the case of a slight viscosity effect, cannot be correct
28 citations
TL;DR: When investigating the influence of an acceleration upon the velocity distribution and upon the resistance in a tube or canal, a distinction can be made between slowly varying motions where the resistance dominates, and quickly varying motion where the inertia dominates.
Abstract: When investigating the influence of an acceleration upon the velocity distribution and upon the resistance in a tube or canal, a distinction can be made between slowly varying motions where the resistance dominates, and quickly varying motions where the inertia dominates. When the motion varies quickly, practically all the liquid moves bodily, and the resistance only affects a small region near the walls. When the motion varies slowly, the velocity distribution differs from that of steady flow in that there is a phase lag of the central layers with respect to the peripheral layers.
TL;DR: In this paper, the authors formulated basic differential equations governing the motion of heterogeneous fluid mixtures through porous media and obtained a solution of these equations by numerical integration for the problem of a column initially filled with liquid saturated with gas, which was closed at one end and kept at a constant low pressure at the other.
Abstract: Muskat and Meres1) have formulated basic differential equations governing the motion of heterogeneous fluid mixtures through porous media. They obtained a solution of these equations by numerical integration for the problem of a column initially filled with liquid saturated with gas, which is closed at one end and kept at a constant low pressure at the other1).
TL;DR: In this article, the behavior of helical compression springs in respect to elastic stability has been investigated and it is shown that for large compressions, the difference occurring for the various end conditions are quite characteristic.
Abstract: A former statement that, as to the behaviour of helical compression springs in respect of elastic stability, it is quite immaterial whether the ends of the springs are hinged, constrained parallel or clamped, appears to be true only for compressions smaller than the original spring length. For larger compressions, on the other hand, the differences occurring for the various end conditions are found to be quite characteristic. Since we were able to realize a (cylindrical) spring with a compression larger than original length, by simply turning it inside out, the new theoretical results found for this region of compressions could be verified by experiment. These experiments demonstrated the remarkable toppling over of the coils which accompanies the transition from the stable to the unstable state. Moreover, they confirmed the existence of the characteristic differences in the behaviour of the spring for the various end conditions, though qualitatively only. An explanation for the numerical deviations occurring is only mentioned here and will be discussed more fully in a second paper.
TL;DR: In this article, the authors measured the compressibility of a 1∶3 nitrogen-hydrogen mixture at temperatures of 0°C, 25°C and 50°C up to densities of 180 Amagat (pressures up to 340 atm).
Abstract: Compressibility isotherms of a 1∶3 nitrogen-hydrogen mixture have been measured at temperatures of 0°C, 25°C, 50°C, 75°C, 100°C, 125°C and 150°C up to densities of 180 Amagat (pressures up to 340 atm). The results are discussed in connection with measurements of other authors.
TL;DR: In this article, tables are given for the thermodynamic functions of nitrogen at integral values of pressure up to 6000 atmospheres and temperatures between −125° and +50°C.
Abstract: Tables are given for the thermodynamic functions of nitrogen at integral values of pressure up to 6000 atmospheres and temperatures between −125° and +50°C.
TL;DR: In this paper, a simple relation is given between the degree of orientation and an empirical constant which makes possible a rapid determination of a sample's degree of crystallization, regardless of the orientation in the sample under investigation.
Abstract: In a foregoing article a description has been given of a method for determining the amount of crystalline rubber in stretched samples. A complication due to varying crystallite orientation in different samples appeared to interfere with the application. A simple relation is given here between the degree of orientation and an empirical constant which makes possible a rapid determination of the degree of crystallization, regardless of the orientation in the sample under investigation.
TL;DR: In this article, it was shown that the shear viscosity and the volume viscous traction can be calculated from η =λ/2(1+σv), ς=λ/3(1-2σv) where σv is a “viscous” Poisson ratio relating the rate of contractionec to the speed of elongationel.
Abstract: Experiments have shown that when concrete creeps under compression, its volume gradually diminishes, the cement flowing into the voids of the concrete. This will generally be the case in porous materials which should show both shear and volume flow, both accompanied by viscous resistances η and ζ of their own. If λ is Trouton's coefficient of viscous traction, it is shown that the shear viscosity and the volume viscosity can be calculated from η=λ/2(1+σv), ς=λ/3(1-2σv), where σv is a “viscous” Poissonratio relating the rate of contractionec to the rate of elongationel. This ratio can be calculated from a “deformational” Poisson-ratio σd by means of σv=σd+σd(d(ln e1)/dt)−1. For a 1∶2∶4 concrete at an age of two months calculation shows the following approximate values σd=0.052, σv=0.075, λ=2.4×1018, η=10.4×1017, ζ=9.4×1017 (the last three in poises).
TL;DR: In this article, an improved X-ray technique has been worked out to determine the degree of crystallinity in natural rubber, and it has been shown that the amount of crystalline rubber, both in frozen samples of raw rubber and in stretched vulcanized rubber, could be determined fairly accurately.
Abstract: An improved X-ray technique has been worked out to determine the degree of crystallinity in natural rubber. Inaccuracies which sometimes occur in quantitative X-ray measurements were eliminated and it has been shown that the amount of crystalline rubber, both in frozen samples of raw rubber and in stretched vulcanized rubber, could be determined fairly accurately. More experiments were carried out and the results are described. These results, which confirm the current views on the problem of crystallization, point to relatively low degrees of crystallization, even in highly stretched rubber, and they agree with some other experimental evidence and with a recent theoretical investigation.
TL;DR: In this article, the specific heat, energy, enthalpy, entropy, free energy, thermodynamic potential and kinetic energy of carbon dioxide have been recalculated for densities up to 600 Amagat units (pressures to 3000 atmospheres) between 25° and 150°C.
Abstract: The specific heats, energy, enthalpy, entropy, free energy, thermodynamic potential and kinetic energy of carbon dioxide have been recalculated for densities up to 600 Amagat units (pressures to 3000 atmospheres) between 25° and 150°C.
TL;DR: In this article, the authors dealt with the problem of dissipation of energy in hydraulic jumps, which is of importance in connection with the flow phenomena along weirs, sluice-gates etc.
Abstract: This paper deals with the problem of the dissipation of energy in hydraulic jumps, which is of importance in connection with the flow phenomena along weirs, sluice-gates etc. In fig. 2 the rough dimensions of the flow region investigated have been indicated. After measuring velocities and pressures in three cross sections, a net of average flow lines and orthogonal trajectories could be plotted (fig. 7) from which we calculated approximate values of the turbulent friction τns at different levels (figs. 9 and 10), making use of equation (5). The amount of energy, converted into heat per cm3 and per sec, then could be calculated with the aid of equation (3), the result being shown in figs. 11 and 12. Due to errors in measurement, to the approximate nature of the calculations and to three-dimensional currents, discrepancies in the total amount of energy were found of −7.8 and −19.3% respectively.
TL;DR: In this article, the thermodynamic functions of a 1∶3 nitrogen-hydrogen mixture were given at the temperatures 0°C, 25°C and 50°C up to 1000 atmospheres for integral values of pressure.
Abstract: Thermodynamical functions of a 1∶3 nitrogen-hydrogen mixture are given at the temperatures 0°C, 25°C, 50°C, 75°C, 100°C, 125°C and 150°C up to pressures of 1000 atmospheres for integral values of pressure.
TL;DR: In this paper, the yield value, breaking strength, elongation and hardness of polycrystalline metals were measured at room temperature and at −183°C, the difference being relatively small for the cubic facecentered and a number of hexagonal metals (e.g. Mg).
Abstract: The yield value, breaking strength, elongation and hardness of a number of pure polycrystalline metals were measured at room temperature and at −183°C. The yield value is always higher at −183°C than at 20°, the difference being relatively small (<75%) for the cubic facecentered and a number of hexagonal metals (e.g. Mg). This difference is large for the body-centered metals and for Zn, Cd and Sn. The former metals have a larger elongation at lower temperature, the latter, however, become more or less brittle at low temperature. The breaking strength and the hardness increase generally with decreasing temperature.
TL;DR: In this article, it was proved that under its own weight no buckling occurs with a vertically submerged tube, and the result is a negative one: the tube does not buckle.
Abstract: The result of this note is a negative one: it is proved that under its own weight no buckling occurs with a vertically submerged tube.
TL;DR: In this article, a hot-wire vacuum gauge connected to a special bridge is described, indifferent to voltage fluctuations or changes in the temperature of the surroundings, and the balance point of the bridge can be controlled independently of the actual gas pressure in the vacuum system.
Abstract: A hot-wire vacuum gauge connected to a special bridge (fig. 2), indifferent to voltage fluctuations or changes in the temperature of the surroundings, is described. The balance point of the bridge can be controlled independently of the actual gas pressure in the vacuum system. The heating current is adjusted in the region of maximum sensitivity for very low pressures. The instrument has been calibrated from 10−5 up to 0.1 mm Hg. Calibration curves for air, hydrogen, helium and argon are shown (fig. 6 and 7).
TL;DR: In this article, the volatility of n-decane contacted under pressure with hydrogen, methane or ethylene is investigated, and experimental data are used to discuss two calculation methods that enable equilibria of similar systems to be predicted.
Abstract: The volatility of n-decane contacted under pressure with hydrogen, methane or ethylene is investigated. The experimental data are used to discuss two calculation methods that enable equilibria of similar systems to be predicted.
TL;DR: In this article, the influence of an electric field on the heat transfer from a wire to a wire is discussed, which is especially suited for the determination of the ammonia content in mixtures of ammonia with air and, under certain limitations, in mixture of hydrogen and nitrogen, is fully automatic and continuous and can be made self-registering.
Abstract: A method of gas analysis is described which makes use of the influence of an electric field on the heat transfer from a wire, discussed in the preceding paper The method, which is especially suited for the determination of the ammonia content in mixtures of ammonia with air and, under certain limitations, in mixtures of ammonia with hydrogen and nitrogen, is fully automatic and continuous and can be made self-registering A possible application to the measurement of humidity is briefly touched upon
TL;DR: In this article, general expressions for the deflection and bending moment at a given point A (6.3 and 6.4) were given for a beam of infinite length, initially at rest, carrying a variable concentrated force.
Abstract: An elastically supported beam of infinite length, initially at rest, carries a variable concentrated force\(\overline K (\overline t )\) at a prescribed point A. General expressions are given for the deflection and the bending moment at A (6.3 and 6.4). Three special cases are considered; the first one is defined by\(\overline K (\overline t )\)=0 for\(\overline t \) and\(\overline K (\overline t )\)=K=const. for\(\overline t \); the second one by\(\overline K (\overline t )\)=0 for 0 >\(\overline t \)>\(\overline t _s \),\(\overline K (\overline t )\) given function of\(\overline t \) for 0⩽\(\overline t \)⩽\(\overline t _s \); the third one applies to problems in which, during the period of impact,\(\overline K (\overline t )\) itself is an unknown. The results given here may be of use in those railway-engineering problems in which a rail can be considered as a beam of infinite length, and in which the supporting ground has the required properties.
TL;DR: In this article, a sensitive interferometric method was developed for studying the abrasive effect of toothpastes and the structure of tooth-material was investigated. But this method is not suitable for the extraction of tooth material.
Abstract: A sensitive interferometric method was developed for studying the abrasive effect of tooth-pastes. This method revcaled also details in the structure of tooth-material.
TL;DR: In this article, it was shown that for turbulent flow of gases in long straight ducts, the factor 1/2 is to be replaced byc=0.55 for a circular, and equal to 0.4 for a flat rectangular cross-section.
Abstract: Part I. Reynolds' analogy between heat transfer and friction leads to the wellknown equationh=1/2fcpϱv. According to improved theories, for turbulent flow of gases in long straight ducts, the factor 1/2 is to be replaced byc=0.55 It is shown that for laminar flow in long ductsc is equal to 0.3 for a circular, and equal to 0.4 for a flat rectangular cross-section. Further in very short ducts an approximate theory is shown to give values that are of the same order of magnitude. Though the equationh=cfcpϱv has an approximative character, it has the advantage of being simple and generally valid for gases flowing in ducts. Applications and experimental data will be given in a subsequent article.
TL;DR: In this article, the buckling load of a prismatic girder, elastically supported and elastically clampled in a number of equidistant points, is investigated. But the endpoints of the girder are fixedly supported.
Abstract: Lately the authors have been engaged in an inquiry with respect to the safety of scaffolding constructions, as used in the erection and the repair of large buildings. A question of detail was presented by the determination of the buckling load of a prismatic girder, elastically supported and elastically clampled in a number of equidistant points. The present paper gives an answer to this problem with the understanding that the endpoints of the girder — though elastically clamped — are fixedly supported.