Measurement Of Terminal Velocity Research Articles

Crack Velocity in Thermally Tempered Glass

Using Cranz-Schardin camera, measurement of terminal velocity for thermally tempered glass has been attempted. Tempered 3.5mm-thick glass plates with three different levels of surface residual compressive stresses were used. It has been shown that the terminal velocity of fully tempered glass is 1.500×103m/s, and that a linear relation exists between the terminal velocity and the suface compressive stress.

Analyses of Wolf-Rayet ultraviolet spectra

Ultraviolet spectra of population I WR stars obtained from IUE archive are used to determine fundamental stellar parameters. Terminal velocities for 85 galactic and LMC Wolf-Rayet stars were obtained by means of the empirical relation between spectral quantities easily measured in low resolution and high-resolution terminal velocity measurements. Temperatures and so-called transformed radii were derived based on available contour plots of spectral characteristics for a grid of NLTE models. The effect of the reddening law on stellar far ultraviolet continua is emphasized and the revised extinction curve towards WR stars is used for dereddening. For the sample of stars attributed to open clusters or associations we construct the stellar distance scale and adopt it for the other WR stars. The remaining fundamental parameters are derived and HR diagram for population I WR stars is presented.

Flow past a sphere in polystyrene-based Boger fluids: the effect on the drag coefficient of finite extensibility, solvent quality and polymer molecular weight

This study experimentally investigates how the drag behavior of a sphere falling in a Boger fluid is affected by the fluid's extensibility, solvent quality and chain molecular weight. By means of terminal velocity measurements under conditions of creeping flow, deviations from Newtonian drag behavior in a homologous series of three polystyrene-based Boger fluids were measured as a function of Weissenberg number ( We). The polymer-solvent quality and polymer molecular weight of each of the Boger fluids were manipulated in a manner that produced a systematic variation in the degree of extensibility of the fluids. Here, we define extensibility in terms of the FENE model parameter L, the ratio of a fully extended coil length to an equilibrium coil length. It is expected that L varies by nearly a factor of three over this series of Boger fluids. The compositions and ranking of the degree of extensibility of the three Boger fluids are the following: a high extensibility fluid of 2.0 × 10 7 g mol −1 polystyrene in a poor, dioctyl phthalate (DOP)-based solvent, a medium extensibility fluid of 2.0 × 10 7 g mol −1 polystyrene in a good, tricresyl phosphate (TCP)-based solvent and a low extensibility fluid of 2.0 × 10 6 g mol −1 polystyrene in a poor DOP-based solvent. The principal result of the falling sphere experiments is that while the low extensibility fluid shows only small deviations from Newtonian behavior at all tested We, the two fluids of greater extensibility show drag enhancement of more than 300% for We > 1. These experiments are in agreement with the earlier work of Tirtaatmadja et al. and Chmielewski et al., indicating that the drag does not correlate with We alone. Here, by using monodisperse polymers and systems in which the polymerssolvent interactions have been characterized, we are also able to determine the sensitivity of the dimensionless drag to polymer molecular weight and polymer-solvent quality.

On the relation of the terminal fall speed of hydrometeors to environmental conditions and particle size and density

Expressions are derived which relate the terminal fall speed of hydrometeors to their size and density and to the environmental parameters of the air, and for extrapolating terminal velocity measurements under known conditions to other conditions and altitudes. The formulation is an extension of previous work and is based on the assumption that on average the drag coefficient is related to the Reynolds number by a simple power law over a reasonable range of Reynolds numbers. This is shown to imply a power law dependence between the terminal fall speed and diameter of a particle, as is often observed, and also to be consistent with empirical power law relations between the Best and Reynolds numbers of falling particles. A set of terminal fall speed parameters is presented which is representative of a variety of precipitation types.

New equations for the terminal velocity of precipitation droplets in a standard atmosphere

New equations are presented which give the terminal velocity of water droplets in three physically distinct drag regimes explicitly as functions of equivalent drop radius and height in a standard atmosphere. It is shown that at h = 0 , the expressions give results which agree with Gunn and Kinzer's terminal velocity measurements with an overall divergence less than the measurement uncertainty of the data. Results are also compared with the semi-empirical formulations of Beard and shown to be in good agreement at all drop sizes 0.25 r0 3500 μm and heights -1.5 h 5 km in the atmosphere.

Terminal velocities of the winds from rapidly rotating OB stars

This paper presents measurements of terminal velocities of OB stars which are rapid rotators, based on archival high-dispersion IUE spectra of the C IV resonance doublet. The terminal velocities of the most rapidly rotating stars appear to be systematically lower than those of the less rapidly rotating stars (at least for the cooler stars), although the number of very rapid rotators is only three. The modified line-radiation driven wind model of Friend and Abbott, which takes into account the finite size of the star as well as its rotation, predicts that the terminal velocity should drop with increasing rotational velocity. However, when a smaller but very homogeneous subset of the data is used (BO giants only), the correlation between terminal velocity and rotational velocity disappears.

Measurement and Interpretation of Hailstone Density and Terminal Velocity

Abstract The mass, density, fall velocity and internal structure have been determined for low-density hailstones from an truly spring storm in Boulder, Colorado, and drag coefficients were calculated. The density of the permeable hail is determined from a new method of volume measurement. The results are compared to those of particles grown in a one-dimensional parcel model using the appropriate sounding. The implications of the results are discussed with reference to hail growth in convective storms.

Measurement of Dynamic Proppant Fall Rates in Fracturing Gels Using a Concentric Cylinder Tester (includes associated paper 9970 )

Summary This paper describes the measurement of proppant terminal velocity in a simple non-Newtonian gel during shear. The shear was imposed between Lucite™cylinders with the outer cylinder rotating. During rotation, a proppant particle was introduced and the terminal velocity was measured. This measurement then was compared with Stokes law measurement then was compared with Stokes law using the fluid's apparent viscosity at the known shear rate for the Newtonian viscosity. This results in a good correlation between measured and theoretical data. Introduction Most of the early work done on sand settling used vertical fracturing models. Kern et al.1 and Babcock et al.2 reported on tests performed in such models which defined equilibrium bank height and equilibrium velocities. Novotny3also used a vertical model in his proppant transport study. Wahl4 studied the transport of proppants in a horizontal model. A knowledge of particle settling velocity is a necessary input in all design techniques that describe the final location of proppants in the fracture. For Newtonian fluids, the measurement of settling velocity is straightforward since their viscosity remains constant with variations in shear rate. For these fluids, particle settling velocity will follow Stokes law for particle Reynolds numbers less than two. For all but very thin fracturing fluids, particle Reynolds numbers will be in this range. Under these conditions, single particle settling velocity will follow Stokes law:Equation 1 This is the settling velocity for a single particle in an infinite media. Most fracturing gels, on the other hand, are non-Newtonian in character and are considered to follow the power law:Equation 2 Under these conditions, Stokes law becomesEquation 3 From this equation, settling velocity becomes a function of shear rate. As shown by Novotny,3 shear rate (?) consists of two components: a horizontal component imposed by fluid motion and a vertical component imposed by particle settling. The vertical shear rate can be expressed by V/d, and the combined shear rate becomesEquation 4 This shear rate expression leads to an altered form of Eq. 3. For the fluids used in these tests, the vertical shear rate V/d is very small and can be ignored without significant error. The experiments conducted were designed to see how closely dynamic particle fall velocity would follow Stokes law for the shear rate range imposed by the test device. If the measured values agreed with Stokes law, only a knowledge of shear rate would be required to predict settling velocity. Novotny3 found a good correlation working with a similar tester. The fluids used in our test were somewhat more viscous than shown by Novotny.3

The influence of shape on the atmospheric settling velocity of volcanic ash particles

Experimental measurements of terminal fall velocities at sea level are reported for pumices, glass shards, and feldspar crystals with mean diameters between 30 and500 μm. The velocities depend significantly on particle shape and rotation mode as well as density and size. Six tumbling modes were observed, of which two are predominant. The measurements have been converted to drag coefficients and Reynolds numbers so that they can be used to compute terminal velocities at any height in the atmosphere. It was found that if the drag coefficient and Reynolds number are defined empirically in terms of the arithmetic mean particle diameter, the effects of shape and rotation can be fully accounted for by defining a shape parameter, F, for each particle. In terms of the lengths of the longest, intermediate and shortest principal axes of the particle, denoted a, b, and c, respectively, F =(b + c)/2a. A simple formula for the drag coefficient, C a, as a function of Reynolds number, R a, and shape parameter is: [Display omitted] A more fundamental analysis allows the measurements made here to be compared with theoretical curves and experimental data on simple particle shapes from wind tunnel studies.

Ice Crystal Terminal Velocities

Terminal velocities of different ice crystal forms were calculated, using the most recent ice crystal drag coefficients, aspect ratios, and densities. The equations derived were primarily for use in calculating precipitation rates by sampling particles with an aircraft in cirrus clouds, and determining particle size in cirrus clouds by Doppler radar. However, the equations are sufficiently general for determining particle terminal velocity at any altitude, and almost any crystal type. Two sets of equations were derived. The 'general' equations provide a good estimate of terminal velocities at any altitude. The 'specific' equations are a set of equations for ice crystal terminal velocities at 1000 mb. The calculations are in good agreement with terminal velocity measurements. The results from the present study were also compared to prior calculations by others and seem to give more reasonable results, particularly at higher altitudes.

An Equivalent Disc for Calculating the Terminal Velocities of Plate-Like Ice Crystals

Abstract Measurements of terminal velocities of metal models of plate-like ice crystals in a tank containing various concentrations of glycerol in water suggest that the terminal velocities of a given model can be predicted from that of a disc made of the same material having the same mass and thickness. The terminal velocities of the models are less than that of the corresponding disc by a factor determined by the shape of the model. This factor is a maximum at 25% for the star-shaped model. These results are independent of the material of the disc or liquid and cover a Reynolds number range of at least 0.5 to 200; they are therefore applicable to plate-like ice crystals falling in air.

On the Drag of a Sphere In Polymer Solutions

The relationship between the coefficient of drag and the Reynolds number on a sphere in the polymer solutions was studied experimentally through on the measurement of terminal velocity and the observation of flow about a falling sphere. And then, the effectiveness of Stokes's law and Perry's curve for the concentrated polymer solutions (CMC & PED) in the range of low Reynolds numbers (less than 103) was examined using Re* instead of Re and the drag reduction of very dilute polymer solutions (PEO) in the range of high Reynolds numbers (more than 5×103) was confirmed. Besides, it was shown that such a drag reduction was characterized by two dimensionless numbers, Reynolds number (Re) and Weissenberg number (Rn*: Reiner-Rivlin model or Ne*: Combination model).

Terminal Velocity of Raindrops Aloft

Abstract The inadequacy of previous calculations of terminal velocities at other than sea level conditions is discussed. Attention is called to actual measurements of terminal velocities at different air densities, and empirical formulae are presented which fit the data very closely.

Internal Circulations within Liquid Drops

IT has long been recognized that under certain conditions some sort of axisymmetric flow is induced within liquid drops as they pass through a viscous medium. The factors which promote and inhibit such internal circulations have been established experimentally for liquid-liquid systems, but there is little or no direct evidence that comparable vortical flows are formed within water drops falling through the atmosphere. In liquid-liquid systems the pattern of flow is generally mapped on a photographic film by the images of small opaque particles moving with the fluid. Garner and Haycock1 made some velocity measurements by obtaining such photographs with a carefully calibrated moving-picture camera and noting the change in position of the particle during a known time interval. However, most of the velocity data have been inferred from terminal velocity measurements and rates of heat and mass transfer between the drop and continuous phases.

The behaviour of particles in a sinusoidal velocity field

A non-linear Langevin equation has been developed that represents the general behaviour of free particles in a sinusoidal velocity field. Analysis shows that a linear drag law, in which the frictional force is directly proportional to the relative particle-fluid velocity (Stokes’s law), does not result in a stable particle motion. However, a non-linear relation in which the drag is proportional to the square of the relative velocity (Newton’s law) leads to the Mathieu equation, wiien it may be shown that stable particle trajectories may occur in certain ranges of frequency and amplitude. Stability criteria based on the Mathieu equation are applied to bubble-liquid systems in the sonic and ultrasonic regions, to liquid drop systems in pulse columns and to solid-liquid systems by using drag coefficients obtained from measurements of terminal velocities. The agreement between the theoretical and observed frequencies indicates that the velocity profile around a particle in a sinusoidal field is approximated by a quasi-steady state distribution and that transient effects may be neglected for the separated flow conditions considered in the present communication.