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In order to study the speed planning of the industrial robots trajectory end under different tasks, the three speed planning methods of the third degree polynomial, the fifth degree polynomial and the five-segment S-curve are compared and studied. Analyze the stability and positioning accuracy of the robot’s end motion process in different occasions, and combine the speed and acceleration changes of the three speed planning methods, and recommend the end speed planning method for common tasks such as palletizing, loading and unloading, and grinding. Taking specific tasks as an example, the simulation results verify the rationality of the recommended method.

Terminal velocity (Vt) is one of the important parameters often required in the pneumatics processes of some postharvest activities. This value is influenced by many factors such as grain type and shape, moisture content, etc. and this is still very difficult to find in Indonesian references. Therefore, this study aims to investigate the effect of types and moisture contents on the terminal velocity of rice. Three rice types namely Javanica (Oryza sativa subsp. Javanica), Japonica (Oryza sativa subsp. Japonica), and Indica (Oryza sativa subsp. Indica) with 9%, 14%, and 19% (w.b) moisture contents (M) were investigated in factorial design 3 × 3 with three replications for each treatment combinations. Terminal velocity values were measured using a hot wire anemometer in a self-constructed apparatus. The results showed that rice types and moisture contents strongly affected the terminal velocity (p < 0.05), however, there was no significant types and moisture contents’ interaction effect on the terminal velocity. Japonica was found to have the largest terminal velocity and Indica had the smallest. The relationship between the moisture content and terminal velocity was expressed as Vt= 0.060M+8.084, Vt= 0.061M+7.676 and Vt= 0.083M+7.056 for Japonica, Javanica, and Indica respectively.

Terminal velocity of grain product is one of aerodynamics properties which needed for design machines or handling agricultural grains in pneumatics bulk handling systems. Terminal velocity is influenced by many factors, the two important factors are type of grain material and moisture content. This research was aimed to investigate the effect of types and moisture contents on terminal velocity of soybeans grain. Three different types of soybeans namely local, import, and local black soybean in three different moisture contents of 10, 13, and 16% (w.b) were investigated in this study, using factorial design 3 x 3. Each combination was replicate three times. Terminal velocities were investigated using self-constructed apparatus and the velocities were measured using hot wire anemometer. Result shows that types of soybeans and moisture contents significantly affected terminal velocity (p

A standard physics experiment for students is to measure the terminal velocity of an object in air or in glycerine. A more difficult challenge is to measure the terminal velocity in water since the depth of the water needs to be large or the object needs to be dropped in the water at a speed close to its terminal velocity. Results obtained by filming the fall in a fish tank are presented for a range of different spheres, showing how the terminal velocity depends on the density of the sphere and its radius. The results provide a useful measurement of the drag force and the drag coefficient for a sphere in water. An additional experiment to measure the Magnus force is described where a ball was spinning when it entered the water.

Measurements are presented of the drag force on several different balls falling vertically through water in a fish tank, at speeds up to 4.5 m/s. Experiments of this type are usually undertaken in a student laboratory by measuring the terminal velocity of an object falling either through air or a viscous liquid. At speeds slightly higher than the terminal velocity, additional effects can be observed visually in water, including flow separation and turbulent flow. Changes in the drag coefficient were observed due to both effects, although different changes were observed with different balls, resulting from the formation of an air cavity behind each ball. Cavity formation was found to depend strongly on the roughness of the ball surface as well as the incident ball speed. Results are presented at Reynolds numbers from about 20,000 up to about 250,000.

This paper describes an experimental set up to examine the relationship between powder properties on powder flow pattern during filling operation. For this purpose, the free fall velocities of four types of agricultural dusts (i.e. castor sugar, oat, semolina and tea powder) in a rectangular enclosure were captured using a Particle Image Velocimetry (PIV). The result reveals that oat powder portrayed greater cloud dispersion due to its flaky shape and a lower bulk density. The characteristics of oat powder allowed more air to be dragged into the particle stream and forced the particle to be dispersed and suspended in air due to drag force and terminal velocity. The result presented here may facilitate improvements in dust control and measures in powder industries.

Abstrac. A fast method presented within this paper to find transparent liquid viscosity. An introduced tracking algorithm in image processing used to find a terminal velocity automatically of a falling ball in a tube that filled with a tested liquid. Terminal velocity considered an important parameter to find a liquid viscosity. Therefore, four iron balls, with different diameters and a smartphone camera are used to measure the falling ball terminal velocity. The estimated velocity from the introduced algorithm is compared with the calculated velocity and shows a good matching. The second algorithm used to estimate the viscosity of the tested liquid. The limitation of the ball diameter around 5mm to measure the terminal velocity. The result shows error matching between the fitting data and the estimated data ranging (0.00-0.1%). This method is a faster and easier experiment to use to find any transparent liquid viscosity comparing with a viscometer.

The purpose of this study is to analyze terminal velocity of a spherical ball in the liquid viscosity experiment. The analysis was performed using a simple calculus approach. Using the limit of v (t) as t approaches infinity (t → ∞) and the asymptotic value (v(t) = ∞) as well as the differential and integral operations, the terminal velocity can be estimated. The time to reach the terminal velocity and the distance traveled by a spherical ball can also be determined. Therefore, the factors that affect the terminal velocity, the time to reach that velocity, and the distance traveled can be analyzed. Such information may be used to improve the design of the experiment.

This paper aims at contributing to a better understanding of the motion of spherical particles in viscous fluids. The classical problem of spheres falling through viscous fluids for small Reynolds numbers was solved taking into account the effects of added mass. The analytical solution for the motion of a falling sphere, from the beginning to the end of the fall, was combined with an iterative numerical method to determine the fluid viscosity coefficient, diameter of the sphere and terminal velocity. The proposed solution was validated with experimental literature data. The study presented may also help understanding the fluid–particle interactions from both theoretical and educational standpoints.

In this article, I will extend the falling ball method to measure the viscosity of liquids regardless of the degree of their viscosity. For this, I will show that one can obtain a measurement of the terminal velocity of a falling spherical ball in a viscous liquid by solving numerically the equation of motion which describes the dynamics of the ball from the beginning to the end of the fall. The present numerical approach is proposed here particularly for measuring the viscosity of weakly viscous liquids using the falling ball viscometer.

Gas dissolved in ordinary tap water is released and forms bubbles when poured into a vessel. The sub-millimeter bubbles move towards the surface with a terminal velocity of only few millimeters per second. The terminal velocity can be used for estimating the average size of the bubbles. The result is confirmed by observing the bubbles visually in a microscope.

Even though the buoyancy force (also known as the Archimedes force) has always been an important topic of academic studies in physics, its point of application has not been explicitly identified yet. We present a quantitative approach to this problem based on the concept of the hydrostatic energy, considered here for a general shape of the cross-section of a floating body and for an arbitrary angle of heel. We show that the location of the point of application of the buoyancy force essentially depends (i) on the type of motion experienced by the floating body and (ii) on the definition of this point. In a rolling/pitching motion, considerations involving the rotational moment lead to a particular dynamical point of application of the buoyancy force, and for some simple shapes of the floating body this point coincides with the well-known metacentre. On the other hand, from the work–energy relation it follows that in the rolling/pitching motion the energetical point of application of this force is rigidly connected to the centre of buoyancy; in contrast, in a vertical translation this point is rigidly connected to the centre of gravity of the body. Finally, we consider the location of the characteristic points of the floating bodies for some particular shapes of immersed cross-sections. The paper is intended for higher education level physics teachers and students.

We experimentally study the motion and shape of a single rising bubble in super-purified water. We develop an apparatus that is equipped with a measurement system for monitoring both the resistivity and amount of total organic carbon of water in order to evaluate the purity of water. We investigate the critical Reynolds number above which the rising bubble motion changes from rectilinear to zigzag or spiral motion. It is revealed that the critical Reynolds number is susceptible to the range of observation height in the experimental tank. Next, we investigate the effects of the amount of contaminant on bubble motion. The drag coefficient of bubbles in the case of low Reynolds numbers is greatly affected by a small amount of contaminant. We also compare the experimental results of both the terminal rising velocity and drag coefficient with theoretical results for ellipsoidal bubble obtained for high Reynolds number. For smaller bubbles, good agreement is found between the experimental and theoretical results. For larger bubbles, however, discrepancies are prominent. Finally, we examine the effects of the bubble shape on its motion. There exist significant discrepancies between the experimental and theoretical results of aspect ratio as a function of Weber number, even in the range where the experimental and theoretical results in both the terminal velocity and drag coefficient show good agreement.

Dynamics of a classical particle in a one-dimensional, randomly driven potential is analysed both analytically and numerically. The potential considered here is composed of two identical spatially-periodic saw-tooth-like components, one of which is externally driven by a random force. We show that under certain conditions the particle may travel against the averaged external force performing a saltatory unidirectional drift with a constant velocity. Such a behavior persists also in situations when the external force averages out to zero. We demonstrate that the physics behind this phenomenon stems from a particular behavior of fluctuations in random force: upon reaching a certain level, random fluctuations exercise a locking function creating points of irreversibility which the particle can not overpass. Repeated (randomly) in each cycle, this results in a saltatory unidirectional drift. This mechanism resembles the work of an escapement-type device in watches. Considering the overdamped limit, we propose simple analytical estimates for the particle's terminal velocity., Comment: 14 pages, 6 figures; appearing in Journal of Physics: Condensed Matter, special issue on Molecular Motors and Friction

A desktop experiment to demonstrate the linear and quadratic velocity dependence of drag on an object falling in a resistive medium was developed for an undergraduate laboratory. The motion of ball bearings dropped into a cylinder filled with fluid is captured and measured using computer-based imaging. The terminal velocity of falling spheres is measured as a function of size at low and high Reynolds number, and the results are compared to predicted scaling laws for models containing a drag force that is linear or quadratic with velocity.

We study the dynamics of a classical particle in a one-dimensional potential composed of two identical spatially periodic components, one of which is externally driven by a random force. We demonstrate that, under certain conditions, the particle may move unidirectionally with a constant velocity, despite the fact that the average external force is zero. We show that the physical mechanism underlying such a phenomenon resembles the work of an escapement-type device in watches; upon reaching a certain level, random fluctuations exercise a locking function creating points of irreversibility which the particle cannot overpass. Repeated (randomly) in each cycle, this results in a saltatory ballistic-type motion. In the overdamped limit, we work out simple analytical estimates for the particle's terminal velocity. Our analytical results are in a very good agreement with Monte Carlo results.

The behavior of a single bubble rising in an ultrasonic standing wave field through vertical pipes filled with a quiescent liquid is analyzed numerically using the cubic-interpolated pseudo-particle(CIP)-combined and unified procedure(C-CUP) method. The calculated terminal velocities of bubbles in pipes agree with the experimental results in silicon oil. As the diameter of the bubble approaches the pipe diameter, the shape of the bubble is deformed into a lengthwise ellipse and rising velocity slows due to the pipe wall. The velocities and shapes of single bubbles are obtained for both standing waves formed in the axial direction of pipes and in the radial direction. When an initial spherical bubble rises through the node of the radially formed standing wave in pipes, it is deformed into a lengthwise elliptical shape by the acoustic radiation force even if the wall effect is small, and the velocity of the bubble is faster than that for when there is no ultrasonic field. In other cases, the average terminal velocity of bubbles is slower than that for when there is no ultrasonic field.

The steady-state migration velocity of a spherical droplet placed in a second liquid is calculated taking into account gravity and several interfacial effects. The effect of insoluble surfactants at the bubble surface, surface tension gradients, surface elasticity, interfacial dilatational viscosity, interfacial diffusivity and convective and diffusive surface excess heat fluxes on the terminal velocity of the droplet are included under the assumption of small Marangoni, Reynolds and capillary numbers. This work extends earlier results, which do not take into account interfacial diffusivity.

In order to study the fragment initial velocity distribution of the cylindrical warhead with terminals and exploded in the air, this paper builds a theoretical calculation model of the side-wall and terminal velocity of the warhead with two terminals based on the energy conservation principle, and considering the explosive energy distribution and proportion. The calculation results obtained by the theoretical model are compared with the experimental results of previous scholars. In this paper, the influence of the warhead L/D and C/M on the side-wall and terminal initial velocity is examined. A good agreement between the theoretical calculation results and the experimental results of previous scholars is observed. This verifies feasibility of the calculation method proposed in this paper. When the warhead L/D is smaller than 2, along with increase of L/D, the side-wall fragment velocity increases and maintains at certain value. In terms of the terminal fragment initial velocity, when the warhead L/D is close to 1, the initial velocity is larger; but, when the L/D is larger than 1, the terminal fragment initial velocity decreases significantly.

In high-school teaching of mechanics, we deal, among other things, with the nature of static and kinetic friction, forces that are proportional to the normal force. Under the influence of frictional forces, a body moves down a rough sloped decline at a fixed rate of acceleration that is independent of its mass. This situation does not apply to cases where the frictional force is dependent upon velocity, such as bodies which are moving through a streaming fluid (such as raindrops falling to the ground). In this case the body moves with a continuously decreasing acceleration, eventually reaching a terminal velocity when the frictional and gravitational forces balance out. This velocity constraint is determined by the dependence of the frictional force on velocity and geometric parameters that determine the strength of the frictional force. We show here that a similar situation takes place when bicycles descend an incline with a fixed slope. We also investigated the dependence of the velocity constraint with mass, using bicycles equipped with sophisticated sensors that metamorphose them into data-processing laboratories.

In an operation, belly landing is mostly applied as recovery method especially on research Unmanned Aerial Vehicle (UAV) such as Aludra SR-10. This type of landing method may encounter tough landing on hard soil and gravel which create high impact load on the aircraft. The impact may cause structural or system damage which costly to be repaired. Nowadays, Parachute Recovery System (PRS) recently used in numerous different tasks such as landing purpose to replace belly landing technique. Parachute use in this system to slow down flying or falling UAV to a safe landing by opening the canopy to increase aerodynamic drag. This paper was described the Computational Fluid Dynamic (CFD) analysis on ALUDRA SR-10 model with two different conditions i.e. the UAV equipped with and without parachute in order to identify the changes of aerodynamic characteristics. This simulation studies using solid models of aircraft and hemisphere parachute and was carried out by using ANSYS 16.0 Fluent under steady and turbulent flow and was modelled using the k-epsilon (k-e) turbulence model. This simulation was limited to determine the drag force and drag coefficient. The obtained result showed that implementation of parachute increase 0.25 drag coefficient of the aircraft that is from 0.93 to 1.18. Subsequent to the reduction of descent rate caused by the parachute, the drag force of the aircraft increase by 0.76N. These increasing of drag force of the aircraft will produce lower terminal velocity which is expected to reduce the impact force on the aircraft during landing.

Multiphase flow are involved in many fields in natural phenomenon as well as industrial applications. Drag coefficient is an important parameter in the modelling and simulation of multiphase flow. Non-sphere particles are usually simplified to sphere particles in multiphase flow simulation. However, non-sphere particles are more common in practice. Hence, it is significant to investigate shape effects on the drag coefficient of non-sphere particles. This article selects several typical shapes of particles as research objects. 3-D printers are used to build particle models. And high speed cameras are used in record the whole process of particle settling. Detailed information of particle path and speed are gotten through image processing of high speed cameras.

The typical spreadsheet, with its in-built mathematical functions and chart plotting facilities, can provide an interesting graphical interface for an insight into the solution of simple practical differential equations. This technique avoids problems that may present a difficulty to those students without certain mathematical tools, which can sometimes cloud the issue. The article explores simple equations such as the exponential decay function, a terminal velocity situation, and the more complex situations of the simple harmonic oscillator and damped oscillations. Microsoft ExcelTM is used throughout, and the article gives a small tutorial on spreadsheets.

Protein molecular weights are commonly characterized by gel electrophoresis. Biology textbooks typically quote an empirical, approximate relationship between migration rate and molecular weight, relying on an inappropriately simplistic model of spherical particles travelling at their terminal velocity through a viscous medium. We show how the model can be modified to derive a physically realistic equation that relates migration rate and molecular weight, and that mirrors experimentally observed behaviour. We suggest that gel electrophoresis provides an interesting interdisciplinary context in which to exercise several basic principles that are encountered through introductory physics courses. Finally, we provide additional examples of practical situations where the concept of terminal velocity can be elaborated and applied.

A frictionless cart in the shape of a right triangle (with the vertical side forward) is elastically impacted by vertically falling raindrops. The speed of the cart as a function of time can be analytically deduced as an exercise in the use of trigonometric and hyperbolic functions. A characteristic time defines the approach to a terminal speed which is a sizeable fraction of the speed of the rain. The treatment is accessible to a student in a calculus-based mechanics course.

This paper describes theoretical calculation of the terminal velocity of falling cat, taking the air drag into account. The results show that a fall from the seventh floor is critical for the cat so we introduce a new quantity called the 'coefficient of the cat's fear' during free fall. A subsequent experiment with a model of a cat carrying the accelerometer confirmed this conclusion. This calculation and experiment can act as a strong motivational factor during introductory physics courses.

A study has been made of a gas-driven gene gun which launches microprojectiles carrying foreign genetic material into living cells. The gene gun consists of a shock tube driver which generates pressure pulses that accelerate a membrane (macroprojectile) fitted across the end of the shock tube. The macroprojectile launches a cloud of high-speed microprojectiles on firing. The performance was studied in terms of the initial macroprojectile geometry and the pressure-time history on its surface. The pressure-time history was altered by varying the length of the shock tube. Direct measurements were made of the macroprojectile velocity and the penetration of microprojectiles into model cell systems. Under conditions of shock acceleration, good agreement was found between measured velocities and those predicted using one-dimensional gas dynamic theory. In terms of the terminal velocity of the macroprojectile, when the macroprojectile was initially planar, best results were obtained with the long shock tube (shock acceleration), but when the macroprojectile was initially domed convex upstream to increase acceleration distance, best results were obtained with the short shock tube (pressure pulse excitation). The difference between the performance of those two configurations was due to interaction of pressure loading mechanics and the structural properties of the macroprojectile as a consequence of its shape. Significant fractions of microprojectiles penetrated at least six cell layers at conditions consistent with a theoretical maximum macroprojectile velocity of 330 m s-1. Transient gene expression was achieved in target wheat suspension cells.

The expression for the terminal velocity of skydivers in the horizontal spreadeagle position is shown to be somewhat insensitive to the mass of the diver. However, the fact that it does depend upon the density of the medium is shown by one numerical illustration.

The literature shows a lack on well established guidelines on the design of the torpedo anchors. This research aims to investigate the effect of various geometric parameters in the torpedo anchors' design to optimize for higher terminal velocity. A CFD model was developed and simulations were carried out using ANSYS FLUENT commercial software. Consequently, correlations between various parameters and its resultant drag coefficient were developed. The parameters of interest included geometric changes of the original design, as well as sea water properties that reflect water depth in South China Sea. New design features are proposed and investigated in the overall parametric studies. As a result, it was found that the terminal velocity can be improved by sharper tip angle, greater aspect ratio, greater diameter ratio, and an optimum rear angle of 30°. Clear relationships between each factor and its resulted terminal velocity were developed. More importantly, the sensitivity of drag coefficient towards each of the parameters was predicted.

Cloud droplet mobility is referred to here as a measure of the droplets ability to move with ambient air. We claim that an important part of the aerosol effect on convective clouds is driven by changes in droplet mobility. We show that the mass-weighted average droplet terminal velocity, defined here as the effective terminal velocity (eta) and its spread (sigma_eta) serve as direct measures of this effect. Moreover, we develop analytical estimations for eta and sigma_eta to show that changes in the relative dispersion of eta (epsilon_eta = sigma_eta/eta) can serve as a sensitive predictor of the onset of droplet-collection processes., Comment: Published in ERL; 10 pages, 4 figures

Starting with a set of basic assumptions and with the application of well-known Newtonian physics, a theoretical model has been established for the flight of the mahogany winged seed. Using a high-speed camera, we successfully confirmed that the mahogany winged seed attains a vertical and rotational terminal velocity. From our model the mahogany seed has a terminal speed of 1.45 m/s. The experimental value of the terminal velocity on the average is 1.47 m/s (only about 1% error). The experimental value of the angular velocity was found to be around 54.33 rad/s, about 14% error compared to the predicted terminal velocity of 47.5 rad/s. The high predictable nature of a mahogany's terminal velocity can facilitate the biologist's study of mahogany mass seed dispersal.

The detonation behavior of high explosives containing quantities of dense additives has been previously investigated with the observation that such systems depart dramatically from the approximately "gamma law" behavior typical of conventional explosives due to momentum transfer and thermalization between particles and detonation products. However, the influence of this non-ideal detonation behavior on the divergence speed of plates has been less thoroughly studied and existing literature suggests that the effect of dense additives cannot be explained solely through the straightforward application of the Gurney method with energy and density averaging of the explosive. In the current study, the acceleration history and terminal velocity of aluminum flyers launched by packed beds of granular material saturated by amine-sensitized nitromethane is reported. It was observed that terminal flyer velocity scales primarily with the ratio of flyer mass to mass of the explosive component; a fundamental feature of the Gurney method. Velocity decrement from the addition of particles was only 20%-30% compared to the resulting velocity if propelled by an equivalent quantity of neat explosive.

In this paper waves generated by two-dimensional mass movement are simulated using a numerical model based on the full hydrodynamic coupling between rigid-body motion and ambient fluid flow. This approach has the capability to represent the dynamics of the moving rigid body, which avoids the need to prescribe the body velocity based on the data measurements. This model is implemented in the CFX code and uses the Reynolds average Navier–Stokes equations solver coupled to the recently developed immersed solid technique. The latter technique allows us to follow implicitly the motion of the solid block based on the rigid body solver. The volume-of-fluid method is used to track the free surface locations. The accuracy of the present model is firstly examined against the simple physical case of a freely falling rigid body into water reproducing Scott Russell's solitary waves. More complex and realistic simulations of aerial and submarine mass-movement, simulated by a rigid wedge sliding into water along a 45° slope, are then performed. Simulated results of the aerial mass movement show the complex flow patterns in terms of the velocity fields and free surface profiles. Results are in good agreement with the available experimental data. In addition, the physical processes associated with the generation of water wave by two-dimensional submarine mass-movement are explored. The effects of the initial submergence and specific gravity on the slide mass kinematics and maximum wave amplitude are investigated. The terminal velocity and initial acceleration of the slide mass are well predicted when compared to experimental results. It is found that the initial submergence did not have a significant effect on the initial acceleration of the slide block centre of mass. However, it depends nonlinearly\vadjust{\newpage} on the specific gravity. The maximum wave amplitude and the time at which it occurred are also presented as a function of the initial submergence and specific gravity.

We have succeeded in the noncontact transportation of ethanol droplets inside a semi cylindrical acoustic waveguide. The waveguide was composed of a vibration bottom plate and a semi cylindrical reflector, and a propagating acoustic field was excited in the waveguide. The droplet was levitated at the nodal position of the standing wave mode in the cross section of the waveguide and transported by the traveling wave component in the horizontal direction. The transportation distance was 65 mm and the terminal velocity reached 2.3 m/s when the droplet was 1.5 mm in diameter and 1.38 g in weight.

The motion of volcanic ash particles is described on large scales by an ordinary differential equation, and the dynamics is chaotic. Deposition with a terminal velocity is found to be influenced by all three components of the wind velocity. The particles sooner or later leave the free atmosphere and enter the planetary boundary layer. Chaos is thus transient, and we point out that quantities like escape rate, average lifetime and topological entropy can efficiently be applied to characterize the volcanic ash dynamics in the free atmosphere. These quantities are evaluated for particular eruption examples of volcano Eyjafjallajokull, as well as for volcanic averages taken at different geographical locations, and for global averages over the Earth.

When powder forms a weak interaction particle cluster in a gas-solid flow, the rate of fall of the cluster exceeds the terminal velocity of the individual particles (Slack, 1963; Marzocchella et al., 1991). However, the relationship between the unsteady characteristics of the free-fall of the particle cluster and the geometric condition of the experiment is not clear. We performed a simple experiment in which powder of a certain mass falls in a vertical pipe. When the powder falls in the vertical pipe, the distribution length of the powder expands, and the particle volume fraction is dense in the lower part, and is thin in the upper part. The fall velocity of the lower edge of the powder cluster and the flow rate of air generated by the powder fall were measured. We obtained the following results. The relative velocity of free-fall of the particle cluster has no relation to the individual particle diameters. The characteristic of a particle cluster exists unless the cluster has very high void fraction.

Recently, a technique using the micro-bubbles is focused. It was applied to many fields such as purification of rivers and lakes, washing the industrial parts, growth of plants and marine products. The characteristics of micro-bubbles are small size, wide surface area, low terminal velocity, and so on. If this micro-bubble is available as tracer of PIV (Particle Image Velocimetry), environment load would become lower because it doesn't need to discard particle. In this paper, we make a micro-bubble generator with Venturi type mechanism. The generated micro-bubbles are applied to a vertical channel flow with contraction. We validate about traceability of the micro-bubble tracer in comparison with the particle tracer.

There have been relatively few studies of turbulent collision rate of sedimenting droplets in the context of cloud physics, for which both the gravitational settling and inertial effects must be simultaneously considered. In this study, direct numerical simulations (DNS) were used to study the geometric collision rates of cloud droplets. Both Stokes drag law and a nonlinear drag law were considered, but the droplet–droplet local aerodynamic interactions were not included. Typical droplet and turbulence parameters of convective clouds were used to determine the flow dissipation rate , characteristic Stokes numbers, and the nondimensional terminal velocities. DNS results from a large number of runs covering the range from 10 to 400 cm2 s− 3 and droplet sizes from 10 to 60 μm in radius are presented. These results show that air turbulence can increase the geometric collision kernel by up to 47%, relative to geometric collision by differential sedimentation. This is due to both a moderate enhancement of the radial relative velocity between droplets and a moderate level of pair nonuniform concentration due to local droplet clustering. The turbulence enhancements increase with the flow dissipation rate and flow Reynolds number. Comparisons with related DNS studies show that our results confirm and extend the previous findings. The mean settling velocity of droplets in a turbulent flow was also obtained, showing that a maximum increase relative to the terminal velocity occurs for 20 μm cloud droplets. This agrees with a previous theory based on simple vortex flows and confirms the importance of a new nondimensional parameter τp3g2/ν for sedimenting droplets, where τp is the droplet inertial response time, g is the gravitational acceleration and ν is the air kinematic viscosity. Limitations of DNS and future directions are also noted.

The effect of air turbulence on the geometric collision kernel of cloud droplets can be predicted if the effects of air turbulence on two kinematic pair statistics can be modeled. The first is the average radial relative velocity and the second is the radial distribution function (RDF). A survey of the literature shows that no theory is available for predicting the radial relative velocity of finite-inertia sedimenting droplets in a turbulent flow. In this paper, a theory for the radial relative velocity is developed, using a statistical approach assuming that gravitational sedimentation dominates the relative motion of droplets before collision. In the weak-inertia limit, the theory reveals a new term making a positive contribution to the radial relative velocity resulting from a coupling between sedimentation and air turbulence on the motion of finite-inertia droplets. The theory is compared to the direct numerical simulations (DNS) results in part 1, showing a reasonable agreement with the DNS data for bidisperse cloud droplets. For droplets larger than 30??m in radius, a nonlinear drag (NLD) can also be included in the theory in terms of an effective inertial response time and an effective terminal velocity. In addition, an empirical model is developed to quantify the RDF. This, together with the theory for radial relative velocity, provides a parameterization for the turbulent geometric collision kernel. Using this integrated model, we find that turbulence could triple the geometric collision kernel, relative to the stagnant air case, for a droplet pair of 10 and 20??m sedimenting through a cumulus cloud at R?=2?104 and =600?cm2?s?3. For the self-collisions of 20??m droplets, the collision kernel depends sensitively on the flow dissipation rate.

The velocities of particle falling in a standing wave field through a vertical pipes filled with a stagnant liquid in are analyzed numerically for Reynolds number (Re)

Factors which govern the efficient propulsion of magnetic flier plates by capacitor banks are discussed. The advantages of a unidirectional crowbarred current discharge for the propulsion of energetic flier plates are demonstrated by an experiment in which 1.4 m2 of 0.046 cm thick copper sheet was accelerated to 310 m s-1. The flier terminal velocity was measured both by multiple-flash open-shutter photography and by contact probes, each measurement being in agreement with the other and with a prediction based on numerical integration of the flier plate circuit equations.

An experimental system for the investigation of the dielectrophoresis of bubbles in isomotive electric fields is described. Nitrogen bubbles of radii less than 0.25 mm are injected into transformer oil filling the interelectrode space of the specially shaped electrodes required to generate the isomotive fields. The electrode assembly is aligned so that the effect of increasing the dielectrophoretic force is to reduce the terminal velocity of rising bubbles. A microcomputer, interfaced to an optoelectronic light detector, is used to measure the transit times of bubbles between a triple light beam arrangement at various applied fields. Details of the measurement procedure are given together with the means used for generating the bubbles. Typical data are presented and their analysis support the present use of the system for the study of bubbles and other types of particles in non-uniform electric fields.

The terminal velocity of aggregates of spheres is determined by means of a dust sampling instrument which deposits them at sites on a collecting plate related to their terminal velocity; the size and relative positions of the spheres in an aggregate are determined microscopically. A test is applied to decide whether an aggregate examined was airborne in the same state or formed by juxtaposition of two or more airborne units at the same site. The free-fall orientation of an aggregate can be inferred from its orientation on the collecting plate. Results are given for the relationship between the Stokes' diameter of a doublet and the size of the components.

The terminal velocities of spheres falling in six flocculated china-clay suspensions have been measured, and corrections applied for the retarding effect of the walls of the containing vessel. The drag experienced by a sphere in the Reynolds number range of 250 to 40 000 is explained in terms of an unsheared envelope of the suspension which surrounds the sphere and which decreases in diameter as the velocity increases, disappearing completely at a velocity which depends primarily upon the concentration of the suspension.

An instrument for sampling airborne particles is briefly described, in which the particles are classified according to their terminal velocities and deposited on a glass plate in a continuously graded sample. It can be employed to determine: (i) the Stokes' diameter-frequency distribution; (ii) the variation of mean projected diameter for a constant value of Stokes' diameter, and the variation of the Stokes' diameter for a constant value of mean projected diameter; (iii) the mean weight of particles of given Stokes' diameter.

The distance a drop of given volume has to fall through in order that it may attain a constant terminal velocity has been determined for both water and methyl salicylate. A relation connecting the distance of fall for constant velocity and the volume of the drop has been obtained. The terminal velocities of drops of water and of methyl salicylate have been determined for drops 0.2 cm. to 0.55 cm. in diameter. A relation connecting the terminal velocity of a drop and its volume has been obtained.

A scaled computer circuit is presented for solving the equation for terminal velocity of a body falling under gravity through a resistive medium, by analogue computing techniques.