Fluid buoyancy

In a stratified fluid, buoyancy resists any vertical displacement of a water parcel. For a small displacement, a fluid parcel experiences an acceleration in the opposite direction linearly dependent on the displacement 1 ... 

Perea-Reeves and Stockman (1997) applied a lattice-gas cellular automaton model to study solute dispersion, including the effect of fluid buoyancy arising from solution density differences, in a pocketed channel. They found good agreement with the indented capillary model discussed in the Variable Shape, Discrete Pore Models section. For Peclet numbers smaller than 3 however, they found that K was actually smaller than the molecular diffusion coefficient. They attributed this to the restriction to diffusion in the direction of flow imposed by the pocket walls. They also observed that density differences between the existing and introduced fluids... 

In a reservoir at initial conditions, an equilibrium exists between buoyancy forces and capillary forces. These forces determine the initial distribution of fluids, and hence the volumes of fluid in place. An understanding of the relationship between these forces is useful in calculating volumetries, and in explaining the difference between free water level (FWL) and oil-water contact (OWC) introduced in the last section. 

A well known example of capillary-buoyancy equilibrium is the experiment in which a number of glass tubes of varying diameter are placed into a tray of water. The water level rises up the tubes, reaching its highest point in the narrowest of the tubes. The same observation would be made if the fluids in the system were oil and water rather than air and water. 

Variable-Area Flow Meters. In variable-head flow meters, the pressure differential varies with flow rate across a constant restriction. In variable-area meters, the differential is maintained constant and the restriction area allowed to change in proportion to the flow rate. A variable-area meter is thus essentially a form of variable orifice. In its most common form, a variable-area meter consists of a tapered tube mounted vertically and containing a float that is free to move in the tube. When flow is introduced into the small diameter bottom end, the float rises to a point of dynamic equiHbrium at which the pressure differential across the float balances the weight of the float less its buoyancy. The shape and weight of the float, the relative diameters of tube and float, and the variation of the tube diameter with elevation all determine the performance characteristics of the meter for a specific set of fluid conditions. A ball float in a conical constant-taper glass tube is the most common design it is widely used in the measurement of low flow rates at essentially constant viscosity. The flow rate is normally deterrnined visually by float position relative to an etched scale on the side of the tube. Such a meter is simple and inexpensive but, with care in manufacture and caHbration, can provide rea dings accurate to within several percent of full-scale flow for either Hquid or gas. 

Taylor instabilities involve effects of buoyancy or acceleration in fluids with variable density a light fluid beneath a heavy fluid is unstable by the Taylor mechanism. The upward propagation of premixed flames in tubes is subject to Taylor instability (11). 

Fluidization may be described as incipient buoyancy because the particles are still so close as to have essentially no mobility, whereas the usual desire in fluidization is to create bed homogeneity. Such homogeneity can be achieved only by violent mixing. This is brought about by increasing the fluid velocity to the point of blowing "bubbles" or voids into the bed, which mix the bed as they rise. The increased fluid velocity at which bubbles form first is referred to as the incipient (or minimum) bubbling velocity. 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

Turner,. S. 1973. Buoyancy Effects in Fluids. Cambridge University Press, Cambridge. 

P. Cooper and P. F. Linden, Natural ventilation of an enclosure containing two buoyancy sources, Journal of Fluid Mechanics, 1996, 311, 153-176. 

In aerosol theory, is the velocity of free fall of a particle, and by extension in the current work is an empirical velocity related to the buoyancy of the contaminant in air. We further assume that the overall fluid flow pattern is unaffected by the minor quantity of the buoyant contaminant. 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

Buoyancy The upward force exerted on any object immersed in a fluid of greater density. Hot pollutant gases rising in cooler air have positive buoyancy. A volume of gas denser than the surrounding air has negative buoyancy. 

An ideal particle moves relative to the fluid with velocity, v, dependent on just four quantities viz. fluid viscosity and density p and p respectively (i.e. fluid properties), and particle solid density and characteristic size ps and d respectively (i.e. particle characteristics), subject to the forces of buoyancy and friction, as illustrated in Figure 2.1. 

Stokes established, from theoretical considerations, that for small particles which settle at very low velocities, the settling velocity is independent of the density of the fluid except in so far as this affects the buoyancy. Show that the settling velocity must then be inversely proportional to the viscosity of the fluid. 

Thermally-Driven Buoyancy Flow. Thermal gradients can Induce appreciable flow velocities in fluids, as cool material is pulled downward by gravity while warmer fluid rises. This effect is Important in the solidification of crystals being grown for semiconductor applications, and might arise in some polymeric applications as well. To illustrate how easily such an effect can be added to the flow code, a body force term of pa(T-T ) has been added to the y-coraponent of the momentum equation, where here a is a coefficient of volumetric thermal expansion. 

In quiescent liquids and in bubble columns, buoyancy-driven coalescence is more important. Large fluid particles with a freely moving surface will also have a low-pressure region at the edge of the particle where the velocity is maximum. This low-pressure region will not only allow the bubble to stretch out and form a spherical cap but also allow other bubbles to move into that area and coalesce. Figure 15.14 shows an example of this phenomenon. 

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

The presence of a lithosphere with a thickness up to 100 km above the plume head obscures observations that could be made in terms of heat flow, gravity field or seismic structure. Establishing the temperature and flow fields beneath a hotspot thus becomes a difficult exercise. Several key parameters (Fig. 2) are poorly constrained and mostly result from theoretical fluid dynamics model, which underlines their large uncertainty. The temperature anomaly within the hotspot region is generally estimated to be approximately 200 100°C with large uncertainties (Shilling 1991 Sleep 1990). These temperature anomalies will induce smaller densities in the plume and the flux of the density anomalies is called buoyancy flux as defined in (Sleep 1990) ... 

When a particle falls under the influence of gravity, it will accelerate until the combination of the frictional drag in the fluid and buoyancy force balances the opposing gravitational force. If the particle is assumed to be a rigid sphere, at this terminal velocity, a force balance gives3,4,7,8... 

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