Force buoyancy

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. 

As well as preventing liquid carry over in the gas phase, gas carry undef must also be prevented in the liquid phase. Gas bubbles entrained in the liquid phase must be given the opportunity (or residence time) to escape to the gas phase under buoyancy forces. 

Buoyant Effect of Air. Weighing operations performed m vacuo are not affected by buoyancy forces. An object in air, however, is subject to a buoyancy force that is equal and opposite to the gravitational force on the mass of air the object displaces (10). If the equal arm balance of Figure 1 is in balance with a test weight of mass, in one pan, and material of mass, m, in the other, m = m if they have the same density. If the densities are different, then the buoyancy forces acting on each pan affect the result. Taking moments about the center pivot point gives... 

Drop Diameter. In extraction equipment, drops are initially formed at distributor no22les in some types of plate column the drops are repeatedly formed at the perforations on each plate. Under such conditions, the diameter is determined primarily by the balance between interfacial forces and buoyancy forces at the orifice or perforation. For an ideal drop detaching as a hemisphere from a circular orifice of diameter and then becoming spherical ... 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Transport Disengaging Height. When the drag and buoyancy forces exerted by the gas on a particle exceed the gravitational and interparticle forces at the surface of the bed, particles ate thrown into the freeboard. The ejected particles can be coarser and more numerous than the saturation carrying capacity of the gas, and some coarse particles and clusters of fines particles fall back into the bed. Some particles also coUect near the wall and fall back into the fluidized bed. 

A buoyant spherical particle of diameter D floating in a Hquid which has no tendency to wet, ie, pull the shoreline up, or to reject, ie, push the shoreline down, the soHd submerges to a depth d at which the downward force of gravity on the sphere equals the upward buoyancy force of the displaced Hquid. This occurs when... 

Considering an analytical solution for the simplest case of dispersion from an isolated source, we note that sources may be located at any point along the z axis, such as sources from industrial chimneys or power plant stacks at some height Hj above the ground. These usually continue to rise an incremental height AH, either by virtue of buoyancy forces acting on the heated effluent, or because their momentum carries them aloft, or both. 

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. 

To characrerizc the airflow in the stratified space, Eltermaii- proposed A which is a ratio of kinetic energy dissipating in the ventilated space to the energy used to suppress the buoyancy forces ... 

The criteria K is similar to the Archimedes number introduced in 19.30 liy Baturin and Shcpelev to characterize air jets influenced by buoyancy, or to ihe Richardson criteria used in meteorology to characterize rhe ratio of the mrbu-lence suppression by rhe buoyancy forces over the turbulence generation by the Reynolds tension, In the case of displacement ventilation, the Richardson criteria can be defined by rhe relationship -... 

Characteristics of the air jet in the room might be influenced by reverse flows, created by the jet entraining the ambient air. This air jet is called a confined jet. If the temperature of the supplied air is equal to the temperature of the ambient room air, the jet is an isothermal jet. A jet with an initial temperature different from the temperature of the ambient air is called a nonisother-mal jet. The air temperature differential between supplied and ambient room air generates buoyancy forces in the jet, affecting the trajectory of the jet, the location at which the jet attaches and separates from the ceiling/floor, and the throw of the jet. The significance of these effects depends on the relative strength of the thermal buoyancy and inertial forces (characterized by the Archimedes number). 

In the general case, a buoyant jet has an initial momentum. In the region close to discharge, momentum forces dominate the flow, so it behaves like a nonbuoyant jet. There is an intermediate region where the influence of the initial momentum forces becomes smaller and smaller. In the final region, the buoyancy forces completely dominate the flow and it behaves like a plume. When the jet is supplied at an angle to the vertical direction, it is turned upward by the buoyancy forces and behaves virtually like a vertical buoyant jet in a far field. A negative buoyant jet continuously loses momentum due the opposite direction of buoyancy forces to the supply air momentum and eventually turns downward. 

Using the relation between the Froude number and the Archimedes number, Atq = 1/F, the length of the linear jet zone, x, where the buoyancy forces are negligibly small can be calculated as follows ... 

To characterize the relationship between the buoyancy forces and momentum flux in different cross-sections of a nonisothermal jet at some distance x, Grimitlyn proposed a local Archimedes number ... 

Introduction of the local Archimedes criterion helped to clarify nonisothermal jet design procedure. Grimitlyn suggested critical local Archimedes number values, Ar , below which a jet can be considered unaffected by buoyancy forces (moderate nonisothermal jet) Ar, 0.1 for a compact jet, Ar, < 0.15 for a linear jet. 

The only force opposing the downward flow of the heated air or upward flow of the cooled air is a buoyancy force. In their analysis, Helander and Jakowatz also suggested accounting for inertial forces due to the entrainment of room air. However, this suggestion is not in an agreement with a principle of momentum conservation used in most of the existing models for isothermal jets. 

For practical use the influence of buoyancy forces on temperature and velocity decay in vertical nonisothermal jets, as proposed by Grimitlyn, can be accounted for by the coefficient of nonisothermality. For compact jets,... 

Buoyancy forces influence the trajectory of horizontally projected air jets or air jets supplied at some angle to the horizontal plane (Fig. 7.24). Most nonisothermal air jet studies were devoted to horizontally projected compact air jets. Based on the analytical studies, 42,77-80 trajectory axis of inclined jets can be described by a polynomial function... 

The analytical method of jet trajectory study developed by Shepelev allows the derivation of several other useful features and is worth describing. On the schematic of a nonisothermal jet supplied at some angle to the horizon (Fig. 7.25), 5 is the jet s axis, X is the horizontal axis, and Z is the vertical axis. The ordinate of the trajectory of this jet can be described as z = xtga a- Az, where Az is the jet s rise due to buoyancy forces. To evaluate Az, the elementary volume dW with a mass equal to dm dV on the jet s trajectory was considered. The buoyancy force influencing this volume can be described as dP — g(p -Pj). Vertical acceleration of the volume under the consideration is j — dP / dm — -p,)/ g T,-T / T. Vertical... 

Sandberg et al. conducted similar tests with a heated linear jet so that the buoyancy forces opposed the forces due to the lower pressure in the circulation zone (bubble). Based on the results of these tests, it was concluded that... 

Studies of nonisothermal mam stream and horizontal directing jet mterac-non were conducted to evaluate the maximum heat load that can be eltectively supplied by such HVAC systems. To summarize experimental data both in free and confined conditions, it was suggested that the above limiting condition is achieved when the current Archimedes number Ar ratio of rhe buoyancy forces over ineiTia forces along the resulting jet axis) does not exceed s[Pg.502]

In the case of a nonisothermal directing jet, the above assumptions are true, except that the momentum vector component along the Y axis changes due to the buoyancy force ... 

Omdehuk, V. 1966. Laws of noni.sothermal jet development, banded by buoyancy forces. Water Supply and Sanitary Technique, no. 2. 

Buoyancy forces creating vertical air movement along tbe passage between two rooms located on different levels, or thermal plumes creating temperature and contaminant differences between two zones located on different levels of the same room (Fig. 7.108c). 

The pollutant sources IG.i and y G 2 niay be without any buoyancy forces or they may be sinks, in other words negative sources or filters. 

A similar temperature and contaminant distribution throughout the room is reached with stratification as with a piston. The driving forces of the two strategies are, however, completely different and the distribution of parameters is in practice different. Typical schemes for the vertical distribution of temperature and contaminants are presented in Fig. 8.11. While in the piston strateg) the uniform flow pattern is created by the supply air, in stratification it is caused only by the density differences inside the room, i.e., the room airflows are controlled by the buoyancy forces. As a result, the contaminant removal and temperature effectiveness are more modest than with the piston air conditioning strategy. 

When some natural forces exist, it is essential to utilize, and not to counteract, these forces. Some examples are buoyancy forces from hot sources or contaminant jets from grinding or spray painting (see Fig. 10.4). To completely isolate a volume from its surroundings only using air is impossible. To achieve... 

Different physical effects interact (e.g., buoyancy forces acting on an air curtain). 

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. 

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