Volume 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. 

The supporting medium was water at 298 K (p = 0.99727), and the density of latex is 1.2049 g cm . The latex particles had an average radius of 2.12 x 10 mm hence, their effective mass corrected for buoyancy is their volume times the density difference Ap between latex and the supporting medium, water... 

If the buoyancy correction is ignored, the pipet s volume is reported as... 

To ensure that S eas is determined accurately, we calibrate the equipment or instrument used to obtain the signal. Balances are calibrated using standard weights. When necessary, we can also correct for the buoyancy of air. Volumetric glassware can be calibrated by measuring the mass of water contained or delivered and using the density of water to calculate the true volume. Most instruments have calibration standards suggested by the manufacturer. 

If a 1-kg stainless weight (m = 1, OOOg, = 8,000 kg/m ) is added to one pan of the balance in Figure 1, and material with a density of 1,000 kg/m is added to the other until equiHbrium is reached, the amount of the material needed is 1001.05 g, using equation 5. Thus, it takes 1001.05 g of this material to counterbalance 1,000 g of stainless steel, because of the buoyancy effects on the dissimilar volumes. 

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. 

Separations. Foams have important uses in separations, both physical and chemical (51,52). These processes take advantage of several different properties of foams. The buoyancy and mechanical rigidity of foam is exploited to physically separate some materials. The large volume of vapor in a foam can be exploited to filter gases. The large surface area of a foam can also be exploited in the separation of chemicals with different surface activities. 

Useful formulas for BLEVE fireballs (CeSP, 1989) are given by equations 9.1-27 thru 9.1-30, where M = initial mass of flammable liquid (kg). The initial diameter describes the short duration initial ground level hemispherical flaming-volume before buoyancy lifts it to an equilibrium height. 

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... 

A characteristic of many industrial halls is that zones of occupancy take up only a small portion of the room volume and height. In addition, the flows are normally buoyancy dominated. This results in a vertical temperature stratification that can be utilized for room air conditioning design in order to achieve effective climatization along with low energy consumption. 

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... 

In displacement ventilation systems air is supplied to the room at low velocity, with a volume flow rate near the floor, and is extracted near the ceiling. The temperature of the supplied air is slightly lower than that of the room. Air is heated by the objects in the room, e.g., computer terminals and photocopying machines, and it rises due to buoyancy. 

The stopwatch technique for determining emission volume flow rate is based on measuring with a stopwatch the elapsed time for fume to rise between two known levels (e.g., Zj, Z,). For this test procedure to be valid, the test must be carried out in a region where the rising fume clearly exhibits buoyancy-dominated plume behavior. The calculation procedure depends on a good estimate of the location of the virtual origin of the plume and the heat release for the process. 

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. 

Another question that arises is the limiting size of the gas bubbles. As the bubble volume Vj, increases, the buoyancy force V gAp of the bubble increases (g is the acceleration of gravity and Ap is the density difference between the liquid and the gas). The bubble will tear away from the electrode surface as soon as this buoyancy force becomes larger than the forceretaining the bubbles. 

This also applies to a body submerged in a fluid that is subject to any acceleration. For example, a solid particle of volume Vs submerged in a fluid within a centrifuge at a point r where the angular velocity is on is subjected to a net radial force equal to Ap on2rVs. Thus, the effect of buoyancy is to effectively reduce the density of the body by an amount equal to the density of the surrounding fluid. 

The prime difficulty of modeling two-phase gas-solid flow is the interphase coupling, which deals with the effects of gas flow on the motion of solids and vice versa. Elgobashi (1991) proposed a classification for gas-solid suspensions based on the solid volume fraction es, which is shown in Fig. 2. When the solid volume fraction is very low, say es< 10-6, the presence of particles has a negligible effect on the gas flow, but their motion is influenced by the gas flow for sufficiently small inertia. This is called one-way coupling. In this case, the gas flow is treated as a pure fluid and the motion of particle phase is mainly controlled by the hydrodynamical forces (e.g., drag force, buoyancy force, and so... 

Saturation (v) is the volume fraction of the total void volume occupied by a specific fluid at a point. Saturation values can vary from zero to 1 with the saturation of all fluids equal to 1. Residual saturation (Sr) is the saturation at which the NAPL becomes discontinuous and immobile due to capillary forces. Residual saturation is dependent upon many factors, including pore size distribution, wettability, fluid viscosity and density ratios, interfacial surface tension, gravity and buoyancy forces, and hydraulic gradients. 

Tate s law makes use of bubble formation in the measurement of the surface tension of a liquid, and hence the fact that surface tension influences the bubble volume is obvious. At flow rates tending to zero, the bubble volume is such that the upward force due to buoyancy is balanced by the downward force of surface tension. So, an increase in surface tension should... 

When the density of a liquid is increased, the buoyancy force corresponding to a specific size of the bubble increases, whereas the surface-tension force may remain constant. Thus, for a definite amount of surface-tension force, the bubble volume obtained is smaller. 

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