Forces buoyant

A buoyant force is given by the product of the volume V of the particle, the density p of the solution, and the radial acceleration ... 

Liquid Level. The most widely used devices for measuring Hquid levels involve detecting the buoyant force on an object or the pressure differential created by the height of Hquid between two taps on the vessel. Consequently, care is required in locating the tap. Other less widely used techniques utilize concepts such as the attenuation of radiation changes in electrical properties, eg, capacitance and impedance and ultrasonic wave attenuation. 

Head meters with density compensation. Head meters such as orifices, venturis, or nozzles can be used with one of a variety of densitometers [e.g., based on (a) buoyant force on a float, (b) hydrauhc couphug, (c) voltage output from a piezoelectric ciystal, or (d) radiation absolution]. The signal from the head meter, which is proportional to pV" (where p = fluid density aud V = fluid velocity), is multiphed by p given by the densitometer. The square root of the produc t is proportional to the mass flow rate. 

Forveiy thin hquids, Eqs. (14-206) and (14-207) are expected to be vahd up to a gas-flow Reynolds number of 200 (Valentin, op. cit., p. 8). For liquid viscosities up to 100 cP, Datta, Napier, and Newitt [Trans. In.st. Chem. Eng., 28, 14 (1950)] and Siems and Kauffman [Chem. Eng. Sci, 5, 127 (1956)] have shown that liquid viscosity has veiy little effec t on the bubble volume, but Davidson and Schuler [Trans. Instn. Chem. Eng., 38, 144 (I960)] and Krishnamiirthi et al. [Ind. Eng. Chem. Fundam., 7, 549 (1968)] have shown that bubble size increases considerably over that predic ted by Eq. (14-206) for hquid viscosities above 1000 cP. In fac t, Davidson et al. (op. cit.) found that their data agreed veiy well with a theoretical equation obtained by equating the buoyant force to drag based on Stokes law and the velocity of the bubble equator at break-off ... 

For conditions approaching constant flow through the orifice, a relationship derivea by equating the buoyant force to the inertia force of the liquid [Davidson et al., Tran.s. In.stn. Chem. Engr.s., 38, 335 (I960)] (dimensionally consistent),... 

The buoyant force is proportional to the mass of fluid displaced by the particle, that is, as the particle falls through the surrounding water, it displaces a volume of fluid... 

FIGURE 7.7 Schematics of air supply (o) with inclined jets toward the occupied zone (b) with horizontal jets and occupied zone ventilated by reverse flow (c) with vertical jets. Shaded areas show the effect of buoyant forces on airflow pattern when supply air is excessively heated over the room air" ... 

Buoyant jets when the buoyant force acts in the direction of the jet supply velocity at the origin, i.e., upward-projected heated air jet or downward-projected cooled air jet... 

Plume when the buoyant force completely dominates the flow, as for flow generated with a heat source... 

When the temperature of an air jet attached to the ceiling is lower than the temperature of the ambient air, the jet will remain attached to the ceiling until the downward buoyant force becomes greater than the upward static pressure (Coanda force). At this point, the jet separates from the ceiling and... 

As gas flows with fixed volumetric flow rate through an orifice gas sparger, bubbles are formed with diameter Analysis of bubble formation is based on the balance of buoyant force, as the bubbles leave the orifice and rise through the media (irApgDl)/6 with rest of the forces resulting from the surface tension, Trad. 

Fluids on the Earth s surface that are in hydrostatic equilibrium may be stable or unstable depending on their thermal structure. In the case of freshwater (an incompressible fluid), density decreases with temperature above ca. 4°C. Warm water lying over cold water is said to be stable. If warm water underlies cold, it is buoyant it rises and is unstable. The buoyant force, F, on the parcel of fluid of unit volume and density p is ... 

The rotating-disk CVD reactor (Fig. 1) can be used to deposit thin films in the fabrication of microelectronic components. The susceptor on which the deposition occurs is heated (typically around lOOOK) and rotated (speeds around 1000 rpm). A boundary layer is formed as the gas is drawn in a swirling motion across the spinning, heated susceptor. In spite of its three-dimensional nature, a peculiar property of this flow is that, in the absence of buoyant forces and geometrical constraints, the species and temperature gradients normal to the disk are the same everywhere on the disk. Consequently, the deposition is highly uniform - an especially desirable property when the deposition is on a microelectronic substrate. 

There are essentially three forces that act on a particle moving through a fluid. They are (i) the external force, gravitational or centrifugal (ii) the buoyant force, which acts parallel with the external force, but in the opposite direction and (iii) the drag force which appears... 

In the general case, the direction of movement of the particle relative to the fluid may not be parallel with the direction of the external and buoyant forces, and the drag force then creates an angle with the other two. This is known as two-dimensional motion. In this situation, the drag force must be resolved into two components, which complicates the treatment of particle mechanics. This presentation considers only the one-dimensional case in which the lines of action of all forces acting on the particle are collinear. 

Thus as pointed out above, further treatment on the mechanics of particle motion remains confined only to one-dimensional motion of particle through fluid. A particle of mass m moving through a fluid under the action of an external force Fe is considered. The velocity of the particle relative to the fluid is taken to be v. The buoyant force on the particle is taken to be Fb, and the drag force be FD. Then, the resultant force on the particle is Fe - Fb - Fd, the acceleration of the particle is dv/dt, and the resulting equation of motion is given by... 

The buoyant force is, by the well-known Archimedes principle, the product of the mass of the fluid displaced by the particles and the acceleration from the external force. The volume of the particle is fn/ps, where ps is the density of the particle, and the particle displaces this same volume of fluid. The mass of fluid displaced is (m/ps) pf, where pf is the density of the fluid. The buoyant force is, then,... 

This is a unit operation process where air bubbles, as gas, are used to remove solid or liquid particles from the liquid wastewater. The air bubbles are often trapped in the morphology of the suspended particles and as a result of buoyant forces, the particles move up and float on the surface where they are skimmed out. The common flotation methods include dissolved air, air flotation, vacuum flotation, and chemical additives.3... 

L Stratified wavy annular Minimum inclination angle to show bubble flow Trajectory of drops tom from liquid film Lift versus buoyant forces... 

For electrochemical reactions involving gaseous reactants and products, the RHSE has an advantage over a downward-faced RDE in sweeping away gas bubbles from its surface because of combined action of centrifugal and buoyant forces. 

Under the influence of a gravitational (centrifugal) field, a solute particle of mass m — M/Ni immersed in a solvent of density p at a distance r from the rotor axis experiences three forces. Within the frame of reference of the rotor, spinning with angular velocity co, these are the centrifugal force Fc, the buoyant force Fb, and the frictional force Ff. 

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