Balances buoyancy

When a spherical particle of diameter d settles in a viscous liquid under earth gravity g, the terminal velocity V, is determined by the weight of the particle-balancing buoyancy and the viscous drag on the... 

This method is smiple but experimentally more cumbersome than the volumetric method and involves the use of a vacuum microbalance or beam balance [22], The solid is suspended from one ann of a balance and its increase in weight when adsorption occurs is measured directly. The dead space calculation is thereby avoided entirely but a buoyancy correction is required to obtain accurate data. Nowadays this method is rarely used. 

With gravimetric methods, the magnitude of the buoyancy correction should be assessed. Particular attention must be paid to the adsorbent temperature because of the unavoidable gap between the sample and the balance case (cf. Section 6.2). 

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. 

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... 

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. 

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 ... 

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. 

Equations 3 to 7 indicate the method by which terminal velocity may be calculated. Erom a hydrodynamic force balance that considers gravity, buoyancy, and drag, but neglects interparticle forces, the single particle terminal velocity is... 

Rotameter A rotameter consists of a vertical tube with a tapered bore in which a float changes position with the flow rate through the tube. For a given flow rate the float remains stationary since the vertical forces of differential pressure, gravity, viscosity, and buoyancy are balanced. The float position is the output of the meter and can be made essentially linear with flow rate by makiug the tube areavaiy hn-early with the vertical distance. 

Several additional studies [Winitzer, Sep. ScL, 8(1), 45 (1973) ibid., 8(6), 647 (1973) Maru, Wasan, and Kintner, Chem. Eng. Set., 26, 1615 (1971) and Rapacchietta and Neumann, J. Colloid Inteiface ScL, 59(3), 555 (1977)] which include body forces such as gravitational acceleration and buoyancy have been made. A typical example of a force balance describing suen a system (Fig. 22-39) is summarized in Eq. (22-41). 

Zeng et al. (1993) proposed that the dominant forces leading to bubble detachment could be the unsteady growth force and buoyancy force. In order to derive an accurate detachment criterion from a force balance, all forces should be accurately known. If a mechanism is not known precisely, then approximate expressions, one or two fitted parameters and comparison with experiments might offer a solution. Such fitting procedures have indeed been applied (Klausner et al. 1993 Mei et al. 1995a Helden et al.l995). 

Schoonover, R. M., and Jones, F. E., Air Buoyancy Correction in High-Accuracy Weighing on Analytical Balances, Anal. Chem. 53, 1981, 900-902. 

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... 

Bubble size at departure. At departure from a heated surface, the bubble size may theoretically be obtained from a dynamic force balance on the bubble. This should include allowance for surface forces, buoyancy, liquid inertia due to bubble growth, viscous forces, and forces due to the liquid convection around the bubble. For a horizontally heated surface, the maximum static bubble size can be determined analytically as a function of contact angle, surface tension, and... 

The hydrodynamic region has received considerable attention over the years. Equations (2-63) and (2-64) follow the buoyancy-drag force balance theory. If we... 

The hydrodynamic boundary layer has an inner part where the vertical velocity increases to a maximum determined by a balance of viscous and buoyancy forces. In fluids of high Schmidt number, the concentration diffusion layer thickness is of the same order of magnitude as this inner part of the hydrodynamic boundary layer. In the outer part of the hydrodynamic boundary layer, where the vertical velocity decays, the buoyancy force is unimportant. The profile of the vertical velocity component near the electrode can be shown to be parabolic. 

Zhou et al. [55], The most effective method to assess the capacity is the flow simulation which includes volumetric formulas and more reservoir parameters rather than other methods [56], Mass balance and constitutive relations are accounted in mathematical models to capacity assessment and dimensional analysis consists of fractional flow formulation with dimensionless assessment and analytical approaches [33], From the formulations demonstrated by Okwen and Stewart for analytical investigation, it can be deduced that the C02 buoyancy and injection rate have affected the storage capacity [57], Zheng et al. have indicated the equations employed in Japanese and Chinese methodology and have noted that some parameters in Japanese relation can be compared to the CSLF and DOE techniques [58]. 

That is, in the floating body, there should be a balance of forces due to the nuclear paramagnetic force as well as the gravity, the diamagnetic force, and the buoyancy (Figure 20A). 

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... 

Considering the case of vanishingly small flows (Q a 0), both the first and the second terms on the right-hand side of Eq. (55) which contain Q, become zero, and the force balance bubble volume is obtained directly by equating the surface tension force with the buoyancy force. Even in the detachment stage,... 

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