Orifice theory

Isentropic orifice theory is just as applicable to liquid nitrogen and liquid hydrogen, for the range of parameters used in these experiments, as to cold water. 

As a consequence of these simple deductions, Graham s experiments c effusion through an orifice came to be regarded as one of the earliest direct experimental checks on the kinetic theory of gases. However, a closer examination of his experimental conditions reveals that this view is mistaken. As mentioned earlier, his orifice diameters ranged upwards from 1/500 in., while the upstream pressure was never very much less thai atmospheric. Under these circumstances the molecular mean free path len ... 

One proposed simplified theory (4) provides reasonably accurate predictions of the internal flow characteristics. In this analysis, conservation of mass as well as angular and total momentum of the Hquid is assumed. To determine the exit film velocity, size of the air core, and discharge coefficient, it is also necessary to assume that a maximum flow through the orifice is attained. 

It has been postulated that jet breakup is the result of aerodynamic interaction between the Hquid and the ambient gas. Such theory considers a column of Hquid emerging from a circular orifice into a surrounding gas. The instabiHty on the Hquid surface is examined by using first-order linear theory. A small perturbation is imposed on the initially steady Hquid motion to simulate the growth of waves. The displacement of the surface waves can be obtained by the real component of a Fourier expression ... 

For a short pipe of circular cross section, the conductance as calculated for an orifice from Eq. (6-82) is multiplied by a correction factor iC which may be approximated as (Kennard, Kinetic Theory of Gases, McGraw-Hill, New York, 1938, pp. 306-308)... 

Figure 2-18. Flow coefficient C for square edged orifices. By permission, Crane Co. [3], Technical Paper 410 Engineering Div. (1976) and Fluid Meters, Their Theory and Application Part 1, 6th Ed., 1971, American Society of Mechanical Engineers and, Tuve, G. L. and Sprenkle, R. E., Orifice Discharge Coefficients for Viscous Liquids, Instruments Nov. 1933, p. 201.

Figure 2-38B. Net expansion factor, Y, for compressible flow through nozzles and orifices. By permission, Crane Co., Technical Paper 410, Engineering Div., 1957. Also see 1976 edition and Fluid Meiers, Their Theory and Application, Part 1, 5th Ed., 1959 and R. G. Cunningham, Paper 50-A-45, American Society of Mechanical Engineers.

According to Knudsen if a small circular orifice of diameter less than the mean free path of the molecules in a container, is opened in the wall of the container to make a connection to a high vacuum surrounding the container, the mass of gas effusing through the orifice, of area A, is given by an equation derived from the kinetic theory, where the pressure is in atmospheres. 

Compound 53 has an orifice just wide enough to allow the potential entry of small ions, atoms (He), or molecules (H2, D2, T2) inside its cavity as judged from high-level transition state calculations at the density functionally theory level (B3LYP/6-31G, Figure 19).1791 The low barrier of insertion for helium makes it a specially attractive target, but other spe-... 

Figure 8.5 shows a Venturi meter. The theory is the same as for the orifice meter but a much higher proportion of the pressure drop is recoverable than is the case with orifice meters. The gradual approach to and the gradual exit from the orifice substantially eliminates boundary layer separation. Thus, form drag and eddy formation are reduced to a minimum. 

The release location influences the vertical distribution of the time-averaged concentration and fluctuations. For a bed-level release, vertical profiles of the time-averaged concentration are self-similar and agreed well with gradient diffusion theory [26], In contrast, the vertical profiles for an elevated release have a peak value above the bed and are not self-similar because the distance from the source to the bed introduces a finite length scale [3, 25, 37], Additionally, it is clear that the size and relative velocity of the chemical release affects both the mean and fluctuating concentration [4], The orientation of the release also appears to influence the plume structure. The shape of the profiles of the standard deviation of the concentration fluctuations is different in the study of Crimaldi et al. [29] compared with those of Fackrell and Robins [25] and Bara et al. [26], Crimaldi et al. [29] attributed the difference to the release orientation, which was vertically upward from a flush-mounted orifice at the bed in their study. 

Let the flow of molecules into the Knudsen cell be F (molecules s l). In the absence of the reactive surface, these molecules are removed when they strike the escape aperture into the mass spectrometer. Let kCM. be the effective first-order rate constant (s ) for escape of the gas from the cell through this orifice, which can be measured experimentally. Alternatively, kcsc can be calculated from kinetic molecular theory since the number of collisions per second, Js, of a gas on a... 

In short lines, nozzles, and orifices, friction and heat transfer may be neglected, which makes the flow essentially isentropic. Work transfer also is negligible in such equipment. The resulting theory is a basis of design of nozzles that will generate high velocity gases for... 

The main variables in the operation of atomizers are feed pressure, orifice diameter, flow rate and motive pressure for nozzles and geometry and rotation speed of wheels. Enough is known about these factors to enable prediction of size distribution and throw of droplets in specific equipment. Effects of some atomizer characteristics and other operating variables on spray dryer performance are summarized in Table 9.18. A detailed survey of theory, design and performance of atomizers is made by Masters (1976), but the conclusion is that experience and pilot plant work still are essential guides to selection of atomizers. A clear choice between nozzles and spray wheels is rarely possible and may be arbitrary. Milk dryers in the United States, for example, are equipped with nozzles, but those in Europe usually with spray wheels. Pneumatic nozzles may be favored for polymeric solutions, although data for PVC emulsions in Table 9.16(a) show that spray wheels and pressure nozzles also are used. Both pressure nozzles and spray wheels are shown to be in use for several of the applications of Table 9.16(a). 

Among the devices used for the measurement of discharge are orifices and nozzles. Tubes are rarely so used but are included here because their theory is the same, and experiments upon tubes provide information as to entrance losses from reservoirs into pipelines. 

For static regime of bubble formation the simplest theory of capillarity based on equality of the elevating force of a bubble and retarding force gives the following dependence of the radius of bubble R on the radius of orifice (pores) r... 

The ratio pgV / (2nrO) is a criterion of the validity of the theory and according to the experimental results of different researchers it varies from 0.6 to 1.88 depending on the radius of the capillary orifice and the properties of the liquid [8,21],... 

The best fit between experimental results and theory is achieved when both the change in hydrostatic pressure along the height of the forming bubble at the moment of its detachment from the capillary orifice and the expansion of bubble during its rising are taken into account. Surface tension and density of foaming solution (see Eq. (1.9)) determine the size of bubbles when they are formed slowly. The surfactant kind and concentration affect both the rate of formation of adsorption layers at bubble surface and the stability of foam obtained. 

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