Radial spreading velocity

The pool spreading models provide the radius or radial spread velocity of the pool from which the total pool area and depth is determined. 

Figure 6.6 uses a particular problem to illustrate some of the salient differences between the semi-infinite and finite-gap configurations. In both cases the net flow rates are the same, and the streamlines in both plots have the same values. The streamlines for the finite-gap problem show pure axial flow at the inlet, whereas the semi-infinite case shows radial spreading everywhere. The radial-velocity profiles are quite different, with the finite-gap profile showing no slip at both boundaries. 

Velocity of radial spread dp/d/ (mmHg/s) Ejection fraction [ o]E x (mmHg/ml)... 

Air jets are used for many purposes. Some of these are described in other parts of this chapter, but it is not possible to describe all the possible types and uses. The fundamentals regarding velocity, flow rate, and spreading of round, radial, and plane jets are described in Sections 7.4 and 7.7. When jets are used inside rooms, they do not need to have any corresponding exhaust air. Exhausted air is needed for supply jets in general ventilation, but if the jet s air is taken from the room and blown into the room again, no exhaust is needed. If the air is taken from outside the room, it is necessary to have the same flow rate exhausted from the room. 

Non membership and/or binarity are not the reasons for the scatter M 67, since both low and high Li stars are confirmed radial velocity members and the spread is still present when considering single stars only. Under the very reasonable assumption that cluster stars were all born with the same Li content, the scatter is therefore intrinsic and due to different amounts of Li depletion. 

Type R. This mode corresponds to low impinging velocities at any surface temperatures considered (200-400 °C). A droplet spreads as a radial film after impinging on a hot surface. Then, it shrinks and rebounds from the surface without breaking up. Hence, the mode is called R type. 

When a tube or pipe is long enough and the fluid is not very viscous, then the dispersion or tanks-in-series model can be used to represent the flow in these vessels. For a viscous fluid, one has laminar flow with its characteristic parabolic velocity profile. Also, because of the high viscosity there is but slight radial diffusion between faster and slower fluid elements. In the extreme we have the pure convection model. This assumes that each element of fluid slides past its neighbor with no interaction by molecular diffusion. Thus the spread in residence times is caused only by velocity variations. This flow is shown in Fig. 15.1. This chapter deals with this model. 

It is easily verified that any function of the form P(r,t) - P0 = (l/r)f(t-r/c0) is a solution, the negative sign corresponding to an outgoing wave about the center. Thus the form of an infinitesimal spherical wave does not change as it spreads out at the same velocity, but its amplitude decreases proportional to 1/r, the inverse of the radial distance... 

Note that even for pure radial flow, w = 0, there is still a circumferential dilatation, Fee 7 0. This is because the radial velocity spreads the flow as seen by the dashed differential element in Fig. 2.7. 

Spinning Disk Atomization. The spinning disk produces a continuous spray which spreads radially outwards from the periphery of the disk. A major difference of this technique in comparison with pressure atomization of liquids is mentioned by Marshall and Seltzer (5F), who give a detailed theory of atomization for both smooth and vaned disks. High velocities are achieved without a pressure increase. 

The problem to be solved in this paragraph is to determine the rate of spread of the chromatogram under the following conditions. The gas and liquid phases flow in the annular space between two coaxial cylinders of radii ro and r2, the interface being a cylinder with the same axis and radius rx (0 r0 < r < r2). Both phases may be in motion with linear velocity a function of radial distance from the axis, r, and the solute diffuses in both phases with a diffusion coefficient which may also be a function of r. At equilibrium the concentration of solute in the liquid, c2, is a constant multiple of that in the gas, ci(c2 = acj) and at any instant the rate of transfer across the interface is proportional to the distance from equilibrium there, i.e. the value of (c2 - aci). The dispersion of the solute is due to three processes (i) the combined effect of diffusion and convection in the gas phase, (ii) the finite rate of transfer at the interface, (iii) the combined effect of diffusion and convection in the liquid phase. In what follows the equations will often be in sets of five, labelled (a),..., (e) the differential equations expression the three processes (i), (ii) (iii) above are always (b), (c) and (d), respectively equations (a) and (e) represent the condition that there is no flow over the boundaries at r = r0 and r = r2. 

Spiral vortex. So far the discussion has been confined to the rotation of all particles in concentric circles. Suppose there is now superimposed a flow with a velocity having radial components, either outward or inward. If the height of the walls of the open vessel were less than that of a liquid surface spread out by some means of centrifugal force, and if liquid were supplied to the center at the proper rate by some means, then it is obvious that liquid would flow outward, over the vessel walls. If, on the other hand, liquid flowed into the tank over the rim from some source at a higher elevation and were drawn out at the center, the flow would be inward. The combination of this approximately radial flow with the circular flow will result in path lines that are some form of spirals. 

Axial mixing Eddy diffusion in the direction of the axis of the extractor and a radial diffusion or spreading, resulting from nonuniform velocity. 

A is an eddy diffusion term to account for the various pathways in packed columns which lead to peak spreading V is the tortuosity factor which often has a value close to unity u is the linear velocity of the carrier gas terms Cg and account for radial diffusion in the gas phase and the liquid phase respectively. We have found experimentally on packed columns that the Cg term is negligible (6J. The expression for the C- term may be written as... 

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