Similar flows

The process is then resumed. Meanwhile, regeneration is occurring by a similar flow system in the regeneration tank, from which the regenerated ion exchanger is transferred periodically to the hopper above the water-rinse tank. In the latter, the resin particles are fluidized to flush away fines and accumulated foreign matter before the resin is returned to the adsorption tank. 

Air supplied in confined space by downward vertical jets creates a similar flow pattern as in the case of air supply by horizontal nonattached jets. With vertical air supply, the occupied zone is ventilated directly by air jets. Grimitlyn suggests that the area of occupied zone ventilated by one jet be sized based on the jet s cross-sectional area at the point it enters the occupied zone. The jet cross-sectional area and configuration depend upon the height of the air supply, the type of air jet, and diffuser characteristics ( K, and K, ). 

Having established that these assumptions are reasonable, we need to consider the relationship between the parameters of the actual offset jet and the equivalent wall jet that will produce the same (or very similar) flow far downstream of the nozzle. It can be shown that the ratio of the initial kinematic momentum per unit length of nozzle of the wall jet to the offset jet,, and the ratio of the two nozzle heights,, depend on the ratio D/B, where D is the offset distance betw een the jet nozzle and the surface of the tank, and h, is the nozzle height of the offset jet. The relationship, which because of the assumptions made in the analysis is not valid at small values of D/hj, is shown in Fig 10.72. 

The assumption of a self-similar flow (Reynolds number-independent flow) simplifies full-scale experiments and is also a useful tool in the formulation of simple measuring procedures. This section will show two examples of self-similar flow where the Archimedes number is the only important parameter. 

This is based on the flow and specific energy produced by the pump at its best efficiency point of performance following the approach stated by Wisclicenus Any fixed value of the specific speed describes a combination of operating conditions that permits similar flow conditions in geometrically similar hydrodynamic machines. ... 

For NRc S 10, the liquid motion moves with the impeller, and off from the impeller, the fluid is stagnant [34]. The Froude number accounts for the force of gravity when it has a part in determining the motion of the fluid. The Froude numbers must be equal in scale-up situations for the new design to have similar flow when gravity controls the motion [16]. 

Obtain the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer and write down the corresponding analogy for mass transfer. For a particular system, a mass transfer coefficient of 8,71 x 10 8 m/s and a heat transfer coefficient of 2730 W/m2 K were measured for similar flow conditions. Calculate the ratio of the velocity in the fluid where the laminar sub layer terminates, to the stream velocity. 

Comparison of the boundaries of the observed flow patterns with the analytical criteria derived by Quandt showed that the bubble, dispersed, and annular flow patterns are subclasses of a pressure gradient-controlled flow. Similarly, flow patterns identified as slug, wave, stratified, and f ailing film are subclasses of a gravity-controlled situation. 

A dynamic similitude embodies both hydrodynamic and thermodynamic similitudes. A hydrodynamic similitude requires a similar flow pattern and similar veloc-... 

Laboratory reactors and industrial scale equipment are seldom operated under similar flow and heat transfer conditions. To obtain a... 

Early studies of the transition to turbulence relied on flow visualization techniques for liquid flow through arrays of spheres. Jolls and Hanratty (1966) found a transition from steady to unsteady flow in the range 110<7 e< 150 for flow in a dumped bed of spheres at N — 12, and they observed a vigorous eddying motion that they took to indicate turbulence at Re — 300. In regular beds of spheres, Wegner et al. (1971) found completely steady flow with nine regions of reverse flow on the surface of the sphere for Re — 82, and similar flow elements but with different sizes in an unsteady flow at Re — 200. Dybbs and Edwards (1984) used laser anemometry and flow visualization to study flow... 

It may be noted that similar flow regimes can be seen with immiscible liquid systems. If the densities of the two liquids are close the flow regimes for horizontal flow will more nearly resemble those for vertical flow. 

A similar flow sheet has been suggested for the treatment of mine waters. However, the similarity is only apparent. The iron content in these... 

In addition, a process for the purification and production of citric acid has been reported, utilizing a similar flow sheet. 

When a conductive material is placed within the electric field, current begins to flow, as characterized by the current density, J, of Eq. (6.1). The current density is also a vector quantity, but since our field is in one dimension only, current will similarly flow only in one direction, so that we will use only the scalar quantity from here on, J. The current density is simply the current, /, per unit area in the specimen. A ... 

Tliis is the well-known dimensionless equation for fluid flow. It represents the pressure coefficient as an unspecified function of the Reynolds and Froude groups. In geometrically similar flow systems, the pressure coefficients will be also equal, provided that the Reynolds and Froude numbers are both equal. 

The success of the ID fluid dynamic model to describe the flow field in the DPF channel (Konstandopoulos and Johnson, 1989 Konstandopoulos et al., 1999, 2003) is an indication for the existence of a (nearly) self-similar flow field. A necessary condition for the application of the ID model for the heat transfer problem as well, is that the wall velocity ww variation must be small along the characteristic channel length required for establishment of a steady heat transfer pattern (i.e. a length of a2ftz/y.lh). In transferring the above to the case of flow and heat transfer in a DPF channel we may formally write the heat balance as... 

Many workers have studied and published correlations between various types of plastimeter, often to show that they do not agree and to illustrate the superiority of the instrument which supposedly agrees best with processing behaviour. Several comparisons are included in the literature already noted and other examples are shown in Figure 6.6. Figure 6.6a shows the relatively close correlation obtained between two compression instruments, the Wallace rapid and Williams plastimeters, for materials of similar flow characteristics (plasticised natural rubber). When such rubbers are compared on two basically different instruments (compression and extrusion) the... 

This also is refetTed to as the Reynolds criterion. Reynolds numbers are only comparable when they refer to geometrically similar flows and. provided that all the boundary conditions can be described by the scale velocity and scale length, flows of the same Reynolds number are dynamically similar. For an airfoil, it is... 

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