By Imre Horváth (Auth.)
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Extra info for Modelling in the Technology of Wastewater Treatment
E. in plate or tube separators and some submerged parts of settling tanks, but even here the Fr and Re numbers act simultaneously. It should also be noted t h a t in some settling tank configurations the definite determination of the Recnt value may also present appreciable difficulties. 44 (d) As a compromise between the Fr and Re numbers a linear combination o f the two has been suggested in the form of the product FrRe from which the invariant group FrRe= — Xg=Xv=l). is obtained, leading to the scale factor λν=1 (in the case of In other words, this is a case of the equal velocity or equal surface load scaling method, often mentioned in the subject literature.
With reference t o these studies, the following dimensionless numbers are suggested as modelling criteria for flow in granular filter media. * λν ην vv (81a) (81b) where MK is the invariant group of Mosonyi and Kovâcs and P ö = — | — = t h e Poiseuille n u m b e r . MK The characteristic length / is preferably replaced with, for example, the particle diameter d. In the range of three-phase flow [74, 77] '-s-? <> 82 where / is the capillary (Horvâth) number. The various hydraulic quantities, such as velocity or discharge, can be converted from one system to the other using the expressions given in the literature referred to above.
Comparison of flocculation results at identical Re numbers (flocculant: iron chloride) Figure 18 implies the existence of a self-modelling range. In fact, along t h e horizontal limb of the plot the residual iron concentration is unaffected by 2 t h e value of GRe~ V . 2 2 Λ 3 4 5 2 Fig. 18. Deflocculation as a function of the GRe~V product Besides t h e experimental evidence a theoretical approach can also be adopted t o demonstrate t h e relationship between t h e Re and Ca numbers  2 2 QV mv t ^ oc Vtr\ 2 2 Vt I V (116a) where m is t h e mass ; v, the mean velocity ; and /, t h e characteristic length.