## Application of Dimensionless Numbers for Surface Aeration

From a fundamental point of view, it is not permissible to exceed the range of experimentally changed parameters considerably, if the results are to be reliable. If we wish to extract information about KLa from Fig. 5.14 for Simplex aerators (Fig. 5.6) of another size, all dimensionless geometric numbers must be constant and we must remain within a range of Fr numbers between 0.08 < Fr < 0.35. Using Frmax = 0.35 and assuming n = 1 s-1, we can calculate:

Although only a small range of Fr numbers was investigated, a relative high range of diameters d is included. However, is it possible to realize the required KLa? We will return to this question in Problem 5.

For practical applications, it is necessary to change geometric numbers and to study their influences. Frequently, the influence of relative small variations (e.g. d/D = 4.0 ^ d/D = 3.5) is low and the freedom to move is given. Fig. 5.14 Power correlation Ne = f (Fr) for surface aerator Symplex Type A, Pushing, H/d = 1.0, D/d = 4.37 (Zlokarnik 1975).
 / / / / y / / Fig. 5.15 Sorption correlation Y = f (Fr) for surface Aerator Simplex, Type A, Pushing, H/d = 1.0, D/d = 4.37 (Zlokarnik 1979). It is very important to prove these methods experimentally with two or three aerators of the same type but different diameters, which differ by a factor of two or three. The same water should be used and all geometric numbers must be the same in all these experiments if the influence of relative small changes has not been studied before. Unfortunately, the expenditure for such experiments is high and such studies are very seldom.
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