## Introduction

There are some important questions to answer if we want to study an aeration process in a laboratory-scale or pilot-scale plant and apply the results to large-scale aeration and activated sludge systems. Let us discuss this problem for the example of a surface aerator constructed and processed as a turbine with a vertical shaft. We assume that it is possible to measure the oxygen transfer rate and the power consumption for clean water or wastewater with activated sludge. The volume, the type of tank and the mean residence time (aeration time) are given. Some important questions are:

• The diameter of the aerator in the laboratory-scale plant was 0.25 m, for example. What may be the best diameter for the large-scale plant?

• The range of speeds in the laboratory-scale experiments was 10-100 min-1. What may be the suitable range of speeds for the large-scale aerator?

• In the laboratory-scale experiments, an efficiency of nearly E = 3 kg O2 (kWh)-1 was obtained. Under what conditions can we expect a relatively high efficiency; and is it possible to find operating conditions yielding E = 3 kg O2 (kWh)-1?

• Is it more economical to install two or four aerators instead of one? What is the optimal diameter, speed and depth of submersion?

These questions are not easy to answer. We need two methods, the method of dimensional analysis and the method to transfer models. Both will be explained for a simple case: the stirred non-aerated tank and the stirred aerated tank without suspended solids.

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