Editor's note: This question is related to a previous Ask the Experts post: http://www.chemicalprocessing.com/experts/answers/2009/096.html


Now you are asking a very difficult question about power number and impeller power, because even with a turbulent power number for a specific impeller design, that value must be corrected for the presence of air.  Gassed power decreases as gas rate increases, often by a considerable amount.  For conventional, disk-style impellers, gas rate often reduces power requirement to only about 40% of the un-gassed conditions.  For cupped-blade disk-style impellers, the gassing effect may be only about 80%.  In any case, a dimensionless aeration number, which is the volumetric flow rate of gas (at actual conditions) divided by the rotational speed of the impeller and the impeller diameter cubed, is used to correlate the gassing effects.
 
Interpretation of dynamic oxygen transfer data from laboratory or experimental conditions to full-scale or production conditions is either a more extensive literature and research project, or work to be assisted by an consultant.  Similar studies have been reported in the literature.  The answer to your question is much more than simply calculating or knowing impeller power number.