On August 29th, I recommended a design based on power per volume at 0.0014 kilowatts/cubic meter (0.007 hp/1000gal).  That power per volume level is sufficient to mix large storage tanks with side-entry mixers.  A submersible mixer creates the same type of motion as a as a side-entry mixer.  Higher mixing intensities will be needed if the waste contains settling solids, such as sand particles.  If other data is available from similar applications, then he should use that information in the form of power per volume.
 
The basin geometry provided in the original question was typical, with length, width, and height of similar magnitudes.  Had the basin been exceptionally wide, long, or shallow, two mixers might have been required, but the total power per volume level would have been similar.
 
The "science" of all mixing is based on empirical observations.  No mathematical methods exist for calculating mixing intensity other than those based on observed results that can be related to design requirements.  Power per volume is a simple but effective method.  Most side-entry and submersible mixers operate at similar rotational speeds, so mixing intensity can be related to power, although torque and thrust are probably the physical effects related to liquid motion.
 
If you want to know the relationship between mixer operation and power: impeller power is proportional to liquid density, rotational speed cubed, and impeller diameter to the fifth power for turbulent conditions.  The constant of proportionality is the impeller power number, which depends on number of blades, blade angle, blade width and blade shape.  The power number is developed through experimental observation and can be unique for different types of impellers.

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