It sounds as if you have the necessary information, although the equation (empirical correlation) involves more than just viscosity.  A vertical mixer in a baffled tank had a constant power number in turbulent conditions.  I assume that the power number you have is the turbulent power number.  The power number actually changes as the viscosity increases, or really as you move away from turbulent conditions into transition or even viscous conditions.  The degree of turbulence is a function of impeller Reynolds number, which involves impeller diameter, rotational speed, fluid density and fluid viscosity.
 
I will provide relationships using typical engineering units and a correlation for a pitched-blade turbine impeller.  Obviously, other units will require different conversion factors to work with dimensionless groups and other impeller types require different correlations.
 
First, calculate the impeller Reynolds number.  (Click here for a relationship for calculating Reynolds number.)  The constant is just a conversion factor to cancel the variable units to a dimensionless value.  Regardless of the units used for the process variables, the Reynolds number should be the same if it is made dimensionless by cancellation of the units and appropriate conversion factors.
 
Then the Reynolds number can be used to find the power number for the actual process conditions.  In order to use your turbulent power number, the correlation has been reduced to a correction factor, which is characteristic of nearly all pitched-blade turbines.  The correction factor provided (click here) is merely a curve fit for the available empirical correlation of test results.  The curve fit is broken into segments corresponding to ranges of Reynolds numbers.  Use the portion of the correction calculation that covers the calculated Reynolds number.
 
The correction factor is always greater than or equal to one, so your corrected power number is always greater than or equal to your turbulent power number.  After applying the correction factor to your impeller power number, use it to calculate impeller power with the expression provided (click here).  Again the units for the variables are important for the correction factor to be appropriate.

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