Expert ForumsMixing

Topic: Re: What is the required power for an anchor agitator?

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Let's start with the basic question about the required power for this agitator and then we can try to straighten out the calculations.  Using your given tank geometry and assuming the anchor is 20" in diameter, submerged to 34" by your liquid volume, operating at 20 rpm, with scrapers and your fluid properties, my estimated impeller power is 0.37 hp.  The reason for "estimated" power is that I know of no adequate correction factors for scrapers. (I used a factor of 1.5 in my calculations)  Scarpers should add power to an anchor impeller, but the number of scrapers, type of scrapers, and the propensity of the fluid to stick to the wall of the tank will all influence the power requirement.  Consequently, I recommend a design for a 1 hp motor, from which the torque will define the strength of the shaft and blades. Now for the formulas.  You have a mixture of turbulent power number and laminar power number in your description.  The different forms are used for different types of impellers in different applications.  For an anchor you want to use the laminar power number.  Your formula for the anchor power number is almost correct:                                           0.5                  0.16      0.67Np(laminar)  =113  (D/(T-D))    (H/D)   (W/D)     (n/2)
The problem with your formula is that the denominator of the first term should have (T - D) in the denominator, since the value is proportional to the spacing between the impeller and the wall.  The power calculation using the laminar power number is as follows:
P = Np(laminar) * Visc * N^2 * D^3
Notice that the calculation using the viscous power number involves viscosity instead of density, as in the turbulent power calculation, and rotational speed squared instead of speed cubed and diameter cubed instead of diameter to the fifth power.  A correction factor must be included for density (as represented in the Reynolds number) if the mixer operates in the transitional range.  This application is in the laminar range with a Reynolds number of about 4.  The other form of the power calculation is for turbulent mixing and commonly used with high speed impellers, such as pitched-blade turbines or hydrofoil impellers. for which a correction factor is related to Reynolds number, which includes the viscosity effect. In each case, the power number is dimensionless.  So, unless you use coherent units, such as SI metric (power in Watts, viscosity in Pascal seconds, rotational speed revolutions per second, and impeller diameter in meters), you must use a conversion factor.  If you want to use common engineering units the power calculation becomes:
P[hp] = {Np(laminar) * Visc[cp] * N[rpm]^2 * D[inches]^3} / 1.637x10^14
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