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Shaft and gearbox size

Q: What should be the required power for agitating a syrup with a density of 1500kg/m3, volume is 15m3, minimum rpm is 350, impeller diameter is 600mm. What should be the size of the shaft and gearbox?

A: First, the fluid properties include only the density, which is typical of a glucose syrup.  That same density often corresponds to a viscosity of 5,000 cp, which I used in my calculations.  Second, and perhaps most important, the question makes no mention of the impeller type.  I chose to use a 4-blade, 45-degree, pitched-blade turbine.  If a straight-blade turbine is used, the power could be triple my calculations.  If the impeller is a hydrofoil or shallow pitch prop, the power could be only one third my estimate.  I also assumed that the tank would have baffles, would make the mixing more effective, but if missing would only make my calculations more conservative.  With those qualifications:
 
    Motor Power - 45 KW
    Shaft Diameter - 65 mm
    Drive Torque - 1,220 N-m
 
    A further qualification, with many unknowns involves the operating speed.  At 350 rpm, the mixer shaft will be operating above the first natural frequency.  By my design estimates, the natural frequency will be around 180 rpm, which means that the mixer cannot be safely operated between 150 rpm and 205 rpm.  Different impeller fabrication methods may change the natural frequency.

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What is the best way to approach gas-gas mixing?
I want to mix two low viscous gas streams in laminar regime. I am planning to mix them by passing through a pipe filled with spherical pebbles or some structured packing. I want to calculate the length required for the mixing expected. My required process stream details are as follows:

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He= 0.99
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We would like to have a general idea of pumping number for our reactors. Can you help us with blend-time calculations?
To characterize one of the reactors at plant scale, we use the discoloration method. The parameters for the mixing time are calculated based according to the following formula:

t_mix= K/(aN(D/T)^b (T/Z)^0.5 )
N = impeller speed
D = diameter stirrer
T = diameter tank
Z = liquid height
The divisor is known as Kmix

Because we don't really know the uniformity (U) reached with this method we don't replace K with

K = -ln (1-U)

But get the best fit for K, a and b by means of the least square method. It is known that the pumping number can be determined by

N_Q= (Vk_mix)/(ND^3 )

We would like to have a general idea of pumping number for our reactors. So if we would like to deviate the pumping number from the above method would it be correct that for T=Z (so at a fixed volume based on the reactor geometry) we use the following formula.

N_Q= (VaN(D/T)^b)/(ND^3 )

Working in a turbulent regime, this result in a constant pumping number related to the tank geometry. Would the above approach be correct to compare pumping and mixing time capabilities of different reactor set ups? I think that not working at a fixed uniformity results in a gap in the above approach.

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