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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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