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What is the formula for laminar mixing?

Q: I wanted to know the formula for power for laminar mixing.

I have read the “Handbook of Industrial Mixing” as you previously advised. But it doesn’t have a clear formula for laminer flow stirrer (power, shaft design, gearbox design, etc.)

tank inner diameter = 36 inches
impeller diameter = 15 inches
impeller type = pitched blade (45 degree)
Reynolds no. = 3
specific gravity = 1.2
cp;(viscosity coefficient)= 10000, nearly. (tomato suspension in boiling water)
tank height = 84 inches
RPM = 15

A:

I stand by my initial advice. The “Handbook of Industrial Mixing” has about as much information as you are going to find in any literature reference, without a more complete background in mixing.  A short course on mixing might fill some of those gaps.  In the laminar range, Reynolds number less than 10, the power number for a pitched-blade turbine is 52.6 divided by the Reynolds number.  The other answers to torque and bending requirements for shaft design and gearbox design can be found in Chapter 21, Mechanical Design of Mixing Equipment, in the “Handbook of Industrial Mixing”.

Beyond that information, the mixer you describe will not effectively mix the "tomato suspension in boiling water" you describe.  The table Mixer Design Total - small shows that one 15-inch diameter pitched-blade turbine running at 15 rpm puts only 0.0025 hp into the process, for a mixing intensity of 0.15.  A mixing intensity of 1.0 is required to effectively move all of the contents in the tank. 

The table Mixer Design Total - small 2 shows using three pitched-blade turbines operating at 125 rpm will possibly mix the contents.  Actually, pitched-blade turbines are probably not the best impeller choice for low Reynolds number (36) applications.  At least more larger impellers are required to handle viscous fluids.

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