Another Reynolds number, that for a stirred tank, is less obvious. The fluid properties seem to
be good choices for rho and µ, but there are problems in
selecting D and V. The impeller diameter is used for D even though
an impeller also has height and usually several blades that must
affect mixing or else engineers would not experiment with impeller
designs. In the quest for something to use for V, the revolutions
per second of the impeller is chosen even though it not a velocity.
There is no length dimension in this term, so the dimensionless
number is created by using the impeller diameter once more. The
mixing Reynolds number is:
Despite its flimsy bases, this illogical Reynolds number is highly useful and correlates quite well when comparing systems that employ roughly similar impellers.
Scale up of mixing uses a correlation of Reynolds number with Power
number defined as:
This equation is notable because the exponents are unusually large; Power number is very strongly affected by rpm and by impeller diameter. A correlation of Power number and Reynolds number is shown in the next figure. There are families of curves for different impellers (propellers, turbine impellers, etc.) and baffle configurations. If you use the same type of impellers in the large and small tanks, the graph is useful for scale up. Experiments are performed in one tank to find the Reynolds number that gives the desired process results. Usually the same Reynolds number will give about the same results in the other tank. The corresponding Power number is read from the graph. Substituting fluid properties and reasonable values for rpm leave power input as the only unknown in the equation. Of course, the power required per unit volume is the key to selecting the motor for the mixer.
Example of calculation.