Example of Using Power Number

by David W. Holmes for assignment at University of Canterbury, September 1999
Java translation of his spreadsheet by H. Bungay

Consider scale up from a tank with diameter of 0.9 m to a tank with diameter 2.7 m.
Effective mixing in the smaller tank was obtained with:
    Impeller speed 8 revolutions per second
    Applied power 1.2 kW

The fluid has a viscosity of 1 centipoise and a specific gravity of 1.2.

We calculate the Power Number and the Reynolds Number for the smaller tank.

We substitute numbers into the equation as follows:

You can confirm the calculation with my applet:

Let's check the Reynolds Number and substitute numbers into the equation:


Now we check the Reynolds Number for the larger tank with the impeller at 4 r/s:

Let's assume that the Reynolds Number is sufficiently high that both vessels will have the same Power Number.
We substitute numbers and solve for the power:


 
  Let's be sure that we have chosen units that cancel to give dimensionless numbers.