CHAPTER
12
where (Re) = (D^{2}Nr/m), (Po) = (P/D^{5}N^{3}r) and this is called the Power number (relating drag forces to inertial forces), (Fr) = (DN^{2}/g) and this is called the Froude number (relating inertial forces to those of gravity); D is the diameter of the propeller, N is the rotational frequency of the propeller (rev/sec), r is the density of the liquid, m is the viscosity of the liquid and P is the power consumed by the propeller. Notice
that the Reynolds number in this instance, uses the product DN for
the velocity, which differs by a factor of p from the actual velocity
at the tip of the propeller.

The Froude number correlates the effects of gravitational forces and it only becomes significant when the propeller disturbs the liquid surface. Below Reynolds numbers of about 300, the Froude number is found to have little or no effect, so that eqn. (12.7) becomes: Experimental results from the work of Rushton are shown plotted in Fig. 12.1.
Unfortunately, general formulae have not been obtained, so that the results are confined to the particular experimental propeller configurations that were used. If experimental curves are available, then they can be used to give values for n and K in eqn. (12.8) and the equation then used to predict power consumption. For example, for a propeller, with a pitch equal to the diameter, Rushton gives n = 1 and K = 41. In cases in which experimental results are not already available, the best approach to the prediction of power consumption in propeller mixers is to use physical models, measure the factors, and then use eqn. (12.7) or eqn. (12.8) for scaling up the experimental results.
Use the subscripts S for the small tank and L for the larger one. To preserve geometric similarity the dimensional ratios should be the same in the large tank as in the small. Given that the fullscale tank is three times larger than the model,
For dynamic similarity, (Re)_{L} = (Re)_{S}
For the large tank (Re) = (D_{L}^{2}N_{L}r/m)
Eqn. (12.8) is applicable, and assuming that K = 41 and n = 1, we have
And since 1 horsepower = 746 J s^{1} Mixing > MIXING EQUIPMENT Back to the top 
