Studies on the Power Requirement of Mixing Impellers (IV) : Empirical Equations Applicable for a Wide Range

Abstract

The present authors have already reported on the empirical equations for the power requirement of paddle agitators. In this report, equations for the three ranges of high, medium, and low viscosity were made and equations for the maximum power required under fully baffled conditions were also formed separately. Although the results are accurate, these equations are not always convenient because of the complexity in deciding which form to be used. On the basis of a reasonable assumption derived from the essential concept of power consumption, the authors derived an empirical equation which covers wide ranges of power data as follows : Nₚ=A/Rₑ + B(10³+1.2Rₑ⁰.⁶⁶/10³+3.2Rₑ⁰.⁶⁶)ᵖ(H/D)⁽⁰.³⁵⁺ᵇ/ᴰ⁾ (sinθ)¹.² (27) where A=14+(b/D){670(d/D-0.6)²+185} (19) B=10{1.3-4(b/D-0.5)²-1.14(d/D)} (22) p=1.1+4(b/D)-2.5(d/D-0.5)²-7(b/D)⁴ (23) The maximum power consumption of paddle agitators can also be calculated by Eq. (27) by substituting Re with the values of Rc and Rθ which can be obtained by the following equations : For the paddle having a blade angle of 90°, Rc=25/(b/D)(d/D-0.4)²+{b/D

0.11(b/D)-0.0048} (28) For the paddle having an arbitrary angle of θ, Rθ=10⁴(1-sinθ)Rc (30) Fairly good agreements were obtained between those values calculated by the equations and those obtained by the experiments.