## Lesson 31. POWER CONSUMPTION OF MIXER-IMPELLER, SELECTION OF MIXING EQUIPMENT IN DAIRY INDUSTRY, MIXING PUMPS

Module 8. Mixing and agitation equipment

Lesson 31
POWER CONSUMPTION OF MIXER-IMPELLER, SELECTION OF MIXING EQUIPMENT IN DAIRY INDUSTRY, MIXING PUMPS

31.1 Introduction

The operation of agitation has to be effective in achieving the objective, at a minimum cost as well as in short time. With increasing cost of electricity, the energy consumption of agitation and mixing has to be carefully audited for energy savings. In the analysis electrical energy consumption, the techniques of optimization, dimensional analysis are done to minimize the cost of installation and operation.

31.2 Circulation, Velocities and Power Consumption in Agitated Vessels

Volume circulated by impeller must be sufficient to sweep out the entire vessel in reasonable time. Velocity of the stream leaving the impeller must be sufficient to carry the currents to the remotest points. Turbulence in moving stream often governs the effectiveness of the operation. It is caused by large velocity gradients.

Volumetric flow rate, q is proportional to the speed and the cube diameter of impeller. Another important parameter is the Flow Number, a dimensionless number.

Flow Number, NQ1 = ${N}_{}$Q1 = q n× (Da )3

Flow number is constant for each type of impeller

For standard flat–blade turbine, in a baffled vessel, NQ ≈ 1.3

For Flat – blade turbines, the total flow, estimated from the average circulation time for particles is

$\text{qT}=0.92×n×{}^{}$ (Da )3 ${{}_{}}^{}×\left(\frac{\text{(Dt}}{\text{Da)}}\right)$

For a $\frac{\text{Dt}}{\text{Da}}$ =3 the qT = 2.76 nDa3 or 2.1 times the value at the impeller (NQ=1.3). The above equation should be used only for Dt / Da ratio between 2 and 4

31.3 Power Consumption

When the flow in the tank is turbulent, the power requirement can be estimated from the product of the flow ‘q’ produced by the impeller and the kinetic energy, per unit volume of the fluid.

$Q=n×{{}^{}}_{}$ (Da )3 ${}_{}×\text{NQ}$

$\text{EK}=\frac{\rho ×{\left({{V}_{}}^{}\right)}^{}}{}$2 1) 2 / 2gc

Where V21 = Actual velocity of the particle at the impeller blade tip, which is slightly smaller than the tip speed $\left({\mu }_{2}\right)$

Power requirement, that is $n×{}^{}$(Da )3 ${}^{}×\text{NQ}=\frac{\rho }{2\cdot \text{gc}}×{\left(\alpha \cdot \pi \cdot \text{n}\right)}^{}$ (Da )2 ${}^{}$

= $\frac{\rho ×{n}^{3}×{\text{(Da)}}^{5}}{}\left({\alpha \right)}^{2}×\frac{{\mathrm{\left(\pi }\right)}^{2}}{}×{}_{}\right)$ N q /2gc

$\left({}_{}\right)$

Where $\alpha =\frac{{{\mathrm{\left(V}}_{}}^{}}{}$1) 2 ( μ) 2