Editing Mixing (process engineering) (section)

==Constitutive equations==
Many of the equations used for determining the output of mixers are empirically derived, or contain empirically derived constants. Since mixers operate in the turbulent regime, many of the equations are approximations that are considered acceptable for most engineering purposes.

When a mixing impeller rotates in the fluid, it generates a combination of flow and shear.  The impeller generated flow can be calculated with the following equation:

<math> Q = Fl*N*D^3 </math>

Flow numbers for impellers have been published in the North American Mixing Forum sponsored Handbook of Industrial Mixing.<ref name=Handbook>{{cite book |title=Handbook of Industrial Mixing: Science and Practice |editor1=Edward L. Paul |editor2=Victor Atiemo-Obeng |editor3=Suzanne M. Kresta |year=2003 |publisher=Wiley |isbn=978-0-471-26919-9 |url=http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471269190.html |url-status=live |archive-url=https://web.archive.org/web/20121121112810/http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471269190.html |archive-date=21 November 2012 |df=dmy-all }}</ref>

The power required to rotate an impeller can be calculated using the following equations:

<math> P= P_{o}\rho N^3D^5 </math> (Turbulent regime)<ref>{{cite web |url=http://cercell.com/support/bactovessel-details/turbine-power/ |title=Power Number (Np) for turbines |publisher=Cercell.com |access-date=2017-06-23 |url-status=live |archive-url=https://web.archive.org/web/20170611213616/http://cercell.com/support/bactovessel-details/turbine-power |archive-date=11 June 2017 |df=dmy-all }}</ref>

<math> P= K_p\mu N^2D^3 </math> (Laminar regime)

<math> P_{o} </math> is the (dimensionless) power number, which is a function of impeller geometry; <math> \rho </math> is the density of the fluid; <math> N </math> is the rotational speed, typically rotations per second; <math> D </math> is the diameter of the impeller; <math> K_p </math> is the laminar power constant; and <math> \mu </math> is the viscosity of the fluid. Note that the mixer power is strongly dependent upon the rotational speed and impeller diameter, and linearly dependent upon either the density or viscosity of the fluid, depending on which flow regime is present. In the transitional regime, flow near the impeller is turbulent and so the turbulent power equation is used.

The time required to blend a fluid to within 5% of the final concentration, <math> {\theta_{95}} </math>, can be calculated with the following correlations:

<math> {\theta_{95}} = \frac {5.40} {P_{o}^{1 \over 3} N} (\frac {T} {D})^2 </math> (Turbulent regime)

<math> {\theta_{95}} = \frac {34596} {P_{o}{1 \over 3} N^2 D^2} (\frac {\mu} {\rho}) (\frac {T} {D})^2 </math> (Transitional region)

<math> {\theta_{95}} = \frac {896*10^3 K_p^{-1.69}} {N} </math> (Laminar regime)

The Transitional/Turbulent boundary occurs at <math> P_{o}^{1 \over 3} Re = 6404 </math>

The Laminar/Transitional boundary occurs at <math> P_{o}^{1 \over 3} Re = 186 </math>