View source for Partition (Density, Pivot)

== Description ==

This article describes the Pivot function for the partition of particles by size and density.{{Scott and Napier-Munn (1992)}}

== Model theory ==

{{Under construction|section}}

== Excel ==

{{Under construction|section}}

The Pivot partition equation may be invoked from the Excel formula bar with the following function call:

<syntaxhighlight lang="vb">=mdPartition_Pivot(MeanSize as Range, RD as Range, Yp as Double, rhop as Double, k as Double, n as Double, Optional returnPartitionMetrics as Bool = false)</syntaxhighlight>

{{Excel (Text, Help, No Arguments)}}

The input parameters and model results are defined below in matrix notation, along with an example image showing the selection of the same cells in the Excel interface:

:{| 
|- style="vertical-align:top;"
|
<math>
\begin{align}
MeanSize & = 
\begin{bmatrix}
\bar{d}_1\text{ (mm)}\\
\vdots\\
\bar{d}_n\text{ (mm)}\\
\end{bmatrix}\\
\\
RD & = \begin{bmatrix}
(\rho_{\rm S})_{1}\text{ (t/m}^\text{3}\text{)} & \dots & (\rho_{\rm S})_m\text{ (t/m}^\text{3}\text{)}\\ 
\end{bmatrix}\\
\\
Y_{\rm p} & = \big [Y_{\rm p} \text{ (frac)} \big ]\\
rhop & = \big [\rho_{\rm p} \text{ (t/m}^3\text{))}\big ]\\
k & = \big [k\text{ (-)} \big ]\\
n & = \big [n\text{ (-)} \big ]\\
returnPartitionMetrics & = \big [(\text{True / False)} \big ]\\
\\
\\
mdPartition\_Pivot & = 
\begin{bmatrix}
\begin{bmatrix}
Y_{11}\text{ (t/h)} & \dots & Y_{1m}\text{ (t/h)}\\
\vdots & \ddots & \vdots\\
Y_{q1}\text{ (t/h)} & \dots & Y_{qm}\text{ (t/h)}\\
\end{bmatrix}

&

\begin{bmatrix}
(\rho_{50})_1\text{ (t/m}^3\text{)}\\
\vdots\\
(\rho_{50})_q\text{ (t/m}^3\text{)}\\
\end{bmatrix}

&

\begin{bmatrix}
(E_{\rm p})_1\text{ (t/m}^3\text{)}\\
\vdots\\
(E_{\rm p})_q\text{ (t/m}^3\text{)}\\
\end{bmatrix}

&

\begin{array}{c}
\begin{bmatrix}
(d_{50})_{1}\text{ (mm)} & \dots & (d_{50})_m\text{ (mm)}\\ 
\end{bmatrix}^{\rm *}
\\
\\
\\
\\
\end{array}

\end{bmatrix}
\end{align}</math>


where:
* <math>q</math> is the number of size intervals
* <math>*</math> indicates optional results returned if <math>returnPartitionMetrics = True</math> 


|- style="vertical-align:top;"
| [[File:PartitionPivot1.png|frame|Figure 2. Example showing the selection of the input parameters (purple, green, pink and brown cells), and the '''MeanSize''' (blue frame), '''RD''' (red frame) and '''Results''' (light blue frame) arrays in Excel. The parameter <math>returnPartitionMetrics =\text{True}</math> in this example.]]
|}

== SysCAD ==

The Pivot partition is available from the '''{{Name (Text, Company Name)|nospace=1}}*GravityConcentrator''' unit model.

The sections and variable names used in the SysCAD interface are described in detail in the following tables.

{{SysCAD (Page, Gravity Concentrator, DLL*GravityConcentrator)}}

==== Pivot page ====

The Pivot page is used to specify the input parameters for the Pivot model.

{{SysCAD (Text, Table Header)}}

|-
! colspan="3" style="text-align:left;" |''Pivot''

{{SysCAD (Text, Help Link)}}

|-
! colspan="3" style="text-align:left;" |''Parameters''
|-
|PivotPartition / Yp
|Input
|Partition at pivot point.
|-
|PivotDensity / Rhop
|Input
|Density at pivot point.
|-
|EpCoefficient
|Input
|Coefficient of the size equation.
|-
|EpExponent
|Input
|Exponentof the size equation.

{{SysCAD (Text, Gravity Concentrator, Liquids)|method=1}}

|}

{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Overflow|DestinationL=overflow|UnitL=cyclone|GravityMetrics=true}}

{{SysCAD (Page, About)}}

== References ==

[[Category:Excel]]
[[Category:SysCAD]]