Thickener (WilhelmNaide)
Description
This article describes a model for thickener sizing or underflow density estimation using the equations of Wilhelm and Naide (1981).^{[1]}
This model is not intended to replace more comprehensive thickener design and performance assessment methods and tools currently available. Rather, it is intended to provide the user with a comparatively simpler tool to quickly compare thickener sizes or estimate underflow pulp densities, in combination with other calculation tools or unit models.
Model theory
This section is currently under construction. Please check back later for updates and revisions. 
Excel
Unit area
The WilhelmNaide thickener unit area equation may be invoked from the Excel formula bar with the following function calls:
=mdSolLiq_Thickener_WilhelmNaide_UA(a as Double, b as Double, Cs as Double, Optional hHRatio as Double = 1, Optional n as Double = 1)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:


Underflow solids concentration
The WilhelmNaide thickener underflow solids concentration equation may be invoked from the Excel formula bar with the following function calls:
=mdSolLiq_Thickener_WilhelmNaide_Cs(a as Double, b as Double, Ua as Double, Optional hHRatio as Double = 1, Optional n as Double = 1)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:


SysCAD
This section is currently under construction. Please check back later for updates and revisions. 
References
 ↑ Wilhelm, J. H. and Naide, Y., 1981. Sizing and operating continuous thickeners. Mining Engineering, 10(1981), p. 1710.