Conversions

Description

This article describes methods for converting:

• Weight fraction retained to cumulative fraction passing particle size distributions
• Cumulative fraction passing to weight fraction retained particle size distributions
• Particle size distributions between different mesh series
• Particle size distribution mesh interval sizes to geometric mean sizes
• Volumetric flow rates of slurry to mass flow rates of solids and liquids

Model theory

This section is currently under construction. Please check back later for updates and revisions.

Geometric mean size

The geometric mean size of a particle, [math]\displaystyle{ \bar d_{i} }[/math] (mm), is defined as:

[math]\displaystyle{ \bar d_{i} = \begin{cases} \sqrt{2} d_1 & i=1\\ \\ \sqrt{d_{i} d_{i-1}} & 1\lt i\lt n\\ \\ 0.5 d_{n-1} & i=n\\ \end{cases} }[/math]

where:

• [math]\displaystyle{ i }[/math] is the index of the size interval, [math]\displaystyle{ i = \{1,2,\dots,n\} }[/math]
• [math]\displaystyle{ n }[/math] is the number of size intervals
• [math]\displaystyle{ d_i }[/math] is the diameter of particles retained in a mesh at size interval [math]\displaystyle{ i }[/math] (mm)
• the value of [math]\displaystyle{ d_i }[/math] decreases as [math]\displaystyle{ i }[/math] increases, i.e. [math]\displaystyle{ d_{i}\gt d_{i+1} }[/math], [math]\displaystyle{ d_1 }[/math] = top size, [math]\displaystyle{ d_n = 0 }[/math]

Excel

This section is currently under construction. Please check back later for updates and revisions.

The interpolation methods may be invoked from the Excel formula bar with the following function calls:

=mdConvert_RetToCumPass(Retained as Range)

=mdConvert_CumPassToRet(CumPassing as Range)

=mdConvert_ToMesh(Size1 as Range, Dist1 as Range, Size2 as Range, Optional axesScale as Integer = 0, Optional interpMethod as Integer = 0)

=mdConvert_ToGeoMeanSize(Size as Range)

=mdConvert_QvToQm(Qv as Double, wtFracSolids as Double, solidsSG as Double, Optional liquidsSG as Double = 1)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.