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* <math>d_i</math> is the diameter of particles retained in a mesh at size interval <math>i</math> (mm) | * <math>d_i</math> is the diameter of particles retained in a mesh at size interval <math>i</math> (mm) | ||
* the value of <math>d_i</math> decreases as <math>i</math> increases, i.e. <math>d_{i}>d_{i+1}</math>, <math>d_1</math> = top size, <math>d_n = 0</math> | * the value of <math>d_i</math> decreases as <math>i</math> increases, i.e. <math>d_{i}>d_{i+1}</math>, <math>d_1</math> = top size, <math>d_n = 0</math> | ||
<!--- | |||
=== Fraction retained and cumulative passing === | === Fraction retained and cumulative passing === | ||
=== Mesh series interpolation === | === Mesh series interpolation === | ||
=== Mass and volume flows === | |||
---> | |||
== Excel == | == Excel == | ||
{{Under construction|section}} | {{Under construction|section}} | ||
<!--- | |||
=== Geometric mean size === | === Geometric mean size === | ||
=== Fraction retained and cumulative passing === | === Fraction retained and cumulative passing === | ||
=== Mesh series interpolation === | === Mesh series interpolation === | ||
=== Mass and volume flows === | |||
---> | |||
== References == | == References == | ||
Revision as of 14:59, 13 December 2022
Description
 This section is currently under construction. Please check back later for updates and revisions.
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Model theory
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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.
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