Template:Model theory (Text, Hydrocyclone, Partition Metrics): Difference between revisions
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The <math>d_{50}</math>, also known as the '''cut or separation size''', is defined as the size of a particle which has an even (50%) chance of appearing in either the underflow or overflow stream. The <math>d_{50}</math> size is estimated via a log-linear [[Interpolation|interpolation]] of geometric mean size (<math>\ln \bar d</math>) against the uncorrected partition to underflow of all solids in the feed. | The <math>d_{50}</math>, also known as the '''cut or separation size''', is defined as the size of a particle which has an even (50%) chance of appearing in either the underflow or overflow stream. The <math>d_{50}</math> size is estimated via a log-linear [[Interpolation|interpolation]] of geometric mean size (<math>\ln \bar d</math>) against the uncorrected partition to underflow of all solids in the feed. | ||
The '''Ecart Probable''', or <math> | The '''Ecart Probable''', or <math>E_{\rm p}</math>, is a measure of the deviation of a partition curve from a perfect separation, and is typically defined for size classification as:{{Gupta and Yan (2016)}} | ||
:<math> | :<math>E_{\rm p} = \dfrac{d_{75} - d_{25}}{2}</math> | ||
where <math>d_{75}</math> and <math>d_{25}</math> are the sizes of particles which have a 75% and 25% probability, respectively, of appearing in the underflow stream. The <math>d_{75}</math> and <math>d_{25}</math> sizes are estimated by log-linear interpolation of geometric mean size against the uncorrected partition to underflow of all solids in the feed. | where <math>d_{75}</math> and <math>d_{25}</math> are the sizes of particles which have a 75% and 25% probability, respectively, of appearing in the underflow stream. The <math>d_{75}</math> and <math>d_{25}</math> sizes are estimated by log-linear interpolation of geometric mean size against the uncorrected partition to underflow of all solids in the feed. | ||
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The '''Imperfection''', <math>I</math>, is a normalised measure of the sharpness of separation, which is suggested to be independent of the magnitude of the <math>d_{50}</math>, and is typically defined for size classification as:{{Gupta and Yan (2016)}} | The '''Imperfection''', <math>I</math>, is a normalised measure of the sharpness of separation, which is suggested to be independent of the magnitude of the <math>d_{50}</math>, and is typically defined for size classification as:{{Gupta and Yan (2016)}} | ||
:<math>I = \dfrac{ | :<math>I = \dfrac{E_{\rm p}}{d_{50}} = \dfrac{d_{75} - d_{25}}{2 d_{50}}</math> | ||
Latest revision as of 13:22, 2 March 2023
Several metrics are provided to characterise the partition curve.
The , also known as the cut or separation size, is defined as the size of a particle which has an even (50%) chance of appearing in either the underflow or overflow stream. The size is estimated via a log-linear interpolation of geometric mean size () against the uncorrected partition to underflow of all solids in the feed.
The Ecart Probable, or , is a measure of the deviation of a partition curve from a perfect separation, and is typically defined for size classification as:[1]
where and are the sizes of particles which have a 75% and 25% probability, respectively, of appearing in the underflow stream. The and sizes are estimated by log-linear interpolation of geometric mean size against the uncorrected partition to underflow of all solids in the feed.
The Imperfection, , is a normalised measure of the sharpness of separation, which is suggested to be independent of the magnitude of the , and is typically defined for size classification as:[1]
