Representation of results of particle size analysis--Part 2:Calculation of average particle size/diameters and moments from particle size distibutions
Some standard content:
JK.S19.120
National Standard of the People's Republic of China
GR/T15445.2—2006/1SO9276-2:2001Presentation of results of particle size analysis-Part 2: Calculation of average particle sizes/diamncters and moments from particle size distributionJSO 9276-2.2001.IDT
Issued on February 5, 2006
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China Administration of Standardization of the People's Republic of China
Implementation on August 1, 2006
Normative references
Number and title
The original text
The average control diameter shall be calculated
such as the weighted half-mean diameter
GiB/T15445.2—2006/180 9276-2:20015.3 From the number or volume weight distribution. (a> or 9, () Calculate M. and the average starting diameter 5.4 The number or volume frequency distribution given in the self-diagram (or calculation 5.5 Calculation of volume specific surface area
5.6 Methods for particle size distribution
Appendix (Data Appendix)
From the known volume frequency distribution
Appendix B (Data Appendix)
Other average rescue methods
GB/T15445.2—2006/ISO9276-2.2Q0 GB/T15445 The particle size analysis system is divided into 6 parts, and the names are as follows: Part 1: Characterization of particle size distribution:
Part 2: Calculation of average particle size/time: Part 2: Fitting the measured cumulative particle size distribution curve to the standard model: Part 4: Construction of the particle size distribution curve Characterization:
Part 1 is used to calculate the relevant initial degree of probability of the item: Part 6: Particle shape and shape tax demarcation characterization, this part is I/T: 45 Part 2
This part is equivalent to 1S [9276-220011 quality analysis system from the table 2: Calculation of particle size distribution average light diameter / diameter and each
This part 159276-2211 compared to do 5 vouchers: a revision of the effect: a "generation" of the international standard | a re-arrangement of the:
Revise the relevant international music standard in the previous part of 1S - add relevant international notes omissions in the preface! Part 1: The production part has a formula (17 formula, the section of the cut-off is the data record,
This part of the national sieve screening and particle inspection method standard This part is under the jurisdiction of the National Technical Committee for Standardization of Screening Methods for Particle Size Analysis. The main drafting parties are: China Iron and Steel Research Institute, China Academy of Mechanical and Materials Science, China Institute of Standardization of Industry and Information Technology. This part is mainly initiated by Zheng, Zhang, Yu, and Yan GR/T15445.2—2006/ISO9276-2:2001. In the particle size analysis, based on representative samples to demonstrate the particle size of the material, finally some other important physical properties of the particle size analysis are linked together, such as particle size distribution, mobility, solubility, etc. If the average particle size is derived or calculated from the previous particle size distribution, in general, the relationship between the performance and the particle size can be obtained, that is, the performance function. This part adopts the short M of particle size classification... to give an exact definition of the average particle size, in addition to the calculation In addition to calculating particle weight, other statistical parameters related to volume and dispersion can be known from the particle size distribution: ■ Scope
GB/T154-5.2—2006/1S09276-2.2001 Expression of particle size analysis results
Part 2: Calculation of average
Particle size/diameter and order
This book provides a related formula to calculate the average particle weight or average particle size and various values from the particle distribution of the case. In this distribution, the particle size distribution is expressed as a straight line diagram. If the particle size distribution is expressed in the form of an analytical function, the corresponding mathematical formula must be used in the same way
In this part, it is also assumed that the diameter of any shape of particle can be obtained by its equivalent sphere, surface and the particle size of the required particle.
2 Specification references
The following documents are used as references in this part of G/T 1544. The meaning of the revised version is that they are not applicable to this part with all the amendments (contents not included in the revised version). However, the latest version of these documents may be used according to the relevant research results of this part. For all references without noting the latest version, the latest version applies to the following:
(:H:60C5-19 Basic size of sieve holes for trial sieves with perforated plates and output thin plates FGB/=1445-1995 3 Characterization of particle size results
The following symbols and abbreviations are applicable to this part: 2 The upper limit of particle weight is, the particle size grade number: 一, ... t.-11d.
Total number of particle size classifications;
Classification of particle size (general description):
r=, classification by individual effect:
1 Classification by length,
r=2: Classification by surface area minus projection value, 3: Classification by body or quality
Classification of particles
(the average height of the closed center of the distribution within the 1st to 2nd particle size range; 2,-1~.2. The height of the square in the interval #
Cumulative distribution;
The difference between the two adjacent cumulative distribution values, that is, the relative distribution within the (individual diameter:; standard deviation of (2 centimeters;
Geometric standard deviation of normal distribution;
Surface area,
CB/T *5425.2bZxz.net
2006/1S0 9276-2:20C1
Rest! ! ;
Chestnut pull machine;
Average to offside recognition:
Accumulate the ball in the detection, the ball is filled with diameter:
The upper limit of the number of particles passing through:
"The limit of the number of particles in the same grid:
The lower limit of the number of particles in a given grid!
The upper limit of the number of particles in a given grid;
The average particle grid is used to infer!
Arithmetic mean particle diameter (general description):
Arithmetic length average is effective diameter;
Arithmetic auxiliary accumulation average is diameter:
Arithmetic forest accumulation average is dangerous diameter:
Weighted average particle diameter (general description) Description)
such as weighted length translation position diameter:
weighted surface flat light, case holding diameter
weighted body flat initial diameter;
geometric average particle diameter (only in the labor pull appendix) with the average particle certificate only in the labor will be attached): cumulative body 1 distribution of the mouth particle grid;
fall, the change of the interval between particles:
logarithmic rate of change price market quantity purchase variable 4 basic definition of moment
frequency distribution) closed drink return 1) I define the integral meter, M.
where:
M means:
--the type of the measured quantity.
+*.c.:2l.
if! 3 represents the distribution of particles according to the number of particles entered, and if the exhibition is to be held from a small or light diameter perspective, then the one described in formula 1 is the combination. Proof. Special fire:
If the phase is divided at a given diameter and at any two small grid diameters, and the non-closed matrix
M..+..+..+
It is implied that the formula 1 and the formula represented by the user are related to the origin of the particle diameter. The given variable distribution can also be deduced that the subcenter of the distribution center is almost related to the grid. (11 Formula determines the determination of the center
Closed order The center can be expressed as,
m.(t: +x.)
5 Average test diameter
The calculation formula of all average particle diameters is
CE/T 15445.2—2006/ISO 927E-2:2001.(?d
xxr = M...
Different average and particle diameters can be obtained by using different subscripts and numerical ranges. The average and particle diameters calculated by the formula may be very different, so the corresponding subscripts and values should be indicated! Usually, there are two types of average diameters involved. 5.1 Arithmetic mean particle size
The half-mean particle size is not the number of particle sizes. Frequency () stop: 2
A typical example is that Liu also used microscopy to count the size and number of individual particles, so that the number () percentage can be obtained. Based on this, the average particle size:
The following is an introduction to the arithmetic half-mean particle size 7
Arithmetic half-mean particle size:
Calculation of this process! Average particle size:
Arithmetic mean particle size:
5.2 Weighted average particle size
The weighted average particle size is defined as
R = M.
After the weighted average particle size is determined, a typical example is established, (8
The average particle size is calculated based on the coordinates of the orthocenter. The recommended small average particle size can be expressed by (1~()):
The number frequency distribution is equivalent to the arithmetic length average particle size (9). It can be expressed by the arithmetic length average:
The weighted half-mean particle size of the length frequency distribution is the weighted length half-mean particle size:.
The product of the weighted average particle size of the frequency distribution must be added and the product of the weighted average particle size:.o M...
The weighted volume average particle size of the volume frequency distribution 9 (.1) is obtained: .M.
5.3From the overall volume frequency distribution () or 9 (calculated..and the average particle size (12:
(1s)
In many practices, the test data are accompanied by individual significant number distribution or volume total distribution). The above-mentioned average particle sizes can be calculated by the formula
GB/T15445.2·-2006/IK)9276-2;2001=
For long:
o. = VM..u
T. - Me -
can be obtained by equation (17)~22. To calculate the average particle size of the above-defined particles, the following matrix is required: For the known volume frequency distribution, we have: MMMW
For the known number distribution, we have MMMM
5. The number or volume distribution described by the given histogram is: or 9: () Calculation If the frequency distribution is given by the right formula, in the time box, we can rewrite it as follows:
When one, the average particle size is
Jingn Send
(21)
. , where ( is a constant, so we can
.—I:
In this way, the distance values M.;M:M:M.·MM-M and M.. can be calculated by equation 2~31 Mu
S( - )-
.0..12. ++-:3
Zacfr-
Smutu*. ,) =
244.(2-2)
220(-to)=
( 24 )
-{ 25
（27)
-（0)
5.5 Calculation of volume specific surface area
GB/T15445.2—2006/1S09276-2;2C01*+,
·( 34 ?
From the distance of a cloth or a particle, the specific surface area of the body can be obtained, four is S, the same weighted weight is about the tooth, the print price, (14) formula is proportional, it can be proved that, .35
Combined with: 31), it can be obtained:
For non-spherical doubts, the above formula is due to the shape factor: 5.6 The variance of the diameter distribution
The degree of particle size distribution can be expressed in terms of the whole, that is, the square of the standard deviation, the square of the distribution (is defined as: =
Introducing the closed year, the ancient difference can be calculated by the following formula: ta.a.(d
$ = mr = hde.r-(Mt.r)
If it is a histogram, then:
tB/T 15445.2—2036/ISO 9276-2:2001 Appendix A
(material supplement)
From the known volume frequency distribution histogram to calculate the various mean diameters, numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) formula is the end of the Zwolle case, the value is as follows: Int/a
In../a...
5km, the deviation s-0.50. Phase point
forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the series of successive inner diameter layers R, that is: x-0
can be used to express! The values of Q are given in the formula (33). By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the basic value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are the values of the R1u series or the R5 series obtained by effective elimination: the calculated values are slightly different from the first column: the values obtained by the analytic calculation can be found in the formula (22). The difference between the analytical results and the results obtained by direct calculation of the R10 and R5 series is very small. The theory of Cheng Ma says that because it produces a small difference in the history of R1C, it will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..1 Arithmetic mean particle size
The half-mean particle size cannot be calculated to get the frequency of the particle size. 2
A typical example, Liu also used a microscope to analyze the size and number of individual particles, so that the number () can be obtained. The average particle size is:
The following is an introduction to the arithmetic half-mean particle size 7
Arithmetic average particle size:
Calculate the frequency! Average particle size:
Arithmetic mean particle size:
5.2 Weighted average particle size
The weighted average particle size is defined as
R = M.
After the weighted average particle size is determined, a typical example is established, (8
The average particle size is calculated based on the coordinates of the orthocenter. The recommended small average particle size can be expressed by (1~()):
The number frequency distribution is equivalent to the arithmetic length average particle size (9). It can be expressed by the arithmetic length average:
The weighted half-mean particle size of the length frequency distribution is the weighted length half-mean particle size:.
The product of the weighted average particle size of the frequency distribution must be added and the product of the weighted average particle size:.o M...
The weighted volume average particle size of the volume frequency distribution 9 (.1) is obtained: .M.
5.3From the overall volume frequency distribution () or 9 (calculated..and the average particle size (12:
(1s)
In many practices, the test data are accompanied by individual significant number distribution or volume total distribution). The above-mentioned average particle sizes can be calculated by the formula
GB/T15445.2·-2006/IK)9276-2;2001=
For long:
o. = VM..u
T. - Me -
can be obtained by equation (17)~22. To calculate the average particle size of the above-defined particles, the following matrix is required: For the known volume frequency distribution, we have: MMMW
For the known number distribution, we have MMMM
5. The number or volume distribution described by the given histogram is: or 9: () Calculation If the frequency distribution is given by the right formula, in the time box, we can rewrite it as follows:
When one, the average particle size is
Jingn Send
(21)
. , where ( is a constant, so we can
.—I:
In this way, the distance values M.;M:M:M.·MM-M and M.. can be calculated by equation 2~31 Mu
S( - )-
.0..12. ++-:3
Zacfr-
Smutu*. ,) =
244.(2-2)
220(-to)=
( 24 )
-{ 25
（27)
-（0)
5.5 Calculation of volume specific surface area
GB/T15445.2—2006/1S09276-2;2C01*+,
·( 34 ?
From the distance of a cloth or a particle, the specific surface area of the body can be obtained, four is S, the same weighted weight is about the tooth, the print price, (14) formula is proportional, it can be proved that, .35
Combined with: 31), it can be obtained:
For non-spherical doubts, the above formula is due to the shape factor: 5.6 The variance of the diameter distribution
The degree of particle size distribution can be expressed in terms of the whole, that is, the square of the standard deviation, the square of the distribution (is defined as: =
Introducing the closed year, the ancient difference can be calculated by the following formula: ta.a.(d
$ = mr = hde.r-(Mt.r)
If it is a histogram, then:
tB/T 15445.2—2036/ISO 9276-2:2001 Appendix A
(material supplement)
From the known volume frequency distribution histogram to calculate the various mean diameters, numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) formula is the end of the Zwolle case, the value is as follows: Int/a
In../a...
5km, the deviation s-0.50. Phase point
forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the series of successive inner diameter layers R, that is: x-0
can be used to express! The values of Q are given in the formula (33). By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the basic value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are the values of the R1u series or the R5 series obtained by effective elimination: the calculated values are slightly different from the first column: the values obtained by the analytic calculation can be found in the formula (22). The difference between the analytical results and the results obtained by direct calculation of the R10 and R5 series is very small. The theory of Cheng Ma says that because it produces a small difference in the history of R1C, it will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..1 Arithmetic mean particle size
The half-mean particle size cannot be calculated to get the frequency of the particle size. 2
A typical example, Liu also used a microscope to analyze the size and number of individual particles, so that the number () can be obtained. The average particle size is:
The following is an introduction to the arithmetic half-mean particle size 7
Arithmetic average particle size:
Calculate the frequency! Average particle size:
Arithmetic mean particle size:
5.2 Weighted average particle size
The weighted average particle size is defined as
R = M.
After the weighted average particle size is determined, a typical example is established, (8
The average particle size is calculated based on the coordinates of the orthocenter. The recommended small average particle size can be expressed by (1~()):
The number frequency distribution is equivalent to the arithmetic length average particle size (9). It can be expressed by the arithmetic length average:
The weighted half-mean particle size of the length frequency distribution is the weighted length half-mean particle size:.
The product of the weighted average particle size of the frequency distribution must be added and the product of the weighted average particle size:.o M...
The weighted volume average particle size of the volume frequency distribution 9 (.1) is obtained: .M.
5.3From the overall volume frequency distribution () or 9 (calculated..and the average particle size (12:
(1s)
In many practices, the test data are accompanied by individual significant number distribution or volume total distribution). The above-mentioned average particle sizes can be calculated by the formula
GB/T15445.2·-2006/IK)9276-2;2001=
For long:
o. = VM..u
T. - Me -
can be obtained by equation (17)~22. To calculate the average particle size of the above-defined particles, the following matrix is required: For the known volume frequency distribution, we have: MMMW
For the known number distribution, we have MMMM
5. The number or volume distribution described by the given histogram is: or 9: () Calculation If the frequency distribution is given by the right formula, in the time box, we can rewrite it as follows:
When one, the average particle size is
Jingn Send
(21)
. , where ( is a constant, so we can
.—I:
In this way, the distance values M.;M:M:M.·MM-M and M.. can be calculated by equation 2~31 Mu
S( - )-
.0..12. ++-:3
Zacfr-
Smutu*. ,) =
244.(2-2)
220(-to)=
( 24 )
-{ 25
（27)
-（0)
5.5 Calculation of volume specific surface area
GB/T15445.2—2006/1S09276-2;2C01*+,
·( 34 ?
From the distance of a cloth or a particle, the specific surface area of the body can be obtained, four is S, the same weighted weight is about the tooth, the print price, (14) formula is proportional, it can be proved that, .35
Combined with: 31), it can be obtained:
For non-spherical doubts, the above formula is due to the shape factor: 5.6 The variance of the diameter distribution
The degree of particle size distribution can be expressed in terms of the whole, that is, the square of the standard deviation, the square of the distribution (is defined as: =
Introducing the closed year, the ancient difference can be calculated by the following formula: ta.a.(d
$ = mr = hde.r-(Mt.r)
If it is a histogram, then:
tB/T 15445.2—2036/ISO 9276-2:2001 Appendix A
(material supplement)
From the known volume frequency distribution histogram to calculate the various mean diameters, numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) formula is the end of the Zwolle case, the value is as follows: Int/a
In../a...
5km, the deviation s-0.50. Phase point
forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the series of successive inner diameter layers R, that is: x-0
can be used to express! The values of Q are given in the formula (33). By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the basic value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are the values of the R1u series or the R5 series obtained by effective elimination: the calculated values are slightly different from the first column: the values obtained by the analytic calculation can be found in the formula (22). The difference between the analytical results and the results obtained by direct calculation of the R10 and R5 series is very small. The theory of Cheng Ma says that because it produces a small difference in the history of R1C, it will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..
Then we establish a typical example of particle size distribution with mass percentage as the average particle size, (8
The average particle size is calculated at the orthocentric coordinate. The recommended average particle size can be expressed by the formula (1~()):
The number frequency distribution is equivalent to the arithmetic length average particle size (9). We can use the arithmetic length average to express it:
The weighted half-mean particle size of the length frequency distribution 9 () is the weighted half-mean particle size:.
The weighted average particle size of the product frequency distribution (9 (.1) must be added and the product is equal to the particle size:.o M...
The weighted volume average particle size of the volume distribution 9 (.1) is obtained:.M.
5.3From the entire volume frequency distribution () or 9 (calculate..and the average particle size (12 :
（1s)
In many practical situations, the test data are expressed as individual effective number distribution or volume distribution). The average particle sizes mentioned above can be calculated by the following formula:
GB/T15445.2·-2006/IK)9276-2;2001=
For length:
o. = VM..u
T. - Me -
can be obtained by equation (17)~22. To calculate the average particle size of the above-defined particles, the following matrix is required: For the known volume frequency distribution, we have: MMMW
For the known number distribution, we have MMMM
5. The number or volume distribution described by the given histogram is: or 9: () Calculation If the frequency distribution is given by the right formula, in the time box, we can rewrite it as follows:
When one, the average particle size is
Jingn Send
(21)
. , where ( is a constant, so we can
.—I:
In this way, the distance values M.;M:M:M.·MM-M and M.. can be calculated by equation 2~31 Mu
S( - )-
.0..12. ++-:3
Zacfr-
Smutu*. ,) =
244.(2-2)
220(-to)=
( 24 )
-{ 25
（27)
-（0)
5.5 Calculation of volume specific surface area
GB/T15445.2—2006/1S09276-2;2C01*+,
·( 34 ?
From the distance of a cloth or a particle, the specific surface area of the body can be obtained, four is S, the same weighted weight is about the tooth, the print price, (14) formula is proportional, it can be proved that, .35
Combined with: 31), it can be obtained:
For non-spherical doubts, the above formula is due to the shape factor: 5.6 The variance of the diameter distribution
The degree of particle size distribution can be expressed in terms of the whole, that is, the square of the standard deviation, the square of the distribution (is defined as: =
Introducing the closed year, the ancient difference can be calculated by the following formula: ta.a.(d
$ = mr = hde.r-(Mt.r)
If it is a histogram, then:
tB/T 15445.2—2036/ISO 9276-2:2001 Appendix A
(material supplement)
From the known volume frequency distribution histogram to calculate the various mean diameters, numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) formula is the end of the Zwolle case, the value is as follows: Int/a
In../a...
5km, the deviation s-0.50. Phase point
forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the series of successive inner diameter layers R, that is: x-0
can be used to express! The values of Q are given in the formula (33). By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the basic value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are the values of the R1u series or the R5 series obtained by effective elimination: the calculated values are slightly different from the first column: the values obtained by the analytic calculation can be found in the formula (22). The difference between the analytical results and the results obtained by direct calculation of the R10 and R5 series is very small. The theory of Cheng Ma says that because it produces a small difference in the history of R1C, it will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series: GR/T15445.2-200G/[S09276-2:2051 Appendix R (Informative Appendix) Other average particle sizes However, the half-average particle size cannot replace the arithmetic mean particle size or the calculation of the volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..
Then we establish a typical example of particle size distribution with mass percentage as the average particle size, (8
The average particle size is calculated at the orthocentric coordinate. The recommended average particle size can be expressed by the formula (1~()):
The number frequency distribution is equivalent to the arithmetic length average particle size (9). We can use the arithmetic length average to express it:
The weighted half-mean particle size of the length frequency distribution 9 () is the weighted half-mean particle size:.
The weighted average particle size of the product frequency distribution (9 (.1) must be added and the product is equal to the particle size:.o M...
The weighted volume average particle size of the volume distribution 9 (.1) is obtained:.M.
5.3From the entire volume frequency distribution () or 9 (calculate..and the average particle size (12 :
（1s)
In many practical situations, the test data are expressed as individual effective number distribution or volume distribution). The average particle sizes mentioned above can be calculated by the following formula:
GB/T15445.2·-2006/IK)9276-2;2001=
For length:
o. = VM..u
T. - Me -
can be obtained by equation (17)~22. To calculate the average particle size of the above-defined particles, the following matrix is required: For the known volume frequency distribution, we have: MMMW
For the known number distribution, we have MMMM
5. The number or volume distribution described by the given histogram is: or 9: () Calculation If the frequency distribution is given by the right formula, in the time box, we can rewrite it as follows:
When one, the average particle size is
Jingn Send
(21)
. , where ( is a constant, so we can
.—I:
In this way, the distance values M.;M:M:M.·MM-M and M.. can be calculated by equation 2~31 Mu
S( - )-
.0..12. ++-:3
Zacfr-
Smutu*. ,) =
244.(2-2)
220(-to)=
( 24 )
-{ 25
（27)
-（0)
5.5 Calculation of volume specific surface area
GB/T15445.2—2006/1S09276-2;2C01*+,
·( 34 ?
From the distance of a cloth or a particle, the specific surface area of the body can be obtained, four is S, the same weighted weight is about the tooth, the print price, (14) formula is proportional, it can be proved that, .35
Combined with: 31), it can be obtained:
For non-spherical doubts, the above formula is due to the shape factor: 5.6 The variance of the diameter distribution
The degree of particle size distribution can be expressed in terms of the whole, that is, the square of the standard deviation, the square of the distribution (is defined as: =
Introducing the closed year, the ancient difference can be calculated by the following formula: ta.a.(d
$ = mr = hde.r-(Mt.r)
If it is a histogram, then:
tB/T 15445.2—2036/ISO 9276-2:2001 Appendix A
(material supplement)
From the known volume frequency distribution histogram to calculate the various mean diameters, numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) formula is the end of the Zwolle case, the value is as follows: Int/a
In../a...
5km, the deviation s-0.50. Phase point
forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the series of successive inner diameter layers R, that is: x-0
can be used to express! The values of Q are given in the formula (33). By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the basic value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are the values of the R1u series or the R5 series obtained by effective elimination: the calculated values are slightly different from the first column: the values obtained by the analytic calculation can be found in the formula (22). The difference between the analytical results and the results obtained by direct calculation of the R10 and R5 series is very small. The theory of Cheng Ma says that because it produces a small difference in the history of R1C, it will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..u
T. - Me -
can be obtained by (17) ~ 22 formulas. To calculate the average particle size of the abandoned species defined above, the following matrix is required: For the known volume frequency distribution, we have: MMMW
For the known number distribution, we have MMMM
5. The number or volume distribution described by the given histogram is: or 9: () Calculation If the frequency distribution is given by the straight right formula, in the box, one will rewrite) as follows:
When one", the average value of the distribution is
京n送
（21)
. , where (is a constant, so we can
.—I:
, so the distance values M.;M:M:M.·MM-M and M.. can be calculated by formula 2~31Mu
S( - )-
.0..12. ++-:3
Zacfr-
Smutu*. ,) =
244.(2-2)
220(-to)=
( 24 )
-{ 25
（27)
-（0)
5.5 Calculation of volume specific surface area
GB/T15445.2—2006/1S09276-2;2C01*+,
·( 34 ?
From the distance of a cloth or a distance, the root specific surface area can be obtained, four is S, the same weighted weight is about the tooth, the print price, (14) formula is proportional, it can be proved that, .35
Combined with: 31) formula, it can be obtained:
For non-spherical doubts, the above formula is due to the shape factor: 5.6 The variance of the diameter distribution
The degree of particle size distribution can be expressed in terms of the whole, that is, the square of the standard deviation, the square of the distribution (is defined as: =
Introducing the closed year, the ancient difference can be calculated by the following formula: ta.a.(d
$ = mr = hde.r-(Mt.r)
If it is a histogram, then:
tB/T 15445.2—2036/ISO 9276-2:2001 Appendix A
(material supplement)
From the known volume frequency distribution histogram to calculate the various mean diameters, numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) formula is the end of the Zwolle case, the value is as follows: Int/a
In../a...
5km, the deviation s-0.50. Phase point
forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the process determines the series of successive internal particle size layers R, that is: x-0
The value of Q can be calculated by using the given number of periods (33) in the formula. By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are calculated by the analytic calculation of the R1u series or the R5 series. There is a little difference between the calculated values and the first column: the values obtained by the analytic calculation are very small,
forget 2 products H17)--(22) formula, the results of the analysis in Table 2 are very different from the results of the R10 and R5 series. The theory says that because it produces a small commission, R1C will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..u
T. - Me -
can be obtained by (17) ~ 22 formulas. To calculate the average particle size of the abandoned species defined above, the following matrix is required: For the known volume frequency distribution, we have: MMMW
For the known number distribution, we have MMMM
5. The number or volume distribution described by the given histogram is: or 9: () Calculation If the frequency distribution is given by the straight right formula, in the box, one will rewrite) as follows:
When one", the average value of the distribution is
京n送
（21)
. , where (is a constant, so we can
.—I:
, so the distance values M.;M:M:M.·MM-M and M.. can be calculated by formula 2~31Mu
S( - )-
.0..12. ++-:3
Zacfr-
Smutu*. ,) =
244.(2-2)
220(-to)=
( 24 )
-{ 25
（27)
-（0)
5.5 Calculation of volume specific surface area
GB/T15445.2—2006/1S09276-2;2C01*+,
·( 34 ?
From the distance of a cloth or a distance, the root specific surface area can be obtained, four is S, the same weighted weight is about the tooth, the print price, (14) formula is proportional, it can be proved that, .35
Combined with: 31) formula, it can be obtained:
For non-spherical doubts, the above formula is due to the shape factor: 5.6 The variance of the diameter distribution
The degree of particle size distribution can be expressed in terms of the whole, that is, the square of the standard deviation, the square of the distribution (is defined as: =
Introducing the closed year, the ancient difference can be calculated by the following formula: ta.a.(d
$ = mr = hde.r-(Mt.r)
If it is a histogram, then:
tB/T 15445.2—2036/ISO 9276-2:2001 Appendix A
(material supplement)
From the known volume frequency distribution histogram to calculate the various mean diameters, numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) formula is the end of the Zwolle case, the value is as follows: Int/a
In../a...
5km, the deviation s-0.50. Phase point
forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the process determines the series of successive internal particle size layers R, that is: x-0
The value of Q can be calculated by using the given number of periods (33) in the formula. By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are calculated by the analytic calculation of the R1u series or the R5 series. There is a little difference between the calculated values and the first column: the values obtained by the analytic calculation are very small,
forget 2 products H17)--(22) formula, the results of the analysis in Table 2 are very different from the results of the R10 and R5 series. The theory says that because it produces a small commission, R1C will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..2001 Appendix A
(material supplement)
Calculate various mean diameters from the known volume frequency distribution histogram. Numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) is the value of the Zwolle transformation case: Int/a
In../a...
5km, the deviation s-0.50. Phase point
Forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the series of successive inner particle size layers R, that is: x-0
can be used to express! The values of Q are given in the formula (33). By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the basic value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are the values of the R1u series or the R5 series obtained by effective elimination: the calculated values are slightly different from the first column: the values obtained by the analytic calculation can be found in the formula (22). The difference between the analytical results and the results obtained by direct calculation of the R10 and R5 series is very small. The theory of Cheng Ma says that because it produces a small difference in the history of R1C, it will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..2001 Appendix A
(material supplement)
Calculate various mean diameters from the known volume frequency distribution histogram. Numerical examples In the following numerical examples, the cumulative volume is divided from the logarithm: =
The loss shows that (A.[) is the value of the Zwolle transformation case: Int/a
In../a...
5km, the deviation s-0.50. Phase point
Forget A.1 product under the following conditions: that is, the median diameter of the distribution: the geometric standard deviation -1.! . Further--the series of successive inner particle size layers R, that is: x-0
can be used to express! The values of Q are given in the formula (33). By dividing the number of people in the formula (1) by the normal distribution, and between m=..=, the value of Q is calculated based on the basic value of the industry table. The first four moments of the liquid A are calculated by analytic calculation: the first three columns are the values of the R1u series or the R5 series obtained by effective elimination: the calculated values are slightly different from the first column: the values obtained by the analytic calculation can be found in the formula (22). The difference between the analytical results and the results obtained by direct calculation of the R10 and R5 series is very small. The theory of Cheng Ma says that because it produces a small difference in the history of R1C, it will be better than the system. Table A.1 Basic data of the normal distribution assumed for calculating the moment: m
n, 4ti
0. 3933 0.9r-9s
. u. 907:
0,#212
0, FT72
3,6772
o,oc19
a,n4s3
a,a883
0. 1720 u.2c26
M/gxrm
M ein ?
Average diameter
2, 31-
Analysis results
Table A.1 (Sys.)
GJ/T15445.2—2006/[S0 9278-2:2001A,/a
Ratio of analytical and numerical moment estimates
RJU series
Yingguan:5
Comparison of average particle size values obtained by analytical method and effective value calculation method Table A.3
Jie Sifangcai
Rle series
R: series
E-0 series
Deguan:5
RS Dong series
R.5 Series:
GR/T15445.2-200G/[S09276-2:2051 Appendix R
(Informative Appendix)
Other average particle sizes
However, the half-average particle size cannot replace the arithmetic mean particle size. The weighted average particle size or the calculation of volume specific surface area. The average size of each piece may vary greatly (which is related to the degree of distribution). Therefore, some necessary conditions and definitions are required. 1. Geometric mean particle size || tt || When the average particle size appears below the base, such experience has found that when the particle size distribution conforms to the log-normal probability function, the particle size distribution represents the maximum probability value. For the logarithmic normal probability function, this value is the median. The arithmetic mean is the sum of the logarithms of the values and then divided by the mean! From the perspective of countable use, the geometric mean is the sum of the logarithms of the values and then divided by the arithmetic mean. And the greater the number of scattered lines, the greater the difference between the arithmetic mean and the geometric mean. When the length is longer than 1, the geometric mean diameter can be obtained by performing a slow operation on (6) [1] as follows: (Bl)
If it is changed from the logarithmic point of view:
InLiaxe.n
B.2Harmonic mean diameter
\Ing.(In.:(Jr)
The harmonic mean of a series of numbers is the arithmetic mean of their reciprocals. The harmonic mean is smaller than the geometric mean, and this difference becomes larger when the number is higher. The harmonic mean diameter can be calculated by the following formula:..
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