Particle diameter harmonic mean

Heating value, Btu/dry pound Particle size, Harmonic mean diameter, /x... 

It may be mentioned here that the mode which represents the most commonly occurring size in a given distribution is not of much use in mineral processing since it does not describe fully the characteristics of a group of particles. The arithmetic mean diameter suffers from the same limitation except when the distribution is a normal one. The harmonic mean diameter is related to the specific surface area. It is, therefore, useful in such mineral processing operations where surface area is an important parameter. 

Polyethylene beads of relatively narrow size distribution with a harmonic mean diameter of 2800 mm and a particle density of 910 kg/m3 were used as the bed material. A static bed height of 1.4 m was employed. 

The harmonic mean is related to the specific surface. Thus, if N is the number of particles per unit-weight considered as spheres, p the density of the particles, and d their mean diameter,... 

For calculations dealing with the specific surface area the harmonic mean would best summarize the data. The harmonic mean is weighted towards the smaller particles because the reciprocal /di is larger for smaller diameters, which have a higher surface to mass ratio. Thus, if the properties of interest are affected by the surface area. e.g.. drug dissolution, then a more representative mean diameter would weight the smaller particles more heavily than the larger particles which have a much smaller specific surface area. 

Example 4. The number of particles that fall between different size ranges are counted using a microscope and shown in Table 2. The arithmetic, geometric, and harmonic mean diameters along with their arithmetic and geometric standard deviations can be calculated using Equations (24)-<33) and is shown in Table 2. 

If the distribution is lognormal, it has a particular value. There is also a harmonic mean, Xh, which is defined as the number of particles divided by the sum of the reciprocals of diameters of the individual particles and is given by ... 

The volume-mean particle diameter rather than the harmonic mean diameter should be used in Eq. (202). Using a wide variety of particles of different densities and sizes, these authors found that the minimum fluidization velocity depended more strongly on the volumetric fraction rather than on the mass fraction of the particles. The minimum fluidization velocity also is closely related to the mixing state of the mixture, confirming the observation by others in earlier investigations. 

Particle size averages This. section describes how to calculate the arithmetic (d) geometric (dg) and harmonic (c/h) means. The derivation of optimal estimates is beyond the scope of this chapter but the interested reader can consult any good statistic book (1.9). The most commonly used averages are the arithmetic averages. The standard formulas for estimating the arithmetic or average diameter and the standard deviation are ... 

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