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The De Brouckere mean diameter is the mean of a particle size distribution weighted by the volume. It is the mean diameter, which is directly obtained in particle size measurements, where the measured signal is proportional to the volume of the particles. The most prominent examples are laser diffraction and acoustic spectroscopy.
The De Brouckere mean is defined in terms of the moment-ratio system as,
D = Σ n i D i 4 Σ n i D i 3 {\displaystyle D={\frac {\Sigma n_{i}D_{i}^{4}}{\Sigma n_{i}D_{i}^{3}}}}
Where ni is the frequency of occurrence of particles in size class i, having a mean Di diameter. Usually in logarithmic spaced classes, the geometric mean size of the size class is taken