One of the applications of using Stokes' law to determine the particle size is the Sedigraph particle analyser. The following table shows the relationship between the cumulative weight percentage of particles and the corresponding particle terminal velocities for a powder samples. The densities of the particle and the dispersing liquid arc 2200 and 745 kg/m3, respectively. The liquid viscosity is 1.156 x 104 kg/m s. Find out the relationship of the mass fraction distribution to the equivalent dynamic diameter. [25 marks)

Table for cumulative weight percentage versus terminal velocity

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V₁ (m/s) 4.4 x 10³ 2.5 x 103 1.7 x 10³ 6.2 x 10 1.5 x 104 6.9 x 10-5 4.4 x 10-5 2.5 x 105 1.7 x 10-5 Cumulative wt(%) 99.9 99.3 99.2 98.5 96.0 93.0 90.1 83.5 76.8 V. (m/s) 1.1 105 6.2 x 106 2.7 x 106 6.9 x 107 4.4 x 107 2.5 x 107 1.7 x 107 1.1 x 107 2.7×10-8 Cumulative wt(%) 65.6 47.2 21.2 1.2 1.0 0.8 0.4 0.2 0.1 V₁ (m/s) 4.4 x 10³ 2.5 x 103 1.7 x 10³ 6.2 x 10 1.5 x 104 6.9 x 10-5 4.4 x 10-5 2.5 x 105 1.7 x 10-5 Cumulative wt(%) 99.9 99.3 99.2 98.5 96.0 93.0 90.1 83.5 76.8 V. (m/s) 1.1 105 6.2 x 106 2.7 x 106 6.9 x 107 4.4 x 107 2.5 x 107 1.7 x 107 1.1 x 107 2.7×10-8 Cumulative wt(%) 65.6 47.2 21.2 1.2 1.0 0.8 0.4 0.2 0.1

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