(a) A diluted suspension of minerals with density p, 2200 kg m³, in water with density p 1000 kg m³, and viscosity μ 1 m

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(a) A diluted suspension of minerals with density p, 2200 kg m³, in water with density p 1000 kg m³, and viscosity μ 1 mN s m², is to be separated on plant by centrifuge. Pilot tests conducted at 10000 rpm with a throughput Q, 5x10 m³s¹ provide a clarified overflow. The test machine has height H= 0.4 m, radius R= 0.03 m, and overflow weir, rom 0.015 m, while the plant machine has height H= 1 m, radius R= 0.1 m, and overflow weir, rom 0.05 m, and operates at 5000 rpm. (1) Calculate the volumetric holdup of liquid V' in the bowl, for the test and plant machines. [3 marks] (i) Define, and calculate the capacity factor, Z, for the test and plant machine. [3 marks] (ii) Calculate the throughput Q; that will provide the same quality of overflow for the plant machine. [3 marks] (iv) Determine the cut size, d, of the separation. [3 marks] (v) Calculate the residence time for the particles to settle. [3 marks]