Problem 10.6: Using the concept from Stokes Law explain why

From Chapter 10 Problem Set. Level 2: Applied Thinking.

Question

Using the concept from Stokes’ Law, explain why a hydrocyclone separator is effective for removing rust particles (density ~5,200 kg/m³, diameter ~50 µm) but ineffective for biological debris (density ~1,050 kg/m³, diameter ~20 µm). You do not need to calculate - explain the reasoning.

Answer

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Stokes’ Law shows that settling velocity depends on the square of the particle diameter and the density difference between the particle and water. Rust particles have a very high density difference (ρp − ρw ≈ 5,200 − 998 = 4,202 kg/m³) and a moderate diameter (50 µm). The hydrocyclone generates centrifugal force that accelerates settling - heavy, dense particles are thrown to the outer wall and separated. Biological debris has a density barely above water (ρp − ρw ≈ 1,050 - 998 = 52 kg/m³) - roughly 80× less density difference - and a smaller diameter (20 µm). The centrifugal force is not sufficient to separate particles with such a small density difference from the water. They simply recirculate with the flow.