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Terminal Velocity

For a small sphere of radius rVolume V = (4/3)πr3density ρs falling through a fluid of density ρw and viscosity ηw weight of sphere = mg = ρsV gupthrust = weight of fluid displaced = ρwVgdrag force from Stokes' law = 6 π r η vAt terminal velocity there is no resultant force therefore:weight of sphere = upthrust + drag forceρsVg = ρwVg + 6 π r ηw vtermRearranging gives:
vterm = Vg (ρs - ρw )
6 π r ηw

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Specification: Edexcel Physics (8PH0), AS-level, Topic 4: Materials, statement 50. Topic: Fluids.

Key terms in this lesson

upthrust
The upward force exerted on an object submerged, fully or partly, in a fluid, equal to the weight of fluid displaced.

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