# State Stokes’ law. Derive Stokes’ law using dimensional analysis.

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State Stokes’ law. Derive Stokes’ law using dimensional analysis.

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Stokes’ law : If a fluid flows past a sphere or a sphere moves through a fluid, for small enough

∴ Viscous force = gravitational force-buoyant force

= mg – mLg

where m = mass of the sphere = $\frac43$$\pi$r3ρ and mL</sub. = mass of the liquid displaced =   $\frac43$$\pi$r3ρL.

At its terminal speed vt, the magnitude of the viscous force by Stokes’ law is

[Note : Theoretically, v → vt as time t → ∞. In practice, if η is appreciable, then vt tends to v in a very small time interval.]

[Data: g = 9.8 m/s2]

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