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Stoke’s Law

•    When a small sphere is moving through a viscous fluid with a constant velocity U, a drag force is experienced by the sphere opposite to its motion. This drag force on the sphere is given by

FD  = 3 π μ U D

Where D = diameter of sphere for low value of Re.
            v  = velocity of sphere
            μ = fluid density

This is known as stoke’s law and is valid for speeds of flow which gives Reynolds’s number less than one.

•    Following are the assumptions made by stoke’s law:

(i)    The inertia force acting on the body is very small as compared to viscous forces and can be neglected.
(ii)    Wall of vessel containing the fluid are not so near as to affect the flow around the sphere.
(iii)    There is no slip between the fluid and the sphere.
(iv)    The sphere is rigid.

•    Falling sphere method of measuring viscosity of a fluid is based on stoke’s law.

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