Stokes law Stokes suggested the formula of viscous drag on a spherical object falling under gravity through a fluid of viscosity h . The sphere gains velocity as it falls. Its velocity finally reaches the terminal velocity, v_t. At this velocity the viscous drag, F is just balanced by the total downward forces on the body. If r is the radius of the sphere, using dimensional analysis we can write,

F = k r^x h ^y v_t^z

where k is a constant. x, y, and z are numbers to be determined. Equating the dimensions * in the two sides of the equation we obtain, x=1; y=1 and z=1. The constant k is equal to 6p . Therefore,

F =6p r h v_t (Stokes law) (s18)

At terminal velocity,

viscous drag = weight - upthurst

= (4/3)p r³D r g

where D r is the difference of density of the material of the sphere and that of the liquid.

Measurement of terminal velocity of a sphere through a liquid is one of the methods of finding the viscosity of a liquid.