Stoke's law:
At the low velocities, the frictional force on the spherical body moving through a fluid at constant velocity is equal to the 6π time's product of the velocity, fluid viscosity, and radius of the sphere. The equation relating terminal settling velocity of the smooth, rigid sphere in the viscous fluid of called as density and viscosity to the diameter of the sphere when subjected to the force field known to us. When small spherical bodies move through a viscous medium, the bodies drag the layers of the medium which are in contact with them. The dragging results in the relative motion in between different layers that are away from the body. The Stoke's law expression can be given by:
Fd = 6ΠµRV
Here Fd is the frictional force acting on the interface between fluid and particle, μ is the fluid's viscosity, R is the radius of spherical object, and V is the velocity particle's. Stokes's law can be used to find the viscosity of the same liquid at different temperatures also. Objects move much slowly through very cold liquids than through the warm liquids. If the density of material of the sphere is r and that of the liquid s, then effective gravitational force will be given by
=weight - upthrust
= 4/3[pr3 (r - s)]
Therefore w viscosity (h) is calculated as,
Viscosity (h) = 2gr2(r -s)/9v where v is terminal velocity of the sphere.
From the formula it can be seen that the frictional drag is smaller for the large spheres than for small ones, and thus the terminal velocity of a large sphere is greater than that for a small sphere of same material. Stokes's law is the basis of the falling sphere viscometer, in which fluid is stationary in the vertical glass tube. A sphere of known density and size is allowed to descend through the liquid. If selected correctly, it reaches terminal velocity, which can be measured by time it takes to pass 2 marks on the tube. Electronic sensing can be used for the opaque fluids. Knowing the terminal velocity, size and density of the sphere, and the density of liquid, Stokes' law can be used to compute the viscosity of the fluid.