As a result of large number of experiments Newton found that viscous force F acting on any layer of fluid is directly proportional to its area A and to the velocity gradient (dv/dy) at the layer, i.e.,
or … (1)
where h is a constant called coefficient of viscosity or simply viscosity of the fluid. The negative sign shows that viscous force on a liquid layer acts in a direction opposite to the relative velocity of flow of fluid. The equation (1) is known as Newton's law of viscous force.
When a body moves through a fluid, the fluid in contact with the body is dragged with it. This establishes relative motion in fluid layer near the body, due to which viscous force starts operating. The fluid exerts viscous force on the body to oppose its motion. The magnitude of the viscous force depends on the shape and size of the body, its speed and the viscosity of the fluid. Strokes established that if a sphere of radius r moves with velocity v through a fluid of viscosity h, the viscous force opposing the motion of the sphere is
F = 6phru … (4)
This law is called Strokes law.
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