Define coefficient of viscosity. What are its units and dimensions?

SI unit of viscosity is deca-poise and CGS unit of viscosity is poise.

Dimensional formula of viscosity is [M¹L^–1T^–1]. 

Suppose a spherical body of radius r and density ρ is falling under gravity in viscous media of coefficient of viscosity η and density a.

Let during fall, v be the velocity of body at any instant. The different forces acting on the body at that instant are:

(i) Weight W, acting downward, (ii) Upward thrust U, acting upward, (iii) Viscous force F, acting upward. Net force on body is,

      

Since the body falls under gravity, therefore, its velocity will increase due to gravity. But as the velocity increases, the viscous force (factor II) acting on the body also increase. Since factor I is constant, therefore the net force on the body decreases with time. At some velocity v = v_o, the resultant of all the forces acting on body reduces to zero and body acquires the constant velocity known as terminal velocity.

Let us take water in a glass and stir it. The water starts rotating in the form of coaxial cylindrical layers with innermost layer with maximum velocity and outermost layer in touch with glass at rest. If we stop stirring, the velocity of different layers start decreasing and finally comes to rest. This is because of the internal resistance between the different layers. This resistance appears only when there is relative motion between the layers and this resistance destroys the relative motion between the layers.

Viscosity is the property of fluid by virtue of which an internal resistance comes into play when fluid is in motion and destroys its motion.