Movement of fluid molecules between two adjacent moving layers

 
 
 
 
 
 
 
  Explanation: Two layers of a flowing fluid are shown. The upper layer is shown by red arrow and the lower one by yellow arrow. Initially the upper layer is moving faster than the lower layer

Molecules from upper layer in course of continuous thermal agitation migrate into layer lower. Momentum from the migrant molecules from upper layer is stored by molecules of layer lower by way of collision. Thus lower layer as a whole is speeded up . Molecules from the lower layer arrive at upper layer and tend to retard the upper layer. Every such migration of molecules causes forces of acceleration or deceleration to drag the layers so as to oppose the differences in velocity between the layers and produce the effect of viscosity.

Finally both the layers move with the same velocity.