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Viscosity

Let us consider the motion of a liquid flowing over a fixed solid surface. If the liquid moves slowly and steadily, the layer of the liquid adjoining the solid surface stays at rest because of molecular cohesion between liquid and solid. The upper layers flow parallel to the fixed surface, each layer flowing past each other. Such a flow is called laminar. The velocity of flow increases uniformly and continuously as we move away from solid surface.

Since an upper layer is moving faster than its adjacent lower layer, the molecules of the upper layer tend to accelerate the molecules of the lower layer, and conversely molecules of the lower layer tend to retard the motion of the upper layer. The two layer tend to destroy their relative motion. Consequently, relative motion between different layers can be maintained only if we apply an external force (push) on the liquid in the direction of flow. In absence of such an external force, the relative motion between different layers would cease and the flow would stop. The property of a liquid to oppose relative motion between its different layers is called viscosity.

Experimental observations show that the tangential viscous force on a layer of the liquid is proportional to its area and the velocity gradient normal to layer:

where η is called coefficient of viscosity of the liquid. Obviously, in order to move the given layer with steady velocity an external force F_ext equal to F_vis must be applied on it.