Viscosity

Viscosity ( μ ) :

• Viscosity is a fluid property whose effect is understood when the fluid is in motion.
• In a flow of fluid, when the fluid elements move with different velocities, each element will feel some resistance due to fluid  friction within the elements.
•  Therefore, shear stresses can be identified between the fluid elements with different velocities.
• The relationship between the shear stress and the velocity field was given by Sir Isaac Newton.

Consider a flow (Fig. 1.5) in which all fluid particles are moving in the same direction in such a way that the fluid layers move parallel with different velocities.

Fig 1.5 Parallel flow of a fluid

Fig 1.6 Two adjacent layers of a moving fluid.

• The upper layer, which is moving faster, tries to draw the lower slowly moving layer along with it by means of a force F along the direction of flow on this layer. Similarly, the lower layer tries to retard the upper one, according to Newton's third law, with an equal and opposite force F on it (Figure 1.6).
• Such a fluid flow where x-direction velocities, for example, change with y-coordinate is called shear flow of the fluid.
• Thus, the dragging effect of one layer on the other is experienced by a tangential force F on the respective layers. If F acts over an area of contact A, then the shear stress τ is defined as

τ = F/A

Viscosity of Fluid