## VISCOSITY

**INTRODUCTION: **A fluid is defined as a material which will continue to deform with the application of a shear force. However, different fluids deform at different rates when the same shear stress (force/ area) is applied.

Viscosity is that property of a real fluid by virtue of which it offers resistance to shear force. Referring to Fig. , it may be noted that a force is required to move one layer of fluid over another. For a given fluid the force required varies directly as the rate of deformation. As the rate of deformation increases the force required also increases. This is shown in Fig. (i).

The force required to cause the same rate of movement depends on the nature of the fluid. The resistance offered for the same rate of deformation varies directly as the viscosity of the fluid. As viscosity increases the force required to cause the same rate of deformation increases. This is shown in Fig.

Newton’s law of viscosity states that the shear force to be applied for a deformation rate of (du/dy) over an area A is given by,

**F =µ A (du/dy)**

**Or (F/A) = T = µ (du/dy) = µ (u/y)**

Where F is the applied force in N, A is area in m^{2,} du/dy is the velocity gradient (or rate of deformation), 1/s, perpendicular to flow direction, here assumed linear, and µ is the proportionality constant defined as the dynamic or absolute viscosity of the fluid.

The dimensions for dynamic viscosity µ can be obtained from the definition as Ns/m^{2 }or kg/ms. The first dimension set is more advantageously used in engineering problems. However, if the dimension of N is substituted, then the second dimension set, more popularly used by scientists can be obtained. The numerical value in both cases will be the same.

**N = kg m/s ^{2}; µ = (kg m/s ^{2}) (s/m^{2)} = kg/ms**

The popular unit for viscosity is Poise named in honor of Poiseuille.

**Poise = 0.1 Ns/m ^{2}**

Centipoise (cP) is also used more frequently as,

**cP = 0.001 Ns/m ^{2}\**

For water the viscosity at 20°C is nearly 1 cP. The ratio of dynamic viscosity to the density is defined as kinematic viscosity, ν, having a dimension of m^{2} /s. Later it will be seen to relate to momentum transfer. Because of this kinematic viscosity is also called momentum diffusivity. The popular unit used is stokes (in honor of the scientist Stokes). Centistoke is also often used.

**1 stoke = 1 cm2 /s = 10 –4 m ^{2} /s**

Of all the fluid properties, viscosity plays a very important role in fluid flow problems. The velocity distribution in flow, the flow resistance etc. are directly controlled by viscosity. In the study of fluid statics (i.e., when fluid is at rest), viscosity and shear force are not generally involved. In this chapter problems are worked assuming linear variation of velocity in the fluid filling the clearance space between surfaces with relative movement.