Main Page/PHYS 3220/Viscosity

Viscosity

The purpose of this experiment is to determine the viscosity of a liquid and to find the variation of viscosity with temperature.

Theory

When a solid is subject to a shearing stress it deforms until the internal elastic forces of the solid exactly balance the external forces. Thus a finite force applied to a solid produces a finite deformation. If a similar force is applied to a liquid, however, the deformation increases indefinitely (the liquid flows). The flow can be imagined as the movement of adjacent layers over one another. The Newtonian friction caused by the relative motion between adjacent layers retards the flow and is called viscosity. This frictional force was assumed by Newton to be proportional to the velocity gradient perpendicular to the direction of the motion of the fluid, i.e., to dv/dr.

Consider an element of volume in a fluid as shown in the following diagram (ref. 1)

Figure 1 - Element of volume of a liquid in a tube.

The shearing stress on this element of volume is F/A where F is the force on the upper surface and A is the cross section. The shear is given by the ratio between the lateral displacement between the two surfaces to the separation between the surfaces. Thus, if we assume that the upper surface is moving with a velocity, dv, greater than that of the lower surface, the amount of shear occurring in unit time is dv/dr. The coefficient of viscosity or simply viscosity is defined as follows (for streamline motion).