# READING #2 - Viscosity of a Liquid

Piotr Habdas and Eric R. Weeks, Physics Department, Emory University, Atlanta, GA
All fluids have a viscosity, which describes the amount of friction between nearby regions of the fluid moving at different velocities. For example, when you stir your coffee, eventually the coffee stops moving, due to viscosity.

### Stokes' Law

George Gabriel Stokes, an Irish-born mathematician, worked most of his professional life describing fluid properties. Perhaps his most significant accomplishment was the work describing the motion of a sphere in a viscous fluid. This work lead to the development of Stokes' Law, a mathematical description of the force required to move a sphere through a viscous fluid at specific velocity. This law will form the basis of one of the experiments you will perform.

Stokes' Law for a falling sphere is written as,

eta=mg /6 pi V d (1)

where **eta** is the fluid viscosity, **m** is the mass of the moving sphere, **g** is the gravitational acceleration (**g** = 9.81 m/s^{2}), **V** is the velocity of the sphere relative to the fluid, and **d** is the diameter of the sphere. Using this equation, we can determine the viscosity of the liquid.

To determine the viscosity of the liquid you will drop a bunch of balls into a tube filled with this liquid. You will measure the time it takes a ball to travel some distance. From that you can calculate the ball's velocity (V=distance/time), and knowing the ball's diameter and mass we can obtain liquids viscosity (using equation 1).

Also, to investigate even further viscosity you will measure the time it takes a given volume of fluid to flow out of a cup with a hole at the bottom. The more viscous the liquid the longer it should take for it to flow out through the hole.