Another important fluid property will be introduced in this section. Viscosity is a fluid property that measures the resistance of the fluid due to an applied force.

Fluid between Two Parallel Plates

To illustrate the concept of viscosity, consider a fluid between two parallel plates, as shown in the figure. If the top plate is moved at a velocity U while the bottom plate is fixed, the fluid is subjected to deformation. The fluid in contact with the top plate moves with the plate velocity U and no-slip condition is applied at the bottom plate (i.e., the fluid is stuck to the bottom plate, u = 0). The velocity profile of the fluid motion between the plates is assumed to be linear and is given by

     u = U y/h

Note that the velocity gradient (also known as the rate of shear strain) in this case is a constant (du/dy = U/h). Experiments have shown that shear stress (τ) is directly proportional to the rate of shear strain:

Shearing Stress versus Rate of
Shearing Strain for Various Fluids

Most common fluids, such as water, air and oil, are called Newtonian fluids in which the shear stress is related to the rate of shear strain in a linear fashion. That is,

The above equation is referred to as Newton's law of viscosity. The proportionality constant (μ) is called the absolute viscosity, dynamic viscosity or simply the viscosity. It has units of N-s/m² in SI units (lb-s/ft² in US units). Sometimes it is also expressed in the CGS system as dyne-s/cm² and this unit is called a poise (P). Note that the shear stress can also be determined by dividing the shear force with the surface area.

For non-Newtonian fluids, the shear stress is not a linear function of the rate of shear strain. Some common types of non-Newtonian fluids are shear thinning fluids, shear thickening fluids and Bingham plastic. To describe these non-Newtonian fluids, an apparent viscosity is introduced and it represents the slope (not constant) of the shear stress versus the rate of shear strain. It is obvious that for Newtonian fluids, the apparent viscosity is the same as the viscosity and is not a function of the shear rate.

For shear thinning fluids, the apparent viscosity decreases with shear rate, whereas for shear thickening fluids, the apparent viscosity increases with shear rate. An example of a shear thinning fluid is latex paint. When brushing paint on a wall, note that the larger the applied shear rate, the less resistance that (viscosity) is encountered.

Examples for shear thickening fluids are quicksand and a water-corn starch mixture. The larger the applied shear rate trying to mix water with corn starch, more resistance will be encountered.

The kinematic viscosity is the ratio of absolute viscosity and density. That is,

     ν = μ / ρ

The SI unit for the kinematic viscosity is m²/s. The unit in the CGS system is cm²/s and this is referred as a stoke (St).