What Is Dynamic Viscosity?

M.J. Casey
M.J. Casey

Dynamic viscosity of a fluid is defined as the shear stress applied divided by the velocity gradient achieved when a shear force is applied to a fluid. Viscosity varies greatly among fluids. It is important in the flow behavior of liquids.

Scientist with beakers
Scientist with beakers

The term used to describe a fluid’s resistance to flow is viscosity. Syrup is more viscous than water; molasses more viscous than syrup. Viscosity is the result of the ease with which molecules slip past each other and is a function of the molecules’ chemistry, shape, and temperature. Gases, too, have varying viscosities. At the same temperature, oxygen is twice as viscous as hydrogen or ammonia, while nitrogen’s viscosity lies in the middle.

The classic measurement of viscosity comes from a test consisting of two smooth plates separated by a thin film of fluid. The bottom plate is stationary. The experimenter, using a known force, attempts to slide the top plate past the bottom plate. Within the film of liquid, the molecules next to the bottom plate have zero velocity. The fluid molecules next to the top plate have the same velocity as the top plate.

While the fluid can be either a gas or liquid, it is easier to think of liquids in this test. If the substance separating the plates is water, the top plate will slide sideways very easily. With molasses as the liquid, the top plate will move sluggishly with the same force applied.

A shear force is in the direction of the force, as opposed to tension forces or compressive forces, which in this case would be the forces necessary to either move the plates apart or closer together. The shear stress is the shear force divided by a unit area and is expressed as newtons per square meter (N/m 2) or pascals (Pa). Viscosity calculations are usually performed in metric units.

The velocity gradient is the difference in the rate of flow of the liquid next to the bottom plate, which is zero, compared to the liquid next to the top plate, which is the same as the rate of the top plate. The dynamic viscosity is then the shear stress divided by the shear rate and is measured in pascal-seconds (Pa-s). Practically, viscosity is measured in centipoise (cPo). One centipoise equals one millipascal second.

Another measure of viscosity is kinematic viscosity. Kinematic viscosity is the dynamic viscosity divided by the density of the fluid. Kinematic viscosity is easier to measure than dynamic viscosity, so it is often used to determine dynamic viscosity.

A Newtonian fluid retains a constant dynamic viscosity independent of the shear rate. Ketchup is a non-Newtonian fluid. It has a high dynamic viscosity when the flow rate is low but becomes almost as fluid as water when the flow rate is increased. This explains why people shake ketchup bottles to speed up the ketchup flow, but then end up with too much on their plate.

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