There is a branch of science called Rheology that deals with the deformation and flow of materials. These behaviors are defined by a collection of measurements. One of the more obscure and confusing parameters is viscosity. Viscosity measurements are used in everything from lubrication and heat transfer fluids, to adhesives and coatings to aerodynamic and hydrodynamic drag.

Viscosity is the measure of a fluid's resistance to flow. Think of viscosity as fluid friction. Thinner liquids, such as water, have lower viscosities, while thicker liquids like oil have higher viscosities.

Viscosity can also be thought of as a measure of the "thickness" of the liquid. Thick liquids are said to have a high viscosity and thin liquids a low viscosity. Molasses and motor oil are thick or high viscosity liquids while gasoline and water are thin, low viscosity liquids.

**Real World Reference Frame:**

Water at approximately 70°F (21°C) has an absolute viscosity of about one centipoise. All other fluids are then measured, calibrated, and thus compared to the viscosity of water. For example;

Blood 10 centipoise

Ethylene glycol 15 centipoise

Honey 2,000 centipoise

Molasses 5,000 centipoise

Lard 100,000 centipoise

**Viscosity Physics:**

Viscosity is actually a measurement of internal friction, or resistance, to flow by external forces. As with most derived measurements in the science of engineering, a model is required.

Consider two plates moving parallel to each other separated a given distance (y) by a viscous fluid. It is the nature of a viscous fluid to attach itself to the surfaces of these plates. Thus, as one plate is moved at a given velocity V (called the shear rate) relative to the other plate, a distribution of fluid velocities is created. At the surface of the fixed plate, the fluid velocity is zero. At the surface of the moving plate, the fluid velocity is that of the moving plate. In the fluid field in between, the fluid velocity varies from zero up to V and at any given point the incremental velocity change is defined as “dV.”

Additionally, a force F (called the shear force) is required to move the plate to overcome this viscous “drag.” We define the ratio between the shear force and the shear rate as viscosity.

Also, a large plate would have much greater viscous drag than a small plate so we limit this surface area by defining this shear force for a given unit of area (A) of the moving plate. This gives us what engineers like to call “shear stress.” This unitized force, or shear stress (s) can be expressed as follows:

F/A = s ( which is in units of pressure or stress, e.g. pounds per square inch, etc.)

As one would intuitively expect, the more viscous the fluid, the greater the force required to maintain a given velocity. So for an extremely low viscosity fluid, the variation in fluid velocity is very large. It is zero at the fixed plate and V at the moving plate with almost an instant change across y. For high viscosity fluids, again the velocity at the fixed plate is zero but as we progress away from the plate the fluid velocity is very slow to change. In fact, it has been found experimentally that this shear stress is directly proportional to the variation of fluid velocity or “velocity profile.” Thus, s is proportional to dV/dy

Now all we need to complete the equation is a proportionality constant that is characteristic of any given specific fluid. This constant is identified by the Greek letter µ.

Thus, we have,

s = µ·dV/dy

Solving for µ, gives us,

µ = s/dV/dy

Let’s look at the physical units of the proportionality constant;

s = force required per unit area, defined as shear stress = lbs/inch2

V = velocity of relative plate movement = inches/second

y = plate separation, or any normal position between the plates = inches

µ = (lbs/in2)/(in/second)/in = (lb-second)/in2 or (lbs/in2)-second

**Dynamic or Absolute Viscosity (Greek symbol: ě):**

We have just defined absolute viscosity (also called dynamic viscosity)—the shear force required to produce a given shear rate. Note that it is completely independent of the density of the fluid.

In the CGS measurement system, this proportionality constant of absolute viscosity is given the name “poise” (P) named after Jean Louis Marie Poiseuille (pronounced Pwa-selli).

It is more commonly expressed in ASTM standards as "centipoise" (abbreviated cP) and represents 1/100 of a poise. The centipoise is most commonly used because water has a viscosity of 1.0020 cP (at 20 °C) and, as with other physical measurements, the base fluid to which all others are compared is water.

In the SI measurement system of internationally recognized units, absolute viscosity is the “Pascal-second” (Pa-s), with fundamental units of (1 kilogram/meter2)-second.

1 poise = 1 Pascal-second

1 centipoise = (1 gram/centimeter2)-second = 0.01 Pascal-second

**Kinematic Viscosity (k):**

For certain purposes (such as for coatings or lubricants) there is an additional type of viscosity defined—“kinematic viscosity.” Kinematic viscosity is measured by the time required for a given volume of liquid to flow through a capillary or restriction. It is related to flow caused by the hydrostatic head of the liquid and therefore strongly dependent on fluid density.

The CGS physical unit for kinematic viscosity is the “Stokes” (abbreviated S or St), named after George Gabriel Stokes. It is usually expressed in terms of centistokes (cS or cSt) which represents 1/100 of a stoke.

In the SI system of internally recognized units, kinematic viscosity has the units: meter2/second

1 stoke = 1 meter2/second = 100 centistokes

1 centistoke = 1 centimeter˛/second = 0.0001 meter˛/second.

**Absolute (Dynamic) Viscosity vs. Kinematic Viscosity Relationship:**

The two parameters are related through specific gravity.

Kinematic Viscosity = Absolute Viscosity/Specific Gravity

Or, where d is density: k = ě/d

For water at 68.4°F (20.2°C):

Specific gravity = 1.0

Absolute viscosity = 1.0 centipoise

Thus, it follows that:

Kinematic viscosity = 1.0 centistoke

**Measuring Viscosity:**

Viscosity is measured with an instrument called a viscosimeter. There are several types of viscosimeters. The two most common methods are the rotating spindle and the cup method. Others methods use bubble tubes.

The Saybolt universal version is the most popular in the United States, and is used to measure liquids of low to medium viscosities. The Saybolt Furol version is for high viscosity liquids. A measured volume of liquid is allowed to flow through an orifice of specified dimensions and the time that it takes to get through is measured in seconds. This is called the SSU number (Seconds Saybolt Universal) or SSF number (Saybolt Seconds Furol). These numbers are widely published in various charts and are often used in addition to, or in place of the actual viscosity measured in centistokes.

The Irany, Zahn and Redwood viscosimeters operate on the same principal. You can compare viscosity readings to each other by means of conversion factors or comparison charts that are widely available.

The Brookfield Viscosimeter is the rotating type where a disc is rotated in the liquid to be tested. The drag is noted and read directly in centipoise.

**Specific Gravity:**

There is sometimes confusion between viscosity and specific gravity yet the two measurements are completely independent of each other. Specific gravity is the relative “heaviness” of a substance compared to that of water, and it is expressed without units. In the metric system specific gravity is the same as in the English system. Specific gravity is a measure of the weight of a given liquid relative to the weight of an equal volume of 20° C (68° F) fresh water.

We measure specific gravity with a hydrometer. It consists of a glass cylinder with a rubber bulb on top, and a float positioned inside the glass tube. The float is calibrated to float on fresh water so if the fluid you are testing has a higher specific gravity, the float will rise in the liquid and at a lower specific gravity it will sink lower in the liquid. This is the same instrument that we use to tell if your automobile battery is fully charged. Another version will determine the concentration of anti-freeze in an automobile radiator. You can observe the little balls floating in the tube.

If something is 3 times the weight of an equal volume of water its specific gravity is 3. If a liquid will float on water it has a specific gravity of less than one (1). If it sinks into the fresh water the specific gravity is more than one.

Motor oil has a low specific gravity (it floats on water), but a high viscosity of more than 500 centistokes. In contrast, mercury has a very high specific gravity (13.7) but a low viscosity of only 0.118 Centistokes.

**Effects of Temperature:**

The viscosity of a liquid can change appreciably with a change in the temperature of the liquid, but seldom changes when the pressure is altered. Common knowledge dictates that hot oil is "thinner" than cold oil, so it is important to know the temperature of a fluid when the viscosity is measured.

**Newtonian Fluids:**

In addition to the effects of temperature on viscosity, there are some fluids that change their viscosity with agitation. Fluids not affected by motion or agitation are called “Newtonian” fluids and includes fluids such as mineral oil and water.

**Thixotropic Fluids:**

Thixotropic fluids exhibit a decrease in viscosity with an increase of movement, stirring or other agitation. Once the movement is stopped, the viscosity increases again. The gel coats and flow coats of polyester resin systems used in fiberglass manufacture are example of thixotropic fluids.

**Dilatant Fluids:**

In the opposite direction, there are fluids that increase their viscosities with agitation. Cream turning to butter is the classic example of this phenomenon.

**Plastic Fluids:**

There is another class of fluids that have a certain shear stress that must be exceeded before flow will start. Viscosity will continue to decrease with further agitation or movement. The next time you are trying to pour tomato ketchup, think of plastic fluids.

**The Pseudo-Plastic Fluids:**

These fluids exhibit a decrease in viscosity with an increase of agitation or movement but do not have a yield value. Heavily loaded emulsions are typical of these fluids.