 # Viscosity

#### Dynamic Viscosity

The dynamic viscosity (sometimes called absolute viscosity) of a fluid can be defined as the resistance to flow and shear under the forces of internal friction. This internal friction is caused by the resistance of the fluid's molecules moving relative to each other. The larger the molecules, the higher the internal resistance and consequently the higher the dynamic viscosity. The metric unit for dynamic viscosity is dyne-second per square centimetre (or sometimes the numerically equivalent gram per centimetre-second is used) called a Poise (named after French physician and physiologist Jean Louis Marie Poiseuille). In practice the centiPoise is used since the Poise is a large unit. Imperial units are either slugs per foot-second, or the equivalent pound-seconds per square foot.

#### Kinematic Viscosity

Kinematic viscosity on the other hand is a measure of a fluid's resistance to flow and shear under the forces of gravity. Again, the larger the molecules, the greater resistance, the higher the kinematic viscosity. Most pipe friction charts and pump correction charts used by engineers refer to kinematic viscosity. The metric units of kinematic viscosity are square centimetre per second, called a Stoke (called after Irish scientist George Gabriel Stokes). In practice the centiStoke is used since the Stoke is a large unit. Imperial units are square foot per second.

#### Viscosity Conversion

The kinematic viscosity of a fluid can be calculated from its dynamic viscosity by dividing it by the fluid's density e.g.
centiPoises (cP) = centiStokes (cSt) / Density

A rough conversion of Redwood Seconds to centistokes is given by the formula:
Centistokes (cSt) = 0.260t - (0.0188/t), where t is the time in Redwood Seconds

ASTM D2161 - 05e1 Standard Practice for Conversion of Kinematic Viscosity to Saybolt Universal Viscosity or to Saybolt Furol Viscosity. This practice establishes the official equations relating SUS and SFS to the SI kinematic viscosity units, mm2/s. Roughly
kinematic vicosity (SSU) = 4.63 x dynamic viscosity (cP) / SG
or
To convert Kinematic viscosity in SSU to centiStokes
centiStokes = 0.226 x SSU - (195/SSU) for SSU values less than 100, and
centiStokes = 0.22 x SSU - (135/SSU) for SSU values greater than 100

#### Temperature Effect

Viscosity is temperature dependent, generally the warmer a liquid the less viscous it is whereas the warmer a gas the higher the viscosity. Therefore for a dynamic or kinematic viscosity to be meaningful a reference temperature must be quoted.

#### Measuring Viscosity

Viscosity measurement can not be measured inline - it is performed in the laboratory using a rheometer. There are three main types of rheometer;
Capillary Tube - sometimes referred to as a viscosity bath, is used to measure kinematic viscosity. This is perhaps the most common method of viscosity measurement
Rotary Viscometer - used to measure dynamic viscosity
Cone & Plate - a variance on the rotary viscometer

#### Other Viscosity Units

Occasionally other units of viscosity are quoted. These have often been named after the viscosity meter used to measure viscosity. For example:
Degree Engler is still occasionally used in the UK. It is a measure of kinematic viscosity based on comparing a flow of the substance under test to the flow of water. Viscosity in Engler degrees is the ratio of the time of flow of 200 cubic centimeters of the fluid under test to the time of flow of 200 cubic centimeters of water at the same temperature in a standardised Engler viscosity meter. The base temperature is usually 20°C, though sometimes 50°C or 100°C is used.
Saybolt Universal Seconds (SUS) is a dated unit of measure of viscosity originating in the oil and petroleum industries. The time measured in seconds required for 60 milliliters of a petroleum product to flow through the calibrated orifice of a Saybolt Universal viscometer, at controlled temperature, is defined as that product's viscosity in Saybolt Universal Seconds (SUS). Sometimes referred to as the SSU number (Seconds Saybolt Universal) for times less than 600 seconds, or SSF number (Saybolt Seconds Furol) for times in excess of 600 seconds.
Redwood Second is another obsolete unit of kinematic viscosity. The time in seconds for 50 milliliters of the sample liquid to flow through a Redwood Viscometer is a measure its viscosity and is given the units of Redwood Seconds.  Optimal Control
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Viscosity Solutions   Mathematical
Theory of
Non-uniform Gases   Sir George
Gabriel Stokes   Engineering Formulas 