Viscosidad

The viscosity of a fluid is an important property in the analysis of liquid behavior and fluid motion near solid boundaries.

The viscosity is the fluid resistance to shear or flow and is a measure of the adhesive/cohesive or frictional fluid property. The resistance is caused by intermolecular friction exerted when layers of fluids attempt to slide by one another.

• Viscosity is a measure of a fluid's resistance to flow

The knowledge of viscosity is needed for proper design of required temperatures for storage, pumping or injection of fluids.

There are two related measures of fluid viscosity - known as dynamic (or absolute) and kinematic viscosity.

Dynamic (absolute) Viscosity

is the tangential force per unit area required to move one horizontal plane with respect to the other at unit velocity when maintained a unit distance apart by the fluid.

The shearing stress between the layers of non turbulent fluid moving in straight parallel lines can be defined for a Newtonian fluid as:

The dynamic or absolute viscosity can be expressed like

τ = μ dc/dy (1)

where

τ = shearing stress

μ = dynamic viscosity

Equation (1) is known as the Newtons Law of Friction.

In the SI system the dynamic viscosity units are N s/m2, Pa s or kg/m s where

• 1 Pa s = 1 N s/m2 = 1 kg/m s

The dynamic viscosity is also often expressed in the metric CGS (centimeter-gram-second) system as g/cm.s, dyne.s/cm2 or poise (p) where

• 1 poise = dyne s/cm2 = g/cm s = 1/10 Pa s

For practical use the Poise is to large and it's usual divided by 100 into the smaller unit called the centiPoise (cP) where

• 1 p = 100 cP

Water at 68.4oF (20.2oC) has an absolute viscosity of one - 1 - centiPoise.

Kinematic Viscosity

is the ratio of absolute or dynamic viscosity to density - a quantity in which no force is involved. Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid with it's mass density

ν = μ / ρ (2)

where

ν = kinematic viscosity

μ = absolute or dynamic viscosity

ρ = density

In the SI-system the theoretical unit is m2/s or commonly used Stoke (St) where

• 1 St = 10-4 m2/s

Since the Stoke is an unpractical large unit, it is usual divided by 100 to give the unit called Centistokes (cSt) where

• 1 St = 100 cSt

• 1 cSt = 10-6 m2/s

Since the specific gravity of water at 68.4oF (20.2oC) is almost one (1), the kinematic viscosity of water at 68.4oF is for all practical purposes 1.0 cSt.

Viscosity and Reference Temperatures

The viscosity of a fluid is highly temperature dependent and for either dynamic or kinematic viscosity to be meaningful, the reference temperature must be quoted. In ISO 8217 the reference temperature for a residual fluid is 100oC. For a distillate fluid the reference temperature is 40oC.

• For a liquid - the kinematic viscosity will decrease with higher temperature

• For a gas - the kinematic viscosity will increase with higher temperature

Other Commonly used Viscosity Units

Saybolt Universal Seconds (or SUS, SSU)

Saybolt Universal Seconds (or SUS) is used to measure viscosity. The efflux time is Saybolt Universal Seconds (SUS) required for 60 milliliters of a petroleum product to flow through the calibrated orifice of a Saybolt Universal viscometer, under carefully controlled temperature and as prescribed by test method ASTM D 88. This method has largely been replaced by the kinematic viscosity method. Saybolt Universal Seconds is also called the SSU number (Seconds Saybolt Universal) or SSF number (Saybolt Seconds Furol).

Kinematic viscosity versus dynamic or absolute viscosity can be expressed as

ν = 4.63 μ / SG (3)

where

ν = kinematic vicosity (SSU)

μ = dynamic or absolute viscosity (cP)

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