Dynamic (absolute) Viscosity

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1 Viscosity Taken from: 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) τ = shearing stress

2 μ = dynamic viscosity Equation (1) is known as the Newtons Law of Friction. In the SI system the dynamic viscosity units are N s/m 2, Pa s or kg/m s 1 Pa s = 1 N s/m 2 = 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/cm 2 or poise (p) 1 poise = dyne s/cm 2 = 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) 1 p = 100 cp Water at 68.4 o F (20.2 o C) has an absolute viscosity of one 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) ν = kinematic viscosity μ = absolute or dynamic viscosity ρ = density In the SI-system the theoretical unit is m 2 /s or commonly used Stoke (St) 1 St = 10-4 m 2 /s Since the Stoke is an unpractical large unit, it is usual divided by 100 to give the unit called Centistokes (cst) 1 St = 100 cst 1 cst = 10-6 m 2 /s Since the specific gravity of water at 68.4 o F (20.2 o C) is almost one (1), the kinematic viscosity of water at 68.4 o F is for all practical purposes 1.0 cst. Viscosity and Reference Temperatures

3 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 100 o C. For a distillate fluid the reference temperature is 40 o C. 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) ν = kinematic vicosity (SSU) μ = dynamic or absolute viscosity (cp) Degree Engler Degree Engler is used in Great Britain as a scale to measure kinematic viscosity. Unlike the Saybolt and Redwood scales, the Engler scale is based on comparing a flow of the substance being tested to the flow of another substance - water. Viscosity in Engler degrees is the ratio of the time of a flow of 200 cubic centimetres of the fluid whose viscosity is being measured - to the time of flow of 200 cubic centimeters of water at the same temperature (usually 20 o C but sometimes 50 o C or 100 o C) in a standardized Engler viscosity meter. Newtonian Fluids Fluids for which the shearing stress is linearly related to the rate of shearing strain are designated as Newtonian Fluids. Newtonian materials are referred to as true liquids since their viscosity or consistency is not affected by shear such as agitation or pumping at a constant temperature. Fortunately most common fluids, both liquids and gases, are Newtonian. Water and oils are examples of Newtonian liquids. Thixotropic Fluids Shear Thinning Fluids or Thixotropic Fluids reduce their viscosity as agitation or pressure is increased at a constant temperature. Ketchup and mayonnaise are examples of thixotropic materials. They appear thick or viscous but are possible to pump quite easily. Dilatant Fluids

4 Shear Thickening Fluids or Dilatant Fluids increase their viscosity with agitation. Some of these liquids can become almost solid within a pump or pipe line. With agitation, cream becomes butter and Candy compounds, clay slurries and similar heavily filled liquids do the same thing. Bingham Plastic Fluids Bingham Plastic Fluids have a yield value which must be exceeded before it will start to flow like a fluid. From that point the viscosity will decrease with increase of agitation. Toothpaste, mayonnaise and tomato catsup are examples of such products. Example - Converting between Kinetic and Absolute Viscosity for Air Kinematic viscosity of air at 1 bar (10 5 Pa, N/m 2 ) and 40 o C is cst ( m 2 /s). The density of air estimated with the Ideal Gas Law ρ = p / R T ρ = density (kg/m 3 ) p = absolute pressure (Pa, N/m 2 ) R = individual gas constant (J/kg K) T = absolute temperature (K) ρ = (10 5 N/m 2 ) / ((287 J/kg/K) (273 o C C) = kg/m 3 Absolute viscosity can be expressed as μ = (1.113 kg/m 3 ) ( m 2 /s) = (kg/m s, Ns/m 2, P) Viscosity and Specific Gravity of some Common Liquids centistokes (cst) Saybolt Second Universal (SSU, SUS) Typical liquid 1 31 Water (20 o C) Milk SAE 20 Crankcase Oil SAE 75 Gear Oil

5 No. 4 fuel oil Cream Vegetable oil SAE 30 Crankcase Oil SAE 85 Gear Oil Tomato Juice SAE 50 Crankcase Oil SAE 90 Gear Oil SAE 140 Gear Oil Glycerine (20 o C) SAE 250 Gear Oil ,000 Honey ,000 Mayonnaise 19,000 86,000 Sour cream Kinematic viscosity can be converted from SSU to Centistokes like ν Centistokes = ν SSU / ν SSU ν SSU < 100 ν Centistokes = ν SSU / ν SSU ν SSU > 100

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