02/21/ :13 AM. Viscosity. The Physics Hypertextbook by Glenn Elert All Rights Reserved -- Fair Use Encouraged.

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1 Viscosity The Physics Hypertextbook by Glenn Elert All Rights Reserved -- Fair Use Encouraged prev up next Discussion definitions Informally, viscosity is the quantity that describes a fluid's resistance to flow. Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them. Formally, viscosity (represented by the symbol η "eta") is the ratio of the shearing stress (F/A) to the velocity gradient (Δv x /Δz or dv x /dz) in a fluid. η = (F ) ( Δv x ) or η = ( F ) ( dv x ) The more usual form of this relationship, called Newton's equation, states that the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. The similarity to Newton's second law of motion (F = ma) should be apparent. F Δv x F dv x = η or = η F = m Δv or F = m dv Δt dt The SI unit of viscosity is the pascal second [Pa s], which has no special name. Despite its self-proclaimed title as an international system, the International System of Units has had very little international impact on viscosity. The pascal second is rarely used in scientific and technical publications today. The most common unit of viscosity is the dyne second per square centimeter [dyne s/cm 2 ], which is given the name poise [P] after the French physiologist Jean Louis Poiseuille ( ). Ten poise equal one pascal second [Pa s] making the centipoise [cp] and millipascal second [mpa s] identical. 1 pascal second = 10 poise = 1,000 millipascal second 1 centipoise = 1 millipascal second There are actually two quantities that are called viscosity. The quantity defined above is sometimes called dynamic viscosity, absolute viscosity, or simple viscosity to distinguish it from the other quantity, but is usually just called viscosity. The other quantity called kinematic viscosity (represented by the symbol ν "nu") is the ratio of the viscosity of a fluid to its density. ν = η ρ Kinematic viscosity is a measure of the resistive flow of a fluid under the influence of gravity. It is frequently measured using a device called a capillary viscometer -- basically a graduated can with a narrow tube at the bottom. When two fluids of equal volume are placed in identical capillary viscometers and allowed to flow under the influence of gravity, a viscous fluid takes longer than a less viscous fluid to flow through the tube. Capillary viscometers are discussed in more detail later in this section. Page 1 of 6

2 The SI unit of kinematic viscosity is the square meter per second [m 2 /s], which has no special name. This unit is so large that it is rarely used. A more common unit of kinematic viscosity is the square centimeter per second [cm 2 /s], which is given the name stoke [St] after the English scientist George Stoke. This unit is also a bit too large and so the most common unit is probably the square millimeter per second [mm 2 /s] or centistoke [cst]. 1 m 2 /s = 10,000 cm 2 /s [stoke] = 1,000,000 mm 2 /s [centistoke] 1 cm 2 /s = 1 stoke 1 mm 2 /s = 1 centistoke Viscosities of Selected Materials (note the different unit prefixes) simple liquids T ( C) η (mpa s) gases T ( C) η (µpa s) alcohol, ethyl (grain) air alcohol, isopropyl hydrogen alcohol, methyl (wood) helium blood nitrogen ethylene glycol oxygen ethylene glycol freon 11 (propellant) -15?? glass, strain point freon 12 (refrigerant) 0?? glass, annealing point freon 12 (refrigerant) glass, softening glycerin glass, working 10 3 glycerin glass, melting 10 2 mercury honey milk 25 3 ketchup oil, vegetable, canola lard oil, vegetable, canola molasses 20 5 oil, vegetable, corn mustard oil, vegetable, corn peanut butter oil, vegetable, olive sour cream oil, vegetable, olive 40?? syrup, chocolate oil, vegetable, soybean syrup, corn oil, vegetable, soybean syrup, maple oil, machine, light tar 20 30,000 oil, machine, heavy vegetable shortening oil, motor, SAE oil, motor, SAE oil, motor, SAE oil, motor, SAE propylene glycol propylene glycol water water water water factors affecting viscosity Viscosity is first and foremost a function of material. The viscosity of water at 20 C is millipascal seconds (which is conveniently close to one by coincidence alone). Most ordinary liquids have viscosities on the order of 1 to 1000 mpa s, while gases have viscosities on the order of 1 to 10 µpa s. Pastes, gels, emulsions, and other complex liquids are harder to summarize. Some fats like butter or margarine are so viscous that they seem more like soft solids than like flowing liquids. Molten glass is extremely viscous and approaches infinite viscosity as it solidifies. Since this process is not as well defined as true freezing, some believe (incorrectly) that glass may still flow even after it has completely cooled, but this is not the case. At ordinary temperatures, glasses are as solid as true solids. Page 2 of 6

3 From everyday experience, it should be common knowledge that viscosity varies with temperature. Honey and syrups can be made to flow more readily when heated. Engine oil and hydraulic fluids thicken appreciably on cold days and significantly affect the performance of cars and other machinery during the winter months. In general, the viscosity of a simple liquid decreases with increasing temperature (and vice versa). As temperature increases, the average speed of the molecules in a liquid increases and the amount of time they spend "in contact" with their nearest neighbors decreases. Thus, as temperature increases, the average intermolecular forces decrease. The exact manner in which the two quantities vary is nonlinear and changes abruptly when the liquid changes phase. Viscosity is normally independent of pressure, but liquids under extreme pressure often experience an increase in viscosity. Since liquids are normally incompressible, an increase in pressure doesn't really bring the molecules significantly closer together. Simple models of molecular interactions won't work to explain this behavior and, to my knowledge, there is no generally accepted more complex model that does. The liquid phase is probably the least well understood of all the phases of matter. While liquids get runnier as they get hotter, gases get thicker. (If one can imagine a "thick" gas.) The viscosity of gases increases as temperature increases and is approximately proportional to the square root of temperature. This is due to the increase in the frequency of intermolecular collisions at higher temperatures. Since most of the time the molecules in a gas are flying freely through the void, anything that increases the number of times one molecule is in contact with another will decrease the ability of the molecules as a whole to engage in the coordinated movement. The more these molecules collide with one another, the more disorganized their motion becomes. Physical models, advanced beyond the scope of this book, have been around for nearly a century that adequately explain the temperature dependence of viscosity in gases. Newer models do a better job than the older models. They also agree with the observation that the viscosity of gases is roughly independent of pressure and density. The gaseous phase is probably the best understood of all the phases of matter. More stuff motor oil Motor oil is like every other fluid in that its viscosity varies with temperature and pressure. Since the conditions under which most automobiles will be operated can be anticipated, the behavior of motor oil can be specified in advance. In the United States, the organization that sets the standards for performance of motor oils is the Society of Automotive Engineers (SAE). The SAE numbering scheme describes the behavior of motor oils under low and high temperature conditions -- conditions that correspond to starting and operating temperatures. The first number, which is always followed by the letter W, describes the low temperature behavior of the oil at start up while the second number describes the high temperature behavior of the oil after the engine has been running for some time. Lower SAE numbers describe oils that are meant to be used under lower temperatures. Oils with low SAE numbers are generally less viscous or runnier than oils with high SAE numbers, which tend to be thicker. sae prefix cranking maximum Viscosity Grades for Motor Oils low temperature specifications dynamic viscosity (mpa s) temperature ( C) pumping maximum temperature ( C) 0W 6, , W 6, , W 7, , W 7, , W 9, , W 13, , sae suffix Viscosity Grades for Motor Oils high temperature specifications kinematic viscosity (mm 2 /s) low shear rate at 100 C dynamic viscosity (mpa s) high shear rate at 150 C > > >2.9* >3.7** >3.7 Page 3 of 6

4 >3.7 * 0W-40, 5W-40, 10W-40 ** 15W-40, 20W-40, 25W-40 Source: Society of Automotive Engineers (SAE), December 1999 For example, 10W-40 oil would have a viscosity no greater than 7,000 mpa s in a cold engine crankcase even if its temperature should drop to -25 C on a cold winter night and a viscosity no less than 2.9 mpa s in the high pressure parts of an engine very near the point of overheating (150 C). non-newtonian fluids Newtonian and Non-Newtonian Fluids The relationship in which viscosity is a constant regardless of shear stress or rate of shear is called Newton's Viscosity Law. Many common solvents, mineral base oils, synthetic base fluids and fully formulated single-grade oils obey Newton's Viscosity Law, and are called Newtonian fluids. Non-Newtonian fluids can be defined as those for which viscosity is not a constant, but varies based upon the rate of shear or the shear stress at which it is measured. The majority of modern motor oils are multiviscosity grade oils that are formulated with high molecular weight polymers called viscosity modifiers. The viscosities of such oils decrease with an increase in shear rate. These are called "shear-thinning" fluids. Examples of other non-newtonian fluids are ceiling paint, quicksand and rubber cement. thixotropy is the property of some substances to behave like a fluid when worked or agitated and settling to a semisolid state when at rest. Describes a fluid that is gel-like at rest but will move with agitation. A Thixotropic fluid's viscosity decreases at a constant shear rate over time while being measured. Examples: ketchup, toothpaste, house paint, etc. see also: superfluidity measuring viscosity poiseuille's law and the capillary viscometer French physician and physiologist who formulated a mathematical expression for the flow rate for the laminar (nonturbulent) flow of fluids in circular tubes. Discovered independently by Gotthilf Hagen, a German hydraulic engineer, this relation is also known as the Hagen-Poiseuille equation. Also called hagen-poiseuille's law. For laminar, non-pulsatile fluid flow through a uniform straight pipe, the flow rate (volume per unit time) is directly proportional to the pressure difference between the ends of the tube, inversely proportional to the length of the tube, inversely proportional to the viscosity of the fluid, and proportional to the fourth power of the radius of the tube. stoke's law and the falling sphere φ = πδpr4 8ηl coaxial cylinders damped harmonic oscillator Summary Viscosity is represented by the Greek letter η "eta". v = 2gr2 Δρ 9η???????? defined informally as the quantity that describes a fluid's resistance to flow. defined mathematically as the ratio of the shearing stress to the velocity gradient in a fluid. F Δv x F dv x ) Page 4 of 6

5 Units η = (F ) ( Δv x ) or η = ( F ) ( dv x ) often expressed using Newton's equation for fluids (which is similar to Newton's second law of motion). F Δv x F dv x = η or = η The SI unit of viscosity is the pascal second [Pa s], but it is not used much. The most common unit of viscosity is the poise [P = dyne s/cm 2 ]. Ten poise equal one pascal second [10 P = 1 Pa s]. Kinematic viscosity is represented by the Greek letter ν "nu". defined informally as a measure of the resistive flow of a fluid under the influence of gravity. defined mathematically as the ratio of the viscosity of a fluid to its density. Units Problems practice ν = η ρ The SI unit of kinematic viscosity is the square meter per second [m 2 /s], but it is not used much. The most common unit of kinematic viscosity is the stoke [St = cm 2 /s] Ten thousand stokes equal one square meter per second [10,000 stoke = 1 m 2 /s] Factors affecting viscosity 1. Write something. Viscosity is a property of materials. The viscosity of simple liquids decreases with increasing temperature increases under very high pressures. The viscosity of gases 2. Write something else. 3. Write something different. increases with increasing temperature is independent of pressure and density. 4. Write something completely different. numerical 1. problems Resources general automotive food polymers water SoftSlide Viscosity Converter Ready Reference for Lubricant and Fuel Performance, Lubrizol In the Thick of It, Lynn A. Kuntz, Food Product Design, September 1992 Using supplies from home, how should I find the viscosity of ketchup? MadSci Network, January 1999 Extrusion Glossary of Terms, PolyDynamics The Science of the Summer Games: Swimming, Inwit Publishing Viscosity of Interfacial Water, Yingxi Zhu and Steve Granick, Physical Review Letters, August 2001 Page 5 of 6

6 Water turns to jelly under pressure, Nature Science Update, 17 August 2001 prev up next Another quality webpage by home contact Glenn Elert bent chaos eworld facts physics Page 6 of 6