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 (∆vx/∆y or dvx/dy) in a fluid.
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.
Or if you prefer calculus symbols (and who doesn't)…
The SI unit of viscosity is the pascal second [Pas], which has no special name. Despite its self-proclaimed title as an international system, the International System of Units has had little international impact on viscosity. The pascal second is more rare than it should be in scientific and technical writing today. The most common unit of viscosity is the dynesecondpersquarecentimeter [dynes/cm2], which is given the name poise [P] after the French physiologist Jean Poiseuille (1799–1869). Tenpoise equal one pascal second [Pas] making the centipoise [cP] and millipascalsecond[mPas] identical.
There are actually two quantities that are called viscosity. The quantity defined above is sometimes called dynamicviscosity, absoluteviscosity, or simpleviscosity to distinguish it from the other quantity, but is usually just called viscosity. The other quantity called kinematic viscosity (represented by the Greek letter ν "nu") is the ratio of the viscosity of a fluid to its density.
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, the more viscous fluid takes longer than the less viscous fluid to flow through the tube. Capillary viscometers will be discussed in more detail later in this section.
The SI unit of kinematic viscosity is the square meter per second [m2/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 [cm2/s], which is given the name stokes [St] after the Irish mathematician and physicist George Stokes (1819–1903). One square meter per second is equal to ten thousand stokes.
Even this unit is a bit too large, so the most common unit is probably the square millimeter per second [mm2/s] or the centistokes [cSt]. One square meter per second is equal to one million centistokes.
The stokes is a rare example of a word in the English language where the singular and plural forms are identical. Fish is the most immediate example of a aword that behaves like this. 1fish, 2fish, redfish, bluefish; 1stokes, 2stokes, somestokes, fewstokes.
factors affecting viscosity
This part needs to be reorganized.
Viscosity is first and foremost a function of material. The viscosity of water at 20°C is 1.0020 millipascal seconds (which is conveniently close to one by coincidence alone). Most ordinary liquids have viscosities on the order of 1 to 1000 mPas, while gases have viscosities on the order of 1 to 10 μPas. 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 the 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.
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. As temperature increases, the average speed of the molecules in a liquid increases and the amount of time they spend "incontact" with their nearest neighbors decreases. Thus, as temperature increases, the average intermolecular forces decrease. The actual 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.
Since viscosity is so dependent on temperature, it shouldn't never be stated without it.
This is a pretty good model for liquids…
|1/T=||the independent variable, x|
|lnη=||the dependent variable, y|
|B=||the slope, m|
|lnA=||the y intercept, b|
Viscosities of selected materials (notethevarietyofunitprefixes)
|alcohol, ethyl (grain)||20||1.1|
|alcohol, methyl (wood)||20||0.59|
|oil, vegetable, canola||25||57|
|oil, vegetable, canola||40||33|
|oil, vegetable, corn||20||65|
|oil, vegetable, corn||40||31|
|oil, vegetable, olive||20||84|
|oil, vegetable, olive||40||?|
|oil, vegetable, soybean||20||69|
|oil, vegetable, soybean||40||26|
|oil, machine, light||20||102|
|oil, machine, heavy||20||233|
|glass, strain pt.||504||1015.2|
|glass, annealing pt.||546||1012.5|
|glass, softening pt.||724||106.6|
|glass, working pt.||103|
|glass, melting pt.||101|
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 the 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 for winter, 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 runnier (less viscous) than oils with high SAE numbers, which tend to be thicker (more viscous).
For example, 10W‑40 oil would have a viscosity no greater than 7,000mPas 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 2.9mPas in the high pressure parts of an engine near the point of overheating (150°C).
Viscosity characteristics of motor oil grades
|00W||06,200mPas (−35°C)||60,000mPas (−40°C)|
|05W||06,600mPas (−30°C)||60,000mPas (−35°C)|
|10W||07,000mPas (−25°C)||60,000mPas (−30°C)|
|15W||07,000mPas (−20°C)||60,000mPas (−25°C)|
|20W||09,500mPas (−15°C)||60,000mPas (−20°C)|
|25W||13,000mPas (−10°C)||60,000mPas (−15°C)|
The the mathematical expression describing the flow of fluids in circular tubes was determined by the French physician and physiologist Jean Poiseuille (1799–1869). Since it was also discovered independently by the German hydraulic engineer Gotthilf Hagen (1797–1884), it should be properly known as the Hagen-Poiseuille equation, but it is usually just called Poiseuille's equation. I will not derive it here (but I probably should someday). For non-turbulent, non-pulsatile fluid flow through a uniform straight pipe, the volume flow rate (qm) is…
- directly proportional to the pressure difference (∆P) between the ends of the tube
- inversely proportional to the length (ℓ) of the tube
- inversely proportional to the viscosity (η) of the fluid
- proportional to the fourth power of the radius (r4) of the tube
Solve for viscosity if that's what you want to know.
Capillary viscometer… keep writing… sorry this is incomplete.
The mathematical expression describing the viscous drag force on a sphere was determined by the 19th century British physicist George Stokes. I will not derive it here (but I probably should someday in the future).
The formula for the buoyant force on a sphere is accredited to the Ancient Greek engineerArchimedes of Syracuse, but equations weren't invented back then.
The formula for weight had to be invented by someone, but I don't know who.
Let's combine all these things together for a sphere falling in a fluid. Weight points down, buoyancy points up, drag points up. After a while, the sphere will fall with constant velocity. When it does, all these forces cancel. When a sphere is falling through a fluid it is completely submerged, so there is only one volume to talk about — the volume of a sphere. Let's work through this.
And here we are.
Drop a sphere into a liquid. If you know the size and density of the sphere and the density of the liquid, you can determine the viscosity of the liquid. If you don't know the density of the liquid you can still determine the kinematic viscosity. If you don't know the density of the sphere, but you know its mass and radius, well then you can calculate its density.
Newton's equation relates shear stress and velocity gradient by means of a quantity called viscosity. A newtonian fluid is one in which the viscosity is just a number. A non-newtonian fluid is one in which the viscosity is a function of some mechanical variable like shear stress or time. Non-newtonian fluids that change over time are said to have a memory.
Some gels and pastes behave like a fluid when worked or agitated and then settle into a nearly solid state when at rest. Such materials are examples of shear-thinning fluids. House paint is a shear-thinning fluid and it's a good thing, too. Brushing, rolling, or spraying are means of temporarily applying shear stress. This reduces the paint's viscosity to the point where it can now flow out of the applicator and onto the wall or ceiling. Once this shear stress is removed the paint returns to its resting viscosity, which is so large that an appropriately thin layer behaves more like a solid than a liquid and the paint does not run or drip. Think about what it would be like to paint with water or honey for comparison. The former is always too runny and the latter is always too sticky.
Toothpaste is another example of a material whose viscosity decreases under stress. Toothpaste behaves like a solid while it sits at rest inside the tube. It will not flow out spontaneously when the cap is removed, but it will flow out when you put the squeeze on it. Now it ceases to behave like a solid and starts to act like a thick liquid. when it lands on your toothbrush, the stress is released and the toothpaste returns to a nearly solid state. You don't have to worry about it flowing off the brush as you raise it to your mouth.
Shear-thinning fluids can be classified into one of three general groups. A material that has a viscosity that decreases under shear stress but stays constant over time is said to be pseudoplastic. A material that has a viscosity that decreases under shear stress and then continues to decrease with time is said to be thixotropic. If the transition from high viscosity (nearly semisolid) to low viscosity (essentially liquid) takes place only after the shear stress exceeds some minimum value, the material is said to be a bingham plastic.
Materials that thicken when worked or agitated are called shear-thickening fluids. An example that is often shown in science classrooms is a paste made of cornstarch and water (mixed in the correct proportions). The resulting bizarre goo behaves like a liquid when squeezed slowly and an elastic solid when squeezed rapidly. Ambitious science demonstrators have filled tanks with the stuff and then run across it. As long as they move quickly the surface acts like a block of solid rubber, but the instant they stop moving the paste behaves like a liquid and the demonstrator winds up taking a cornstarch bath. The shear-thickening behavior makes it a difficult bath to get out of. The harder you work to get out, the harder the material pulls you back in. The only way to escape it is to move slowly.
Materials that turn nearly solid under stress are more than just a curiosity. They're ideal candidates for body armor and protective sports padding. A bulletproof vest or a kneepad made of of shear-thickening material would be supple and yielding to the mild stresses of ordinary body motions, but would turn rock hard in response to the traumatic stress imposed by a weapon or a fall to the ground.
Shear-thickening fluids are are also divided into two groups: those with a time-dependent viscosity (memory materials) and those with a time-independent viscosity (non-memory materials). If the increase in viscosity increases over time, the material is said to be rheopectic. If the increase is roughly directly proportional to the shear stress and does not change over time, the material is said to be dilatant.
ketchup, heatherhoney, quicksand, snakevenom, polymericthickfilmink
cream being whipped
paint, stylinggel, whippedcream, cakebatter, applesauce, ballpointpenink, ceramic-metalink
starchpastes, sillyputty, synovialfluid, chocolatesyrup, viscouscouplingfluids, liquidarmor
|materials with a yieldstress||binghamplastic|
toothpaste, drillingmud, blood, cocoabutter, mayonnaise, yoghurt, tomatopuree, nailpolish, sewagesludge
With a bit of adjustment, Newton's equation can be written as a power law that handles the pseudoplastics and the dilantants — the Ostwald-de Waele equation…
where η the viscosity is replaced with k the flow consistency index [Pasn] and the velocity gradient is raised to some power n called the flow behavior index [dimensionless]. The latter number varies with the class of fluid.
A different modification to Newton's equation is needed to handle Bingham plastics — the Bingham equation…
where σy is the yield stress [Pa] and ηpl is the plastic viscosity [Pas]. The former number separates Bingham plastics from newtonian fluids.
Combining the Ostwald-de Waele power law with the Bingham yield stress gives us the more general Herschel-Bulkley equation…
where again, σy is the yield stress [Pa], k is the flow consistency index [Pasn], and n is the flow behavior index [dimensionless].
When a force (F) is applied to an object, one of four things can happen.
- It could accelerate as a whole, in which case Newton's second law of motion would apply…
This term is not interesting to us right now. We've already discussed this kind of behavior in earlier chapters. Mass (m) is resistance to acceleration (a), which is the second derivative of position (x). Let's move on to something new.
- It could flow like a fluid, which could be described by this relationship…
This is the simplified model where drag is directly proportional to speed (v), the first derivative of position (x). We used this in terminal velocity problems just because it gave differential equations that were easy to solve. We also used it in the damped harmonic oscillator, again because it gave differential equations that were easy to solve (relatively easy, anyway). The proportionality constant (b) is often called the damping factor.
- It could deform like a solid according to Hooke's law…
The proportionality constant (k) is the spring constant. Position (x) is not the part of any derivative nor is it raised to any power.
- It could get stuck…
That symbol f makes it look like we're discussing static friction. In fluids (non-newtonian fluids, to be specific) a term like this is associated with yield stress. Position (x) is not involved in any way.
Put everything together and state acceleration and velocity as derivatives of position.
This differential equation summarizes the possible behaviors of an object. The interesting thing is that it mixes up the behaviors of fluids and solids. The more interesting thing is that there are occasions when both behaviors will be present in one thing. Materials that both flow like fluids and deform like solids are said to be viscoelastic — an obvious mash-up of viscosity and elasticity. The study of materials with fluid and solid properties is called rheology, which comes from the Greek verb ρέω (reo), to flow.
What old book gave me this idea? What should I write next?
Foods generally exhibit what is called viscoelastic behaviour, whereby a mix of the characteristic elastic properties of solids and flow properties of liquids are both found to varying extents
- Cheese pull occurs when melting fats lubricate linked protein strands. The fats flow like a liquid and the proteins stretch like a solid.
Viscosity is the resistance of a fluid (liquid or gas) to a change in shape or movement of neighbouring portions relative to one another. Viscosity denotes opposition to flow.What is viscosity and its SI unit? ›
The SI unit of viscosity is the pascal second (Pa·s) or kg·m−1·s−1.What is viscosity in physics class 11? ›
Viscosity is the property of a fluid by virtue of which an internal resistance comes into play when the liquid is in motion, and opposes the relative motion between its different layers. Thus, it is the resistance of a fluid to flow.How do you find viscosity in physics? ›
There are several formulas and equations to calculate viscosity, the most common of which is Viscosity = (2 x (ball density – liquid density) x g x a^2) ÷ (9 x v), where g = acceleration due to gravity = 9.8 m/s^2, a = radius of ball bearing, and v = velocity of ball bearing through liquid.What are the types of viscosity? ›
There are two types of viscosity: Dynamic viscosity and Kinematic viscosity.How is viscosity measure? ›
The viscosity of a liquid (see Viscosity) is measured using a viscometer, and the best viscometers are those which are able to create and control simple flow fields.What is the use of viscosity? ›
Viscosity measurements are used in the food industry to maximize production efficiency and cost effectiveness. It affects the rate at which a product travels through a pipe, how long it takes to set or dry, and the time it takes to dispense the fluid into packaging.Why is viscosity important? ›
Viscosity of a liquid is an important parameter as it can be used as an indicator of quality by the consumer, in some instances a thicker liquid being thought of as superior quality when compared to a thinner product. Viscosity is also a characteristic of the texture of food.What is viscosity short? ›
Viscosity is a measure of a fluid's resistance to flow.What is simple viscosity? ›
Viscosity is a physical property of fluids. It shows resistance to flow. In a simple example, water has a low viscosity, as it is "thin". Syrup and tar, on the other hand, have a high viscosity, as they are "thick". A way to test for viscosity is the speed at which the substance runs down a slope.
According to Newton, the viscous force acting between liquid layers of area A and velocity gradient ΔzΔv is given by F=−ηadzdv, where η is constant called.What is the process of viscosity? ›
Viscosity is the measure of the internal friction of a fluid. This friction becomes apparent when a layer of fluid is made to move in relation to another layer. The greater the friction, the greater the amount of force required to cause this movement, which is called shear.What is viscosity number? ›
There are two numbers that define viscosity meaning. The first number precedes the letter 'W' which stands for Winter. This measurement is related to how an oil flows when it is cold, such as at engine start-up. The second number is defined by how an oil flows at normal engine operating temperatures.Where is viscosity found? ›
By definition, viscosity is a type of property found in liquids and gases that measures the matter's resistance to flow or change shape.What factors affect viscosity? ›
The viscosity of a material is affected by temperature, pressure, nature of fluid, velocity gradient , etc.What is viscosity materials? ›
Viscosity is the material property which relates the viscous stresses in a material to the rate of change of a deformation (the strain rate). Although it applies to general flows, it is easy to visualize and define in a simple shearing flow, such as a planar Couette flow.What is viscosity matter? ›
Viscosity is another type of bulk property defined as a liquid's resistance to flow. When the intermolecular forces of attraction are strong within a liquid, there is a larger viscosity. An example of this phenomenon is imagining a race between two liquids down a windshield.What are the 3 factors of viscosity? ›
Temperature, composition, and volatile (gas) content largely determine the viscosity of lava. Temperature: The hotter the lava, the lower the viscosity (the thinner it is). The cooler the lava, the higher the viscosity (the thicker it is).What is viscosity level? ›
In layman's terms, viscosity defines a fluid's resistance to flow. The higher the viscosity of a liquid, the thicker it is and the greater the resistance to flow. Temperature will affect the viscosity of most materials.What is normal viscosity? ›
Many cardiovascular handbooks consider blood viscosity values between 3.5 and 5.5 cP to be normal.
The viscosity of water at a temperature of 20 degrees Celsius is approximately 0.01 poise or 10-3 Pa. s (Pascal seconds). Viscosity is a measure of the resistance of a fluid to deformation at a given rate.What is viscosity introduction? ›
Viscosity is a fundamental characteristic property of all liquids. When a liquid flows, it has an internal resistance to flow. Viscosity is a measure of this resistance to flow or shear. Viscosity can also be termed as a drag force and is a measure of the frictional properties of the fluid.Why is viscosity important in physics? ›
Viscosity is an important property of liquids used for lubrication, such as lubricating oils and grease. The viscosity of a liquid is the resistance it produces to flow. Fast-moving liquids, such as water, have low viscosity, whereas slow-moving liquids, such as honey, have high viscosity.
Viscosity generally increases as the temperature decreases. The viscosity of a liquid is related to the ease with which the molecules can move with respect to one another. Thus the viscosity of a liquid depends on the: strength of attractive forces between molecules, which depend on their composition, size, and shape.What is simple viscosity? ›
Viscosity is a physical property of fluids. It shows resistance to flow. In a simple example, water has a low viscosity, as it is "thin". Syrup and tar, on the other hand, have a high viscosity, as they are "thick". A way to test for viscosity is the speed at which the substance runs down a slope.What is viscosity and what causes it? ›
Viscosity is a measure of the resistance of a fluid towards being deformed when under shear stress. Hence, it is also known as shear viscosity. It is caused by the attractive forces between molecules in close contact, and the friction between molecular chains.What does viscosity mean kid definition? ›
Viscosity is the property of a liquid that describes how fast or slowly it will flow. You can think of viscosity as how thick a liquid is. A liquid with high viscosity - that is thick, like peanut butter - will flow slowly.Is water a viscosity? ›
The viscosity of water at a temperature of 20 degrees Celsius is approximately 0.01 poise or 10-3 Pa. s (Pascal seconds). Viscosity is a measure of the resistance of a fluid to deformation at a given rate.Why is viscosity important? ›
Viscosity of a liquid is an important parameter as it can be used as an indicator of quality by the consumer, in some instances a thicker liquid being thought of as superior quality when compared to a thinner product. Viscosity is also a characteristic of the texture of food.What factors affect viscosity? ›
The viscosity of a material is affected by temperature, pressure, nature of fluid, velocity gradient , etc.
The viscosity of a liquid (see Viscosity) is measured using a viscometer, and the best viscometers are those which are able to create and control simple flow fields.What are the 3 factors of viscosity? ›
Temperature, composition, and volatile (gas) content largely determine the viscosity of lava. Temperature: The hotter the lava, the lower the viscosity (the thinner it is). The cooler the lava, the higher the viscosity (the thicker it is).What is the process of viscosity? ›
Viscosity is the measure of the internal friction of a fluid. This friction becomes apparent when a layer of fluid is made to move in relation to another layer. The greater the friction, the greater the amount of force required to cause this movement, which is called shear.What is viscosity made of? ›
Viscosity refers to the thickness of fluid. Viscosity results from the interaction, or friction, between molecules in a fluid. Similar to friction between moving solids, viscosity will determine the energy required to make a fluid flow.
Definition of Viscosity. the thickness of a liquid or its resistance to movement. Examples of Viscosity in a sentence. 1. The syrup flows slowly from the bottle because of its viscosity.What is viscosity introduction? ›
Viscosity is a fundamental characteristic property of all liquids. When a liquid flows, it has an internal resistance to flow. Viscosity is a measure of this resistance to flow or shear. Viscosity can also be termed as a drag force and is a measure of the frictional properties of the fluid.Is viscosity high or low? ›
Fluids with low viscosity have a low resistance and shear easily and the molecules flow quickly; high viscosity fluids move sluggishly and resist deformation. Some liquids, like pitch, glass and peanut butter, have such high viscosity they behave like solids.What quantity is viscosity? ›
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.What matter is viscosity? ›
Viscosity is the measure of resistance of a fluid to flow. A fluid that is highly viscous has a high resistance (like having more friction) and flows slower than a low-viscosity fluid. To think of viscosity in everyday terms, the easier a fluid moves, the lower the viscosity.Is viscosity a flow rate? ›
A frequent question regarding peristaltic pumps is how viscosity affects flow rate. The short answer is; as viscosity increases, flow rates decrease. That being said, there are various factors which need to be understood when considering a peristaltic pump for any application that requires pumping viscous fluids.