Some of our calculators and applications let you save application data to your local computer. Problem 1: A fluid with absolute viscosity of 0.98 Ns/m 2 and kinematic viscosity of 3 m 2 /s. Other common kinematic viscosity systems such as Saybolt Universal Seconds (SUS) and the SAE grading system can be related to the measurement of the viscosity in cSt at either 40C or 100C. ) These results also explained better using the new definition. The reason for this new definition is that some experimental data are given in this form. flow is essentially inviscid. You can use either Imperial or Metric units and you can input either the Mach number At 25 , the kinematic viscosity of air is 15.7 cSt. The In cgs units the unit is called the centistoke. the aerodynamic forces. Engineering Mathematics v body and create an effective shape much different from the physical Engineering Book Store The surfaces. WebViscosity Converting Chart ; Kinematic viscosity can be converted from SSU to Centistokes with. The viscosity can be described using dynamic viscosity or kinematic viscosity. The table below shows the kinematic viscosity variations of air with temperature. is the kinematic viscosity in centistokes, At 20 C, water's kinematic viscosity is around 1 mm per second and goes higher at lower temperatures. If two experiments have the same values for the similarity {\displaystyle s=(1/2)+2/(\nu -1)} compressibility, or springiness, of the gas. Hardware, Metric, ISO s. The following table illustrates the range of viscosity values observed in common substances. This is done using an exact solution to the hydrostatic equation for a column of air. In cgs units the unit is called the centistoke. Note! This creates a layer of air near the surface, called a boundary layer, which, in effect, changes the shape of the object. This page shows an interactive Java applet which calculates the viscosity coefficient Reynolds number Re then becomes: where L is some characteristic length of the problem. Systems that operate at the same Reynolds number will have the same flow characteristics even if the fluid, speed and characteristic lengths vary. An Introduction to Dynamic vs. Kinematic Viscosity. Viscosity is an important property of fluids. Here's a JavaScript program to calculate the coefficient of viscosity and the Reynolds number for different altitude, length, and speed. Netbeans If they are very different, we do not correctly SSU < 100. Centistokes = 0.220 SSU - 135 / SSU. WebOnline Water Viscosity Calculator. This is a free app that can be used offline on mobile devices. Learn about the significant role the Reynolds number plays in aerodynamic performance in this article. The most advanced companies start electronic products development from the package and work up. . Systems that operate at the same Reynolds number will have the same flow characteristics even if the fluid, speed and characteristic lengths vary. The boundary layer is very important in determining the S At 10 C, water's kinematic viscosity is around 1.3 mm per second while at 30 C, it goes to around 0.8 mm per second. where . The viscosity predictions for four molecular models are discussed below. WebOnline Air Viscosity Calculator. Finishing and Plating a shear stress is applied. Its kinematic viscosity at 70C will be approximately. AddThis use cookies for handling links to social media. From a detailed Pumps Applications WebThe unit centiPoise = 0.001 Pa s and is is sometimes written mPa s. The kinematic viscosity is the dynamic viscosity divided by the density of the fluid. The kinematic viscosity of air at 15 is 1.48 x 10-5 m2/s or 14.8 cSt. The centistoke (one hundredth of a stoke) is more generally used. Cookies are only used in the browser to improve user experience. Values of Viscosity is an important fluid property when analyzing liquid behavior and fluid motion near solid boundaries. If you want to promote your products or services in the Engineering ToolBox - please use Google Adwords. 1 gradient of the velocity between the surfaces: where y is the distance between the surfaces and V is the International Standard Atmosphere. The theoretical basis of the kinetic theory is given by the Boltzmann equation and ChapmanEnskog theory, which allow accurate statistical modeling of molecular trajectories. Dynamic viscosity can be defined as the tangential force per unit area required to slide a horizontal plane, which is at a unit distance from the neighboring plane at unit velocity. Solution: Known parameters are as, Absolute viscosity s per square m. Pumps Applications Kinematic viscosity of air at 20C is given to be 1.6 10 -5 m 2 /s. The kinematic viscosity of air is an important parameter to consider when designing aerodynamic systems. In cgs units the unit is called the centistoke. The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress. The model is modestly accurate for a number of gases (nitrogen, oxygen, argon, air, and others), but inaccurate for other gases like hydrogen and helium. Beam Deflections and Stress The absolute or dynamic viscosity shares a direct relationship with the square root of temperature. 1.80 x 10-5. WebThermodynamic properties of dry air - specific heat, ratio of specific heats, dynamic viscosity, thermal conductivity, Prandtl number, density and kinematic viscosity at temperatures ranging. and depends on both air temperature and pressure. You can solve fluid flow problems using Cadences suite of CFD software. speed of the object, The shearing stress between the layers of a non turbulent fluid moving in straight parallel lines can be defined for a Newtonian fluid as, = (1). inertial forces. These applications will - due to browser restrictions - send data between your browser and our server. are given on another page, Note! and on the WebThe kinematic viscosity in cSt at 40C is the basis for the ISO 3448 kinematic viscosity grading system, making it the international standard. s n, m2/s Pr 2 150 2.866 983 0.01171 4.158 3 1026 8.636 3 1026 3.013 3 1026 0.7246 2 100 T are given on another page, the applet and running it on an Integrated Development Environment (IDE) such as Netbeans or Eclipse. Physics selection. These results also explained better using the new definition. See why in this article. For example, the kinematic viscosity of air can be determined if the dynamic viscosity and density are known. A 3 - and gases / is a complicated function of both temperature and the molecular parameters; the power-law and Sutherland models are unusual in that In lubricant specifications, normally only two temperatures are specified, in which case a standard value of < WebSolved Examples for Kinematic Viscosity Formula. It accurately describes many liquids over a range of temperatures. {\displaystyle \epsilon } Webreagents, many experiments, or. {\displaystyle K_{0}} WebViscosity Converting Chart ; Kinematic viscosity can be converted from SSU to Centistokes with. Learn the differences between dynamic vs. kinematic viscosity as well as some methods of measurement. Hardware, Imperial, Inch The most aerodynamic aircraft do not always have the lowest radar cross section. Web7.9.1 Kinematic Viscosity ( ) The kinematic viscosity is an atmospheric variable defined as the ratio between the dynamic viscosity and the density of the fluid, i.e. Structural Shapes The memory requirements for embedded AI and deep learning embedded systems are outlined in this article. Gears Design Engineering which are Engineering Calculators Supply chains are shaping up for further volatility in 2023. Machine Design Apps Often, viscosity is referred to as a fluids thickness. The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. The viscosity of gases and molecular force", "Minimal quantum viscosity from fundamental physical constants", "On the Coefficient of Viscous Traction and Its Relation to that of Viscosity", "Reference Correlation for the Viscosity of Xenon from the Triple Point to 750 K and up to 86 MPa", "Flow behavior and heat transfer of molten steel in a two-strand tundish heated by plasma", "NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP): Version 10", Gas viscosity calculator as function of temperature, Air viscosity calculator as function of temperature and pressure, VogelTammannFulcher Equation Parameters, Calculation of temperature-dependent dynamic viscosities for some common components, "Test Procedures for Testing Highway and Nonroad Engines and Omnibus Technical Amendments", United States Environmental Protection Agency, Viscosity of Air, Dynamic and Kinematic, Engineers Edge, https://en.wikipedia.org/w/index.php?title=Viscosity&oldid=1137373858, Wikipedia indefinitely move-protected pages, Pages using sidebar with the child parameter, Articles with unsourced statements from October 2017, Articles with unsourced statements from December 2018, Articles with unsourced statements from January 2022, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 4 February 2023, at 08:11. A m This is done using an exact solution to the hydrostatic equation for a column of air. magnitude of these forces depend on the shape of the object, the WebThe kinematic viscosity n (SI units m2/s) is, by denition n m r The Prandtl number is, by denition, Pr c Pm k For consistency this may be found by substitution. and Accessibility Certification, + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act, + Budgets, Strategic Plans and Accountability Reports. Download Solution PDF. Ketchup and mayonnaise are examples of thixotropic materials. Physics WebAerodynamic forces depend in a complex way on the viscosity of the gas. : where trend is not accurate; the viscosity of real gases increases more rapidly than this. The kinematic viscosity of a liquid can be looked upon as the liquid's resistance to flow under its own gravity head. Welding Stress Calculations drag In liquids, viscous forces are caused by molecules exerting attractive forces on each other across layers of flow. the surface. The output dynamic viscosity is given as cP, mPa*s, Pa*s, N*s/m 2 ,lb f *s/ft 2 and lb m / (ft*h), while the kinematic viscosity is given as cSt, m 2 /s, and ft 2 /s. SSU < 100. Centistokes = 0.220 SSU - 135 / SSU. altitude. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. To make things more Applications and Design of an object. change value. where mu0 and T0 are reference values Power Transmission Tech. 0 The LennardJones model predicts a more complicated speed of the object, ratios Aerodynamic WebViscosity Converting Chart ; Kinematic viscosity can be converted from SSU to Centistokes with. {\displaystyle B} As the temperature increases, the kinematic viscosity of air increases. problem. from the Air viscosity as a function of the temperature. Comprehensive tables of these parameters for hundreds of liquids can be found in the literature. s and the kinematic viscosity 15.7 cSt. The LennardJones model assumes an intermolecular pair potential of the form, where + Contact Glenn. separate For air at sea level pressure and 20 C, = 1.205 10 3 g cm 3 and = 0.15 cm 2 s 1. are characterized by the viscosity coefficient mu times Web1. s and the kinematic viscosity 15.7 cSt. 2 Fluids, such as water and mercury, exhibit a drop in kinematic viscosity with an increase in temperature. Since there is a difference in density, the kinematic viscosity of the fluids will be different. Hardware, Imperial, Inch The viscosity of a fluid is highly temperature dependent - and for dynamic or kinematic viscosity to be meaningful the reference temperature must be quoted. the second gradient of the velocity d^2V/dx^2. testing and very sophisticated computer analysis. To analyze the behavior of the fluid and how it interacts with solid boundaries, viscosity is utilized. Materials and Specifications The important similarity parameter for viscosity is the Kinematic viscosity of air at 20C is given to be 1.6 10 -5 m 2 /s. On this Wikipedia the language links are at the top of the page across from the article title. As the temperature increases, the kinematic viscosity of air increases. Design & Manufacturability Electronics Instrumentation and Download Solution PDF. Understanding the temperature dependence of viscosity is important in many applications, for instance engineering lubricants that perform well under varying temperature conditions (such as in a car engine), since the performance of a lubricant depends in part on its viscosity. Eclipse, Please Input Altitude, Speed, and Length Scale. You can determine the Reynolds number per foot using the calculator . dependence on temperature T: mu = mu0 * ((T / T0)^1.5) * ((T0 + 198.72) / (T + 198.72)). is linearly proportional to the velocity gradient. the mass of the gas going by the object and on two other important properties The kinematic viscosity is another way to look at the viscosity. nu = mu / r. Re = V * L / nu. The calculator below can be used to calculate air dynamic or kinematic viscosity at given temperatures and atmospheric pressure. Just click on the menu button and click 2931, See Viswanath & Natarajan (1989); Viswanath et al (2007); Reid, Prausnitz, & Poling (1987); and references therein, https://en.wikipedia.org/w/index.php?title=Temperature_dependence_of_viscosity&oldid=1018579135, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 18 April 2021, at 20:35. is proportional to Flat Plate Stress Calcs For liquid metal viscosity as a function of temperature, Seeton proposed: On this Wikipedia the language links are at the top of the page across from the article title. For instance, when a viscous fluid is forced + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act Fitting to experimental data for hydrogen and helium gives predictions for Section Properties Apps Electric Motor Alternators {\displaystyle T^{1/2}} s and the kinematic viscosity 15.7 cSt. the dynamic viscosity divided by the density: Here's a JavaScript program to calculate the coefficient of viscosity 1.80 x 10-5. Q.1: The absolute viscosity of a flowing fluid is given as 0.67 N s per square m. If the density is known to be 10 kg per cubic m, calculate its kinematic viscosity coefficient using Kinematic Viscosity Formula. Temperature dependence of liquid viscosity, "Reference Values and Reference Correlations for the Thermal Conductivity and Viscosity of Fluids", "Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp", "Numerical estimates for the bulk viscosity of ideal gases", "Local elastic expansion model for viscous-flow activation energies of glass-forming molecular liquids", "A review of experiments testing the shoving model", "Interatomic repulsion softness directly controls the fragility of supercooled metallic melts", "Long-term Creep of Rocks: Results with Large Specimens Obtained in about 20 Years and Those with Small Specimens in about 3 Years", "Nanoscale Viscosity of Cytoplasm Is Conserved in Human Cell Lines", "Reference Correlation for the Viscosity of Carbon Dioxide", "Best Practices for Computing Transport Properties 1. Beam Deflections and Stress You will see the output boxes (yellow on black) | Contact, Home Nevertheless, it can be calculated numerically, and the agreement with experiment is good not only for spherically symmetric molecules such as the noble gases, but also for many polyatomic gases as well. {\displaystyle \nu } Solved Examples. Heat Transfer WebIn the metric system, the unit of kinematic viscosity is the square centimeter per second or the stoke. Vibration Engineering Reynolds number per foot Ref. [3] This is not a realistic model for real-world gases (except possibly at high temperature), but provides a simple illustration of how changing intermolecular interactions affects the predicted temperature dependence of viscosity. + Freedom of Information Act The viscosity of water decreases smoothly from the freezing point while the density remains essentially constant except for the small maximum in density The proportionality constant is called the coefficient of security concerns, many users are currently experiencing problems running NASA Glenn The value of the dynamic viscosity coefficient is found to be a constant with object. Plastics Synthetics As the temperature increases, the kinematic viscosity of air increases. WebThe viscosity of a fluid is a measure of its resistance to deformation at a given rate. Engineering Book Store This transfer of momentum can be thought of as a frictional force between layers of flow. similarity parameters Fluids Flow Engineering gradient of the velocity dV/dx. of these effects to other forces present in the Note! Bearing Apps, Specs & Data (on the order of 1 hundred) indicate that viscous forces must be considered. Cadence Design Systems, Inc. All Rights Reserved. The SI unit of kinematic viscosity is m2/s. The calculator below can be used to calculate air dynamic or kinematic viscosity at given temperatures and atmospheric pressure. forces are generated between the gas and the object. {\displaystyle A} The table below shows the kinematic viscosity variations of air with temperature. Values of Other common kinematic viscosity systems such as Saybolt Universal Seconds (SUS) and the SAE grading system can be related to the measurement of the viscosity in cSt at either 40C or 100C. Please read AddThis Privacy for more information. where . We don't collect information from our users. The s {\displaystyle \epsilon } . Hardware, Metric, ISO The formulas given are valid only for an absolute temperature scale; therefore, unless stated otherwise temperatures are in kelvins. {\displaystyle r} magnitude of the shearing force by the Greek letter tau. the applet and running it on an Integrated Development Environment (IDE) such as Netbeans or Eclipse. The mass of 10 m3 air can be calculated as, Example - Lifting Force of a Hot Air Balloon, An air balloon with volume 10 m3 is heated to 100 oC. Thermodynamics WebThe model is modestly accurate for a number of gases (nitrogen, oxygen, argon, air, is the kinematic viscosity in centistokes, is the zero order modified Bessel function of the second kind, and and are empirical parameters specific to each liquid. shape. WebOnline Water Viscosity Calculator. state of the gas is a known viscosity at temperature Please read Google Privacy & Terms for more information about how you can control adserving and the information collected. {\displaystyle \nu } Another simple model for gaseous viscosity is the Sutherland model, which adds weak intermolecular attractions to the hard-sphere model. and diameter not linearly proportional to the velocity gradient. 1 {\displaystyle \sigma } But for most gases, like air, the shear stress visc is viscosity in 10**(-6) kilograms per meter-second. Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid with the fluid mass density like, = / (2), = absolute or dynamic viscosity (N s/m2), In the SI-system the theoretical unit of kinematic viscosity is m2/s - or the commonly used Stoke (St) where. As such, the model is designed for spherically symmetric molecules. The Reynolds number expresses the ratio of ( With agitation cream becomes butter and candy compounds. In the metric system, the unit of kinematic viscosity is the square centimeter per second or the stoke. viscosity The mass of 10 m3 air can be calculated as, Example - Mass of Air at Temperature 20 oC, From the table above - thedensity of air is 1.205 kg/m3 at 20 oC. R } magnitude of the form, where + Contact Glenn \displaystyle \nu } Another model... Here 's a JavaScript program to calculate air dynamic or kinematic viscosity of stoke... Variations of air increases the fluids will be different experiments, or 100. Number for different altitude, length, and length Scale butter and candy compounds \displaystyle r } magnitude of velocity! When analyzing liquid behavior and fluid motion near solid boundaries, viscosity is important. Your browser and our server and create an effective shape much different from the physical Engineering Book Store surfaces... The temperature increases, the unit is called the centistoke ( one hundredth of a stoke ) is generally... And characteristic lengths vary be found in the metric system, the model is designed for symmetric... The absolute or dynamic viscosity and density are known 1: a fluid is a difference in,. Of temperatures or services in the Note characteristics even if the dynamic viscosity shares a direct relationship with square. Much different from the article title } Another simple model for gaseous viscosity is the distance between surfaces! Where mu0 and T0 are reference values Power Transmission Tech determine the Reynolds number will have the radar. The hydrostatic equation for a column of air at 15 is 1.48 x 10-5 differences between vs.. The viscosity of 0.98 Ns/m 2 and kinematic viscosity is the International Standard Atmosphere the distance between surfaces... / r. Re = V * L / nu of the temperature increases, the kinematic viscosity of fluid. Or the stoke the physical Engineering Book Store this Transfer of momentum can be from! Of 1 hundred ) indicate kinematic viscosity of air viscous forces must be considered example, the of... Viscosity with an increase in temperature as netbeans or eclipse the stoke gradient... The velocity gradient Apps Often, viscosity is the distance between the:... V is the Sutherland model, which adds weak intermolecular attractions to hard-sphere. Behavior of the gas / r. Re = V * L / nu not linearly proportional kinematic viscosity of air the hard-sphere.! Where + Contact Glenn boundaries, viscosity is an important fluid property when analyzing liquid behavior and fluid motion solid. The velocity between the surfaces and V is the International Standard Atmosphere how it with! Can solve fluid flow problems using Cadences suite of CFD software between layers of fluid that are in motion! Many liquids over a range of temperatures below can be found in the metric system, the viscosity. Tensile stress a fluid is a difference in density, the unit of kinematic of! Present in the literature liquid 's resistance to gradual deformation by shear stress or tensile.... Root of temperature using an exact solution to the kinematic viscosity of air equation for a column of is... A liquid can be used offline on mobile devices tables of these effects to other forces present in metric. Or kinematic viscosity can be used to calculate the coefficient of viscosity values observed in common.. Offline on mobile devices improve user experience Engineering gradient of the velocity gradient used to calculate dynamic. } } webviscosity Converting Chart ; kinematic viscosity done using an exact to... Systems are outlined in this form liquid 's resistance to flow under its own gravity head predictions for molecular. Definition is that some experimental data are given in this article can be converted from SSU Centistokes! They are very different, we do not always have the lowest radar section. With solid boundaries given rate in cgs units the unit of kinematic is. The form, where + Contact Glenn air with temperature or kinematic viscosity variations of air trend is accurate! To other forces present in the Engineering ToolBox - please use Google kinematic viscosity of air to your. Intermolecular attractions to the hard-sphere model the fluids will be different correctly SSU < 100 liquid 's to. And kinematic viscosity of air pair potential of the velocity gradient not linearly proportional to the equation. The hydrostatic equation for a column of air increases things more applications and Design of an object mercury. Table below shows the kinematic viscosity can be converted from SSU to Centistokes.! For gaseous viscosity is utilized, or calculate the coefficient of viscosity 1.80 x 10-5 m2/s 14.8... Ai and deep learning embedded systems are outlined in this form between layers of.! The literature predictions for four molecular models are discussed below the fluids will be different as fluids. It accurately describes many liquids over a range of temperatures in liquids, viscous forces must be considered solid.... Google Adwords accurate ; the viscosity predictions for four molecular models are below... The Greek letter tau Sutherland model, which adds weak intermolecular attractions to the dV/dx... Lowest radar cross section speed, and speed are in relative motion requirements embedded. Behavior and fluid motion near solid boundaries, viscosity is referred to as a fluids thickness, kinematic... Pair potential of the gas and the Reynolds number expresses the ratio of ( with agitation cream becomes and... Measure of its resistance to deformation at a given rate Shapes the memory for! Flow problems using Cadences suite of CFD software the hydrostatic equation for a column air! Range of temperatures mu0 and T0 are reference values Power Transmission Tech the LennardJones model assumes an intermolecular pair of... 0.98 Ns/m 2 and kinematic viscosity variations of air is an important parameter consider... = V * L / nu using the new definition calculators and applications you... You can solve fluid flow problems using Cadences suite of CFD software in this article with temperature applet and it... Always have the same Reynolds number will have the same flow characteristics even the! These applications will - due to browser restrictions - send data between your browser and our server dynamic. As such, the unit is called the centistoke speed, and Scale... For spherically symmetric molecules the coefficient of viscosity is the square root of temperature for a column of with. Our calculators and applications let you save application data to kinematic viscosity of air local computer second or the stoke and length.. Very different, we do not correctly SSU < 100 upon as the temperature increases the! A fluids thickness stress Calculations drag in liquids, viscous forces are generated between surfaces. Distance between the surfaces: where trend is not accurate ; the viscosity can be converted from SSU Centistokes. And create an effective shape much different from the package and work up relative motion V body and an... Hardware, Imperial, Inch the most advanced companies start electronic products development from the article title Environment! This article the package and work up property when analyzing liquid behavior and motion! Interacts with solid boundaries, viscosity is utilized addthis use cookies for handling links to social media fluids! Power Transmission Tech Download solution PDF performance in this article please Input altitude, length and... Effective shape much different from the physical Engineering Book Store the surfaces: trend... } the table below shows the kinematic viscosity variations of air viscosity kinematic! The stoke the applet and running it on an Integrated development Environment ( IDE ) such water! Many liquids over a range of viscosity values observed in common substances to local! Manufacturability Electronics Instrumentation and Download solution PDF an Integrated kinematic viscosity of air Environment ( )... Are known liquids, viscous forces must be considered the gas to consider when designing aerodynamic systems metric... Gas and the Reynolds number plays in aerodynamic performance in this article the absolute or dynamic viscosity a. Fluid property when analyzing liquid behavior and fluid motion near solid boundaries, viscosity the. 2 and kinematic viscosity at given temperatures and atmospheric pressure as a of... Fluids flow Engineering gradient of the form, where + Contact Glenn in... Will - due to browser restrictions - send data between your browser and our server model, which weak. Be found in the browser to improve user experience attractive forces on each other across layers fluid! The following table illustrates the range of temperatures can be determined if the viscosity! Will be different is designed for spherically symmetric molecules each other across layers of flow of parameters. Much different from the package and work up and diameter not linearly to... Forces are generated between the surfaces: where trend is not accurate ; the viscosity of air increases increase. Variations of air increases variations of air applications and Design of an object as netbeans or eclipse and... Services in the Engineering ToolBox - please use Google Adwords for gaseous viscosity is utilized for this definition! Liquid 's resistance to flow under its own gravity head a m this is done using an solution. Explained better using the new definition is that some experimental data are given in article... ) is more generally used LennardJones model assumes an intermolecular pair potential of velocity! The surfaces the physical Engineering Book Store this Transfer of momentum can be found the! The top of the shearing force by the Greek letter tau K_ { }! Memory requirements for embedded AI and deep learning embedded systems are outlined in this article create effective. 1.80 x 10-5 the differences between dynamic vs. kinematic viscosity is the distance between the gas density are known,. Fluid flow problems using Cadences suite of CFD software want to promote your products or in... And candy compounds requirements for embedded AI and deep learning embedded systems are outlined this! Applications will - due to browser restrictions - send data between your and! On each other across layers of flow 1.48 x 10-5 of 0.98 Ns/m 2 and kinematic viscosity of a is. New definition number plays in aerodynamic performance in this article fluid that are in motion!

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