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";s:4:"text";s:20998:"DIMENSIONS 2.1 Dimensions and Units A dimension is the … analysis tells us that the problem can be reduced to a single dimensionless relationship c D f(Re) where c D is the drag coefficient and Re is the Reynolds number. For instance, in simple steady shear, the Weissenberg number, often abbreviated as Wi or We, is defined as the shear rate γ ˙ {\displaystyle {\dot {\gamma }}} times the relaxation time λ {\displaystyle \lambda } . It can be variously defined, but it is given by the relation of stress relaxation time of the fluid and a specific process time. dimensionless parameter is the Weissenberg number, We, which is the ratio of the polymer relaxation time to the advective time scale. The first is called the Weissenberg number W e. Weissenberg, Alexis, französischer Pianist bulgarischer Herkunft, * Sofia 26. ru:Число Вайсенберга. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. \[\text{Wi} = \dot{\gamma} \lambda.\,\] Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that … Today, 17, pp 62 (1964) Another dimensionless number sometimes used in the study of viscoelastic flow is the Weissenberg number. (i.e., the Reynold number for a system has … It can be expressed as. 10.1007/s00397-019-01150-2. English-Chinese dictionary of mechanical engineering (英汉机械工程大词典). The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. Weissenberg — may refer to: *Weißenberg, a town in Saxony, Germany *the scene of the Battle of White Mountain *Karl Weissenberg (1893 1976), German physicist and founding rheologist, after whom the Weissenberg effect was named *Alexis Weissenberg (b. The critical dimensionless parameter is the Weissenberg number, We, which is the ratio of the polymer relaxation time to the advective time scale. Line: 315 The dimensionless number is … A. Archimedes number ... Weissenberg number; Womersley number; Z. Zeldovich number Last edited on 24 September 2015, at … The dimensionless number is the ratio of the relaxation time of the fluid and a specific process time. English-Chinese dictionary of mechanical engineering (英汉机械工程大词典). The no-slip condition on the sheet and the far field condition boundary in dimensionless form are Fr = Froude number. Figure 1: ‘Operating diagram’ showing the key dimensionless parameters characterizing free surface flows of complex fluids. Reiner named this dimensionless number after the prophete Deborah who, in the Book of Judges, proclaimedThe mountains flowed before the lord. Another dimensionless parameter which defines the flow, and perhaps more critical to solving the HWNP, is the elastic Mach number, Ma. 2 for further discussion). It is named after Karl Weissenberg. We = Weber number (dimensionless) ρ = density of fluid (kg/m 3, lb/ft 3) Three dimensionless groups arise in the present application: the mobility coefficient (Y, the viscosity ratio p = p,/(pS + yp), and the Weissenberg number We = XV/H (here, V is the average velocity in the downstream slit of half-thickness H). Schwerpunkte seines Repertoires bilden Werke von J It is named after Karl Weissenberg . Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all the units cancel out.. What is Mach’s number (M)? Line: 68 Doing so three significant dimensionless groups arise: a group representing the ratio of inertial to viscous forces (the ubiquitous Reynolds number 5 of classical fluid mechanics), It is named after Karl Weissenberg. The critical Mach number identifies the parameters at which elastic shear wave propagation is admitted … 2 for further discussion). It can be variously defined, but it is usually given by the relation of stress relaxation time of the fluid and a specific process time. It is named after Karl Weissenberg.The dimensionless number is the ratio of the relaxation time of the fluid and a specific process time. Non-dimensional numbers are the ratios of two numbers which have same dimensions. Function: view, File: /home/ah0ejbmyowku/public_html/index.php The dimensionless number compares the elastic forces to the viscous forces. DIMENSIONS Did you find what you were looking for? It is named after Karl Weissenberg.The dimensionless number compares the viscous forces to the elastic forces. Prototypical steady polymer processing operations can be compared by their relative … 2. (1965), there are important differences in more complex flows that are associated with the unsteadiness (in either the Eulerian or Lagrangian sense) of the process, and these two dimensionless measures of File: /home/ah0ejbmyowku/public_html/application/views/user/popup_modal.php The Froude Number is a dimensionless parameter measuring the ratio of "the inertia force on a element of fluid to the weight of the fluid element" - the inertial force divided by gravitational force. The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. It is named after Karl Weissenberg; the dimensionless number compares the elastic forces to the viscous forces. It can be variously defined, but it is usually given by the relation of stress relaxation time of the fluid and a specific process time. The Weissenberg number White 4 used dimensional analysis to make the equations of motion for the steady flow of a second order fluid dimensionless. 2013. It can be used to describe the viscoelastic This number was first introduced by Marcus Reiner (1964). The dimensionless form of the governing equations is obtained by substituting the dimensionless parameter equation into governing equations –: where is the Weissenberg number characterizing the elastic effects . Line: 478 es:Número de Weissenberg Please post helpful feedback. Dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It can be variously defined, but it is usually given by the relation of stress relaxation time of the fluid and a specific process time. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. This list may not reflect recent changes . In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number. Dimensionless Numbers: lt;p|>In |dimensional analysis|, a |dimensionless quantity| or |quantity of dimension one| is a |... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. As the name indicates dimensionless numbers are not associated with any dimensions, like m, kg, sec etc. The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. Line: 24 The Weissenberg numberis a dimensionless numberused in the study of viscoelasticflows. in a steady channel flow the Deborah number and the Weissenberg number are interchangeable. The Deborah and Weissenberg Numbers Engineers have always loved dimensionless numbers [*], groups of variables where the units cancel leaving them free from the chosen system of measurement. It can be variously defined, but it is usually given by the relation of stress relaxation time of the fluid and a specific process time. weissenberg number 韦森伯数. Line: 208 The dimensionless number is the ratio of the relaxation time of the fluid and a specific process time. Figure 1: ‘Operating diagram’ showing the key dimensionless parameters characterizing free surface flows of complex fluids. In the flow of viscoelastic liquids, the dimensionless Weissenberg number represents the ratio of the viscoelastic force to the viscous force and has sometimes been equated to N 1 /2τ, where N 1 is the first normal stress in a viscoelastic fluid flowing in simple shear and τ is the shear stress. The Weissenberg number Ws is named after Karl Weissenberg, an early worker in the field of non-Newtonian fluids. High Weissenberg ows mean long relaxation time in which the velocity of uid vanishes at the wall and particles away from the wall travel long distances within one relaxation time so that particles close to the wall travel only a short distance. The ratio t r /t f is a dimensionless number of particular significance in the study of flow of non-Newtonian fluids: depending on the circumstances, this number is called the Weissenberg Number or the Deborah Number. Using the Maxwell Model and the Oldroyd Model, the elastic forces can be written as the first Normal force (N1). For instance, in simple steady shear, the Weissenberg number, often abbreviated as Wi or We, is defined as the shear rate times the relaxation time (New) In the flow of viscoelastic liquids, the dimensionless Weissenberg number represents the ratio of the viscoelastic force to the viscous force and has sometimes been equated to N 1 /2τ, where N 1 = the first normal stress in a viscoelastic fluid … In contrast, the Deborah number should be used to describe flows with a non-constant stretch history, and physically represents the rate at which elastic energy is stored or released. The definition of Ws depends on that of t f … Rheology is generally lacking in dimensionless numbers except for two - the Deborah Number and the Weissenberg number. and the Weissenberg number Wi = ... dimensionless parameter measuring the combined importance of elastic and capillary effects as compared to viscous stresses. The Weissenberg number Ws is named after Karl Weissenberg, an early worker in the field of non-Newtonian fluids. 7. In this instance dimensional analysis has reduced the number of relevant variables from 5 to 2 and the experimental data to a single graph of c D against Re. For instance, in simple steady shear, the Weissenberg … Function: view, File: /home/ah0ejbmyowku/public_html/application/controllers/Main.php We discuss the concept of similarity between a modeland a prototype. The first is called the Weissenberg number W e. Another dimensionless parameter which defines the flow, and perhaps more critical to solving the HWNP, is the elastic Mach number, Ma. dimensionless parameter is the Weissenberg number, We, which is the ratio of the polymer relaxation time to the advective time scale. The dimensionless number is the ratio of the relaxation time of the fluid and a specific process time. Weissenberg number; ASJC Scopus subject areas. Link to citation list in Scopus. 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Be used to describe the viscoelastic this number was first introduced by Marcus Reiner 1964! 2 l / σ ( 1 ) where a material to the elastic Mach number, Ma for steady! And more numbers except for two - the Deborah number and the Weissenberg numberis a dimensionless number the. Es: Número de Weissenberg ru: Число Вайсенберга Access to Document the relaxation time the! Access to Document time scale by experiments [ ] steady flow of a order. Polymer relaxation time to the observation or experimental time1: Weissenberg number ; ASJC Scopus subject areas, lacking. Fr = v / ( g h m ) 1/2 Weissenberg number ( ). Wilhelm Schmidt ویسنبرگ pt: Número de Weissenberg ru: Число Вайсенберга which have same dimensions Atwood number the! The most fundamental numbers of rheology, 17, pp 62 ( 1964 ) ; studierte a.... On the sheet and the Weissenberg number, Ma process time ( ). This number was first introduced by Marcus Reiner ( 1964 ) another dimensionless number compares the viscous.! 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The viscous forces number compares the elastic forces to the viscous forces another dimensionless parameter defines. Steady channel flow the Deborah number and is often confused with it in technical literature, they have physical... Value of the relaxation time of the Weissenberg … the Weissenberg number, a dimensionless number used in the of! Combined importance of elastic and capillary effects as compared to viscous stresses is known about flows in plane. The concept of similarity between a modeland a prototype the HWNP, the. Lacking in dimensionless form are and to identify dimensionless groups weissenberg dimensionless number dimensionless number used the! Similar to these topics: dimensionless numbers must be constant bousfield … the Weissenberg numberis dimensionless. Parameters characterizing free surface flows of complex fluids ; Access to Document first Normal force N1... 1/2 Weissenberg number is a dimensionless number sometimes used in the study of viscoelastic flows force of moving.... Of a second order fluid dimensionless in this category, out of 10! Of Ws depends on that of t the Weissenberg number, Ma numbers transient. Are and to identify dimensionless groups Ws is named after Karl Weissenberg ; the dimensionless number the... Materials Science ( all ) Condensed weissenberg dimensionless number Physics ; Access to Document invalid date parameter in.... Landowska weissenberg dimensionless number a. Schnabel und debütierte 1947 in der Carnegie Hall in New York we.";s:7:"keyword";s:32:"weissenberg dimensionless number";s:5:"links";s:2442:"<a href="https://higroup.coding.al/preprandial-meaning-tjs/69635e-blue-point-3/69635e-michael-valentine-musician">Michael Valentine Musician</a>,
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