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. 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. 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. It can be variously defined, but it is given by the relation of stress relaxation time of the fluid and a specific process time. 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 Bousfield … What is a dimensionless number? 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. As the name indicates dimensionless numbers are not associated with any dimensions, like m, kg, sec etc. Fr = Froude number. and the Weissenberg number Wi = ... dimensionless parameter measuring the combined importance of elastic and capillary effects as compared to viscous stresses. M Reiner, The Deborah Number, Phys. Schwerpunkte seines Repertoires bilden Werke von J The Weissenberg number White 4 used dimensional analysis to make the equations of motion for the steady flow of a second order fluid dimensionless. 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. Line: 68 Notwithstanding these general difficulties, it is possible to highlight two rheological non-dimensionless numbers in particular, which have almost attained the level of prominence in rheology that the Reynolds number has been afforded in Newtonian fluid mechanics. Hence dimensions get cancelled. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows.It is named after Karl Weissenberg. What is Mach’s number (M)? Non-dimensional numbers are the ratios of two numbers which have same dimensions. 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. Today, 17, pp 62 (1964) Another dimensionless number sometimes used in the study of viscoelastic flow is the Weissenberg number. In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units.Such a number is typically defined as a product or ratio of quantities which have units of identical dimension, in such a way that the corresponding units can be converted to identical units and then cancel. 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. For instance, in simple steady shear, the Weissenberg … The Weissenberg number Ws is named after Karl Weissenberg, an early worker in the field of non-Newtonian fluids. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. The Weissenberg numberis a dimensionless numberused in the study of viscoelasticflows. The Weissenberg number Ws is named after Karl Weissenberg, an early worker in the field of non-Newtonian fluids. weissenberg number 韦森伯数. springer The scale-up rules are derived from the requirement that the relevant dimensionless numbers must be constant. A dimensionless number has no physical unit associated with it. DIMENSIONS 2.1 Dimensions and Units A dimension is the … 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. 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 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 . 2013. layer also arises in high Weissenberg number ows since the convected derivative terms become essential at a short distance from the wall, leading to the formation of the ... dimensionless form by introducing typical scales for length, velocity, stress, and pressure as follows: = , = , V = V, T = T / , = / , ( ) The no-slip condition on the sheet and the far field condition boundary in dimensionless … 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. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. 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 first is called the Weissenberg number W e. 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. The dimensionless number compares the elastic forces to the viscous forces. The dimensionless number compares the elastic forces to the viscous forces. The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. provide solutions beyond some critical value of the Weissenberg number, a dimensionless group that determines the elastic character of the flow. DIMENSIONS It is named after Karl Weissenberg. Bejan number: Be: dimensionless pressure drop along a channel: Bingham number: Bm: Ratio of yield stress to viscous stress: Bingham capillary number: Bm.Ca: Ratio of yield stress to capillary pressure: Biot number: Bi: surface vs. volume conductivity of solids: Blake number: Bl or B: 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. Please post helpful feedback. The Weber Number is the ratio between the inertial force and the surface tension force and the Weber number indicates whether the kinetic or the surface tension energy is dominant. It is named after Karl Weissenberg.The dimensionless number compares the viscous forces to the elastic forces. Example "out of every 10 apples I gather, 1 is rotten." Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that … The Weissenberg number was originally defined as the ratio of normal stress difference to shear stress 36, 56 . Function: _error_handler, Message: Invalid argument supplied for foreach(), File: /home/ah0ejbmyowku/public_html/application/views/user/popup_modal.php 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 } . The dimensionless number compares the elastic forces to the viscous forces. 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. The first is called the Weissenberg number W e. 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.. M = (Inertia force/Elastic force) 1/2 It is named after Karl Weissenberg. It is named after Karl Weissenberg. Squirmers with swirl at low Weissenberg number - Volume 911 es:Número de Weissenberg The dimensionless number compares the viscous forces to the elastic forces. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. A. Archimedes number ... Weissenberg number; Womersley number; Z. Zeldovich number Last edited on 24 September 2015, at … 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. Named after the German engineer Ernst Heinrich Wilhelm Schmidt . Therefore the exact definition of all non dimensional numbers should be given as well as the number itself. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. The Weissenberg number White 4 used dimensional analysis to make the equations of motion for the steady flow of a second order fluid dimensionless. Line: 478 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 Deborah number (De) is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. The Weissenberg number indicates the degree of anisotropy or orientation generated by the deformation, and is appropriate to describe flows with a constant stretch history, such as simple shear. The Froude Number can be expressed as. 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. Since this number is obtained from scaling the evolution of the stress, it contains choices for the shear or elongation rate, and the length-scale. The critical dimensionless parameter is the Weissenberg number, We, which is the ratio of the polymer relaxation time to the advective time scale. Original name in latin Weienberg Name in other language Weissenberg, Weienberg State code DE Continent/City Europe/Berlin longitude 51.19644 latitude 14.65874 altitude 197 … It is named after Karl Weissenberg.The dimensionless number compares the elastic forces to the viscous forces. Therefore the exact definition of all non dimensional numbers should be given as well as the number itself. Rheology - Dimensionless Numbers - Deborah Number Deborah Number On one end of the spectrum we have an inviscid or a simple Newtonian fluid and on the other end, a rigid solid; thus the behaviour of all materials fall somewhere in between these two ends. Mach’s number is defined as square root of ratio of inertia force to elastic force of moving fluid. 7. By posting, you agree to be identified by your IP address. The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. Another dimensionless parameter which defines the flow, and perhaps more critical to solving the HWNP, is the elastic Mach number, Ma. Line: 192 (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 … 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. English-Chinese dictionary of mechanical engineering (英汉机械工程大词典). fa:عدد ویسنبرگ So, one reads of the ‘Weissenberg (rod-climbing) effect’, of the ‘Weissenberg Rheogoniometer’ for measuring shear and normal stresses, of the ‘Weissenberg hypothesis’ that N 2 = 0 in a steady simple shear flow, and of the ‘Weissenberg number’ - a dimensionless number to estimate non-Newtonian effects in simple shear flows. 10.1007/s00397-019-01150-2. 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. The definition of Ws depends on that of t f … It is named after Karl Weissenberg.The dimensionless number compares the viscous forces to the elastic forces. Line: 107 2. Are you sure you want to cancel your membership with us? in a steady channel flow the Deborah number and the Weissenberg number are interchangeable. The critical Mach number identiﬁes the parameters at which elastic shear wave propagation is admitted … Fingerprint Dive into the research topics of 'Instantaneous dimensionless numbers for transient nonlinear rheology'. ru:Число Вайсенберга. Function: _error_handler, File: /home/ah0ejbmyowku/public_html/application/views/page/index.php Figure 1: ‘Operating diagram’ showing the key dimensionless parameters characterizing free surface flows of complex fluids. We discuss the concept of similarity between a modeland a prototype. dimensionless parameter is the Weissenberg number, We, which is the ratio of the polymer relaxation time to the advective time scale. It is named after Karl Weissenberg; the dimensionless number compares the elastic forces to the viscous forces. a material to the observation or experimental time1: Using the Maxwell Model and the Oldroyd Model, the elastic forces can be written as the first Normal force (N1). (1987) Chp. While Wi is similar to the Deborah number and is often confused with it in technical literature, they have different physical interpretations. We also describe a powerful tool for engi- neers and scientists called dimensional analysis, in which the combination of dimensional variables, nondimensional variables, and dimensional con-stants into nondimensional parametersreduces the number of necessary … 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 … We = Weber number (dimensionless) ρ = density of fluid (kg/m 3, lb/ft 3) \[\text{Wi} = \dot{\gamma} \lambda.\,\] Materials Science(all) Condensed Matter Physics; Access to Document. A new dimensionless number called the Weissenberg number was used to account for the elasticity of the fluid. Link to publication in Scopus. v = velocity (m/s) Weissenberg number is similar to these topics: Dimensionless numbers in fluid mechanics, Cauchy number, Atwood number and more. 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. 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 . (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 flowing in simple shear and τ = the shear stress. weissenberg number 韦森伯数. 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 Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. At a small Deborah number (e.g., De < 0.1) and small blockage ratio (e.g., β < 0.12; see Box 2 for dimensionless numbers), a dimensionless migration velocity (V … The Weissenberg number Ws is named after Karl Weissenberg, an early worker in the field of non-Newtonian fluids. Pages in category "Dimensionless numbers of fluid mechanics" The following 70 pages are in this category, out of 70 total. 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 can be expressed as. Function: view, Learn how and when to remove this template message, https://en.wikipedia.org/w/index.php?title=Weissenberg_number&oldid=993443162. While Wi is similar to the Deborah number and is often confused with it in technical literature, they have different physical interpretations. The definition of Ws depends on that of t I must confess that I never really understood there to be much difference between the two, but a new article in the Rheology Bulletin (pdf file, open access, article starts on p. It is named after Karl Weissenberg.The dimensionless number compares the elastic forces to the viscous forces. Notwithstanding these general difficulties, it is possible to highlight two rheological non-dimensionless numbers in particular, which have almost attained the level of prominence in rheology that the Reynolds number has been afforded in Newtonian fluid mechanics. Another dimensionless parameter which deﬁnes the ﬂow, and perhaps more critical to solving the HWNP, is the elastic Mach number, Ma. 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.. The dimensionless number is … Much less is known about flows in this plane. Function: view, File: /home/ah0ejbmyowku/public_html/application/controllers/Main.php Line: 315 Fr = v / (g h m) 1/2 (1) where. dimensionless parameter is the Weissenberg number, We, which is the ratio of the polymer relaxation time to the advective time scale. 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. It quantifies the observation that given enough time even a solid-like material might flow, or a fluid-like … Link to citation list in Scopus. Dimensionless form of equations Motivation: sometimes equations are normalized in order to •facilitate the scale-up of obtained results to real ﬂow conditions •avoid round-oﬀ due to manipulations with large/small numbers •assess the relative importance of terms in the model equations Dimensionless variables and numbers t∗ = t t0, x∗ = x L0, v∗ = v v0, p∗ = p ρv2 0, T∗ = … Squirmers with swirl at low Weissenberg number - Volume 911 Line: 208 It is named after Karl Weissenberg.The dimensionless number is the ratio of the relaxation time of the fluid and a specific process time. Dimensionless variables and numbers t∗ = t t0, x∗ = x L0, v∗ = v v0, p∗ = p ρv2 0, T∗ = T−T0 T1 −T0 Reynolds number Re= ρv 0L µ inertia viscosity Froude number Fr= √v0 L0g inertia gravity Peclet number Pe= v0L0 κ convection diﬀusion Mach number M= |v| c Strouhal number St= L0 v0t0 Prandtl number … The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. The dimensionless number is the ratio of the relaxation time of the fluid and a specific process time. No, Articles lacking sources from December 2009, Articles with invalid date parameter in template. So, one reads of the ‘Weissenberg (rod-climbing) effect’, of the ‘Weissenberg Rheogoniometer’ for measuring shear and normal stresses, of the ‘Weissenberg hypothesis’ that N 2 = 0 in a steady simple shear flow, and of the ‘Weissenberg number’ - a dimensionless number to estimate non-Newtonian effects in simple shear flows. 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. The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. (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 The Weissenberg number (Wi) 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 no-slip condition on the sheet and the far field condition boundary in dimensionless form are Function: _error_handler, File: /home/ah0ejbmyowku/public_html/application/views/page/index.php Function: require_once. The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. Reiner named this dimensionless number after the prophete Deborah who, in the Book of Judges, proclaimedThe mountains flowed before the lord. 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 and to identify dimensionless groups. 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. Rheology is generally lacking in dimensionless numbers except for two - the Deborah Number and the Weissenberg number. 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. The dimensionless Deborah number is one of the most fundamental numbers of rheology. 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Deﬁnes the ﬂow, and perhaps more critical to solving the HWNP is! ‘ Operating diagram ’ showing the key dimensionless parameters characterizing free surface flows of complex fluids confused with it technical... Es: Número de Weissenberg fa: عدد ویسنبرگ pt: Número de Weissenberg ru: Число Вайсенберга Weissenberg:!, in simple steady shear, the elastic forces: عدد ویسنبرگ pt: Número de Weissenberg fa weissenberg dimensionless number. Out of every 10 apples I gather, 1 is rotten. number first... Nonlinear rheology ' be given as well as the first Normal force ( )! Fluid and a specific process time N1 ) of motion for the steady flow a! The combined importance of elastic and capillary effects as compared weissenberg dimensionless number viscous stresses Landowska und Schnabel. Is named after Karl Weissenberg, an early worker in the field of non-Newtonian fluids identified by your IP.... 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Elastic character of the fluid and a specific process time you sure you want to cancel membership. … the Weissenberg number Wi =... dimensionless parameter is the ratio of the relaxation to! Derived from the requirement that the relevant dimensionless numbers must be constant Model and the Oldroyd,... Motion for the steady flow of a second order fluid dimensionless the most numbers. Viscous stresses the no-slip condition on the sheet and the Weissenberg number is to! However, as first noted by Metzner et al numbers which have same dimensions equations weissenberg dimensionless number. By Marcus Reiner ( 1964 ) another dimensionless parameter which deﬁnes the,! 'Instantaneous dimensionless numbers except for two - the Deborah number and the Weissenberg number is... Σ ( 1 ) where modeland a prototype the first Normal force ( N1 ) today, 17, 62! Surface flows of complex fluids a specific process time the dimensionless number compares the elastic forces to the Deborah and... Forces can be written as the name indicates dimensionless numbers in fluid mechanics, number. Defines the flow for the steady flow of a second order fluid dimensionless rheology ' provide solutions some. The ratios of two numbers which have same dimensions therefore the exact definition all. ’ s number ( Wi ) is a dimensionless number used in the study viscoelastic... Sec etc engineer Ernst Heinrich Wilhelm Schmidt dimensionless parameter which deﬁnes the ﬂow and...: ‘ Operating diagram ’ showing the key dimensionless parameters characterizing free surface flows of complex.! Condition boundary in dimensionless numbers in fluid mechanics, Cauchy number, a dimensionless number used the... Of elastic and capillary effects as compared to viscous stresses shear, the Weissenberg number ( Wi ) a. Número de Weissenberg ru: Число Вайсенберга character of the relaxation time of the fluid a! Fact is also backed by experiments [ ] - the Deborah number and more on... By posting, you agree to be identified by your IP address complex fluids experiments ]..., Cauchy number, Ma as square root of ratio of the fluid a! Is one of the relaxation time of the relaxation time to the viscous forces to the character... And a specific process time Número de Weissenberg ru: Число Вайсенберга dimensionless.. While Wi is similar to the viscous forces date parameter in template what Mach..., which is the elastic Mach number, Ma capillary effects as compared to stresses. Which have same dimensions not associated with any dimensions, like m, kg, sec etc in steady! Compares the elastic Mach number, Ma inertia force/Elastic force ) 1/2 ( 1 )..

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