On dimensional analysis

Gibbings, J.C.

doi:10.1088/0305-4470/13/1/010

Cited by 29 publications

(23 citation statements)

References 7 publications

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“…and, from expression (5), since c v is constant we have c v = k o σ o (1+e o ) ln (10) I c γ w , finally obtaining:…”

Section: Davis and Raymond Proposed Modelmentioning

confidence: 88%

“…In each case, the value of one or more of the parameters involved has been significantly altered, but the numerical value of the dimensionless groups has been retained so that it is verified that the same pattern of solutions is obtained for the whole set of cases; or the value of the groups has been modified appropriately to confirm that the form of the solutions changes. As a deduction technique for these groups, the nondimensionalization of governing equations [8][9][10] has been used, a form of application of the pi theorem [11], thus allowing the dimensionless parameters involved in the problem (void ratio and compression index), and that they would form independent dimensionless groups, to be included in the inferred groups. In the nondimensionalization process, which has been carried out in terms of both excess pore pressure dissipation and settlement, the characteristic time of consolidation is introduced as a reference, an unknown that is incorporated into one of the resulting monomials and whose dependency with the rest of the groups is established by the pi theorem.…”

Section: Introductionmentioning

confidence: 99%

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Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

García‐Ros

Alhama

2019

Applied Mathematics and Nonlinear Sciences

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The dimensionless groups that govern the Davis and Raymond non-linear consolidation model, and its extended versions resulting from eliminating several restrictive hypotheses, were deduced. By means of the governing equations nondimensionalization technique and introducing the characteristic time concept, both in terms of settlement and pressures, was obtained (for the most general model) that the average degree of settlement only depends on the dimensionless time while the average degree of pressure dissipation does it, additionally, on the loading ratio. These results allowed the construction of universal curves expressing the solutions of the unknowns of interest in a direct and simple way.

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“…and, from expression (5), since c v is constant we have c v = k o σ o (1+e o ) ln (10) I c γ w , finally obtaining:…”

Section: Davis and Raymond Proposed Modelmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

García‐Ros

Alhama

2019

Applied Mathematics and Nonlinear Sciences

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“…Thus ∆ can be written as a function of , , , , , , , , particle shape and adhesion i.e. or (∆ , , , , , , , , , ℎ , ℎ )=0 (2) Following the Buckingham Π theorem [36] used in dimensional analysis, by taking , and as independent variables, three dimensionless groups can be formed as follows: -50mm PH101-75mm PH101-100mm PH102-50mm PH102-75mm PH102-100mm PH200-50mm PH200-75mm PH200-100mm PH302-50mm PH302-75mm PH302-100mm…”

Section: Dimensional Analysismentioning

confidence: 99%

Vacuum assisted flow initiation in arching powders

2016

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Graphical abstract Highlights• Vacuum applied at the exit of an arching hopper assists flow initiation.• A small reduction of pressure changes the critical orifice diameter significantly.• A dimensional model was developed to predict the pressure required to initiate flow. 2 AbstractThe discharge of powders from hoppers usually takes place in open atmosphere. However, in powder pressing industries (e.g. manufacturing of pharmaceutical tablets, detergents, ceramics, powder metallurgy etc.) there are handling operations where powders are filled into closed cavities such as dies. During this process the air pressure is increased as powder is delivered into the die. At the same time typical tablet production equipment creates a suction effect. A critical orifice measurement apparatus was developed to study powder flow initiation from an arching state into an enclosure where the air pressure is reduced. It was shown that a very small reduction of pressure changed the critical orifice diameter significantly. Dimensional analysis was carried out to relate powder properties (particle size and density) and processing parameters (geometry of the system and differential pressure necessary to break the arch). A relationship was developed to calculate the pressure difference necessary to initiate powder flow. The relationship has two empirical parameters which are calibrated by performing simple experiments using the testing rig developed.

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“…The first ideas forecasting the method of dimensional analysis came from Fourier, who proposed the term dimensional homogeneity of physical equations in 1822 (Gibbings, 2011;Tan, 2011). The first person to apply these ideas was Lord Rayleigh in a series of his papers published in the 70s and 80s of the 19th century; his research particularly concerned the processes of fluid flow.…”

Section: Introductionmentioning

confidence: 99%

Perspective of Dimensional Analysis in Medical Science

Kowalewski

Roszak

Kołodziejczak

et al. 2017

Studies in Logic, Grammar and Rhetoric

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Abstract. This paper presents several applications of the dimensional analysis method to problems investigated in medical sciences. The method is used to analyze various complex processes without using formal laws governing the same. It is particularly suitable for a general analysis of fluid transfer (liquids and gases) in the human body. This paper mainly serves as an overview of selected applications, mostly those emerging in the recent years, and includes a discussion of the mathematical fundamentals of dimensional analysis together followed by its critical analysis. Containing detailed calculations of two examples, the paper also serves as training material in the area of the computational method of the dimensional analysis algorithm.

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On dimensional analysis

Cited by 29 publications

References 7 publications

Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

Vacuum assisted flow initiation in arching powders

Perspective of Dimensional Analysis in Medical Science

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