scholarly journals The influence of vortices upon the resitance experienced by solids moving through a liquid

1928 ◽  
Vol 119 (781) ◽  
pp. 146-156 ◽  
Keyword(s):  
Perfect Fluid ◽  
Relative Motion ◽  
Constant Velocity ◽  
Fluid Motion ◽  
Resultant Force ◽  
The Other ◽  
Two Dimensional ◽  
Perfect Fluids ◽  
Potential Problems ◽  
The Moment

(1) It is not so long ago that it was generally believed that the "classical" hydrodynamics, as dealing with perfect fluids, was, by reason of the very limitations implied in the term "perfect," incapable of explaining many of the observed facts of fluid motion. The paradox of d'Alembert, that a solid moving through a liquid with constant velocity experienced no resultant force, was in direct contradiction with the observed facts, and, among other things, made the lift on an aeroplane wing as difficult to explain as the drag. The work of Lanchester and Prandtl, however, showed that lift could be explained if there was "circulation" round the aerofoil. Of course, in a truly perfect fluid, this circulation could not be produced—it does need viscosity to originate it—but once produced, the lift follows from the theory appropriate to perfect fluids. It has thus been found possible to explain and calculate lift by means of the classical theory, viscosity only playing a significant part in the close neighbourhood ("grenzchicht") of the solid. It is proposed to show, in the present paper, how the presence of vortices in the fluid may cause a force to act on the solid, with a component in the line of motion, and so, at least partially, explain drag. It has long been realised that a body moving through a fluid sets up a train of eddies. The formation of these needs a supply of energy, ultimately dissipated by viscosity, which qualitatively explains the resistance experienced by the solid. It will be shown that the effect of these eddies is not confined to the moment of their birth, but that, so long as they exist, the resultant of the pressure on the solid does not vanish. This idea is not absolutely new; it appears in a recent paper by W. Müller. Müller uses some results due to M. Lagally, who calculates the resultant force on an immersed solid for a general fluid motion. The result, as far as it concerns vortices, contains their velocities relative to the solid. Despite this, the term — ½ ρq 2 only was used in the pressure equation, although the other term, ρ ∂Φ / ∂t , must exist on account of the motion. (There is, by Lagally's formulæ, no force without relative motion.) The analysis in the present paper was undertaken partly to supply this omission and partly to check the result of some work upon two-dimensional potential problems in general that it is hoped to publish shortly.

scholarly journals On the two-dimensional steady flow of a viscous fluid behind a solid body.―I

1933 ◽  
Vol 142 (847) ◽  
pp. 545-562 ◽  
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Velocity Distribution ◽  
Asymptotic Approximation ◽  
Constant Velocity ◽  
Boundary Layer Theory ◽  
The Other ◽  
Main Stream ◽  
Two Dimensional ◽  
Prandtl Equations

1.1. The purpose of this paper is to exhibit, for reasons given below, calculations of the velocity distribution some distance downstream behind any symmetrical obstacle in a stream of viscous fluid, but particularly behind an infinitely thin plate parallel to the stream, the motion being two-dimensional. For a slightly viscous fluid, Blasius worked out the velocity distribution in the boundary layer from the front to the downstream end of the plate; and in a previous paper, I calculated the velocity in the wake for a distance varying from 0.3645 to 0.5 of the length of the plate from its downstream end (according to distance from its plane). In these calculations the fluid was supposed unlimited, and the undisturbed velocity in front of the plate was taken as constant. The viscosity being assumed small, the work was carried out on the basis of Pranstl's boundary layer theory, with zero pressure gradient in the direction of the stream. The velocity is then constant everywhere expect within a thin layer near the plate, and in a wake which must gradually broaden out downstream. (The broadening of the wake just behind the plate is so gradual that it could not be shown by calculations of the accuracy obtained in I). Pressure variations in a direction at right angles to the stream are negligible, and so is the velocity in that direction. Later, Tollmien attcked the problem from the other end, and found a first asymptotic approximation for the velocity distribution in the wake at a considerable distance downstream. He simplified the Prandtl equations by assuming that the departure from the constant velocity, U 0 , of the main stream is small, and neglecting terms quadratic in this departure. In other words, he applied the notion of the Oseen approximation to the Prandtl equations. His result for the velocity is U = U 0 {1 - a X -½ exp (-U 0 Y 2 /4νX)}.

scholarly journals Wave resistance: Some cases of three-dimensional fluid motion

1919 ◽  
Vol 95 (670) ◽  
pp. 354-365 ◽  
Keyword(s):  
Surface Pressure ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Wave Resistance ◽  
The Other ◽  
Two Dimensional ◽  
Pressure System ◽  
Submerged Body ◽  
Submerged Sphere ◽  
The Waves

1. Calculations of wave resistance, corresponding to a pressure system travelling over the surface, have hitherto been limited to two-dimensional fluid motion; in those cases, the distribution of pressure on the surface is one-dimensional, and the regular waves produced have straight, parallel crests. The object of the following paper is to work out some cases when the surface pressure is two-dimensional and the wave pattern is like that produced by a ship. A certain pressure system symmetrical about a point is first examined, and more general distributions are obtained by superposition. By combining two simple systems of equal magnitude, one in rear of the other, we obtain results which show interesting interference effects. In similar calculations with line pressure systems, at certain speeds the waves due to one system cancel out those due to the other, and the wave resistance is zero; the corresponding ideal form of ship has been called a wave-free pontoon. Such cases of perfect interference do not occur in three-dimensional problems; the graph showing the variation of wave resistance with velocity has the humps and hollows which are characteristic of the resistance curves of ship models. Although the main object is to show how to calculate the wave resistance for assigned surface pressures of considerable generality, it is of interest to interpret some of the results in terms of a certain related problem. With certain limitations, the waves produced by a travelling surface pressure are such as would be caused by a submerged body of suitable form. The expression for the wave resistance of a submerged sphere, given in a previous paper, is confirmed by the following analysis. It is also shown how to extend the method to a submerged body whose form is derived from stream lines obtained by combining sources and siuks with a uniform stream; in particular, an expression is given for the wave resistance of a prolate spheroid moving in the direction of its axis.

scholarly journals Hydrodynamic forces acting on a cylinder in motion, and the idea of a "hydrodynamic centre."

1929 ◽  
Vol 124 (794) ◽  
pp. 296-303 ◽  
Keyword(s):  
General Theory ◽  
General Result ◽  
Complex Variable ◽  
Velocity Potential ◽  
Fluid Motion ◽  
Rotating Cylinder ◽  
The Other ◽  
Two Dimensional ◽  
Effects Of Rotation ◽  
Surrounding Liquid

There are two general methods of determining the forces acting on a cylinder due to the two-dimensional motion of a surrounding liquid. One is applicable to the case of a stationary cylinder in a stream, in the form X - Y = 1/2 p ∫( dw / dz ) 2 dz . (1.1) M = -1/2 pR ∫( dw / dz ) 2 z . dz (1.2) where X and Y are the components of the resultant force, parallel to the x and y axes, and M is its moment about tbs origin; p is the density of the fluid, and w is the velocity potential-stream-function for the fluid motion; z is as usual the complex variable x + y . The other is that obtained from the general theory of the "impulse. The first of these is unable to deal with a rotating cylinder, and the second is unable to include "circulation." In the course of an investigation of the effects of rotation upon the circulation round, and the forces acting upon, a Joukowski aerofoil, to which problem neither method applies, since the combined effect of rotation and circulation is needed, a quite general result was obtained, which it is thought worth while to publish separately.

scholarly journals Examining the horizontal displacement of diaphragm wall embraced by strut affected by piled foundations adjacent to urban deep excavations

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Alireza Darvishpour ◽  
Amirmohammad Amiri ◽  
Asadollah Ranjbar
Keyword(s):  
Horizontal Displacement ◽  
Pile Group ◽  
The Other ◽  
Diaphragm Wall ◽  
Horizontal Distance ◽  
Two Dimensional ◽  
Deep Excavations ◽  
Adjacent Structures ◽  
The Moment ◽  
Piled Foundations

Utilizing the piled foundation is extremely important and applicable in the civil and geotechnical engineering due to the improvementin the bearing capacity. Employing urban deep excavations, on the other hand, is inevitable and examining the effect of the pile groupis significantly vital due to the nearness of adjacent structures. In this research, the effect of the pile group foundation on the diaphragm wall embraced with struts in urban deep excavations is examined using two-dimensional numerical modeling. The resultsobtained from modeling show that the horizontal distance between the foundation and the excavation edge and also the pile lengthcan significantly affect the horizontal displacement of the wall and the moment diagram imposed on the wall, so that the effect ofthe foundation on the wall is considerably reduced for the distance greater than a certain value.

scholarly journals A generalization of Mehta-Wang determinant and Askey-Wilson polynomials

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Victor J. W. Guo ◽  
Masao Ishikawa ◽  
Hiroyuki Tagawa ◽  
Jiang Zeng
Keyword(s):  
Gamma Function ◽  
Jacobi Polynomials ◽  
The Other ◽  
Two Dimensional ◽  
Moment Sequence ◽  
International Audience ◽  
Pfaffian Formula ◽  
The Moment ◽  
Wilson Polynomials ◽  
Gaussian Symplectic Ensemble

International audience Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the two dimensional dimer system in 2011. Recently we have generalized the latter Pfaffian formula with a $q$-analogue by replacing the Gamma function by the moment sequence of the little $q$-Jacobi polynomials. On the other hand, Nishizawa has found a q-analogue of the Mehta–Wang formula. Our purpose is to generalize both the Mehta-Wang and Nishizawa formulae by using the moment sequence of the little $q$-Jacobi polynomials. It turns out that the corresponding determinant can be evaluated explicitly in terms of the Askey-Wilson polynomials.

The Elastic Strip With Prescribed End Displacements

1971 ◽  
Vol 38 (4) ◽  
pp. 929-936 ◽  
Author(s):  
P. J. Torvik
Keyword(s):  
Variational Principle ◽  
Shear Force ◽  
Resultant Force ◽  
The Other ◽  
Two Dimensional ◽  
Elastic Strip

The stresses and displacements in an elastic strip arising from displacements prescribed over one end are determined in terms of the eigenfunctions of the strip, with the coefficients being determined through a variational principle. Certain elementary solutions are included to account for the resultant force and moment induced by an arbitrarily prescribed displacement. Stresses and displacements resulting from pressing a strip against rough flat and parabolic surfaces were determined as were the deflections of a two-dimensional beam with one end built-in and the other subjected to a moment or a shear force. Differences between the results obtained and the predictions of elementary formulas are small.

Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

1990 ◽  
Vol 48 (1) ◽  
pp. 258-259
Author(s):  
J.L. Carrascosa ◽  
G. Abella ◽  
S. Marco ◽  
M. Muyal ◽  
J.M. Carazo
Keyword(s):  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Series Method ◽  
Three Dimensional Reconstruction ◽  
Structural Components ◽  
E Coli ◽  
Dimensional Reconstruction ◽  
Morphogenetic Factors ◽  
Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

The Final ‘Thank You’

Derrida Today ◽  
2010 ◽  
Vol 3 (1) ◽  
pp. 21-36
Author(s):  
Grant Farred
Keyword(s):  
South Africa ◽  
South African ◽  
Jacques Derrida ◽  
Political Transition ◽  
The Other ◽  
World Cup ◽  
The Core ◽  
Nelson Mandela ◽  
Black President ◽  
The Moment

‘The Final “Thank You”’ uses the work of Jacques Derrida and Friedrich Nietzsche to think the occasion of the 1995 rugby World Cup, hosted by the newly democratic South Africa. This paper deploys Nietzsche's Zarathustra to critique how a figure such as Nelson Mandela is understood as a ‘Superman’ or an ‘Overhuman’ in the moment of political transition. The philosophical focus of the paper, however, turns on the ‘thank yous’ exchanged by the white South African rugby captain, François Pienaar, and the black president at the event of the Springbok victory. It is the value, and the proximity and negation, of the ‘thank yous’ – the relation of one to the other – that constitutes the core of the article. 1

Macaronics as What Eludes Translation

Paragraph ◽  
2015 ◽  
Vol 38 (2) ◽  
pp. 214-230
Author(s):  
Haun Saussy
Keyword(s):  
Print Culture ◽  
The Other ◽  
Digital Code ◽  
Avant Garde ◽  
The Moment

‘Translation’ is one of our all-purpose metaphors for almost any kind of mediation or connection: we ask of a principle how it ‘translates’ into practice, we announce initiatives to ‘translate’ the genome into predictions, and so forth. But the metaphor of translation — of the discovery of equivalents and their mutual substitution — so attracts our attention that we forget the other kinds of inter-linguistic contact, such as transcription, mimicry, borrowing or calque. In a curious echo of the macaronic writings of the era of the dawn of print, the twentieth century's avant-garde, already foreseeing the end of print culture, experimented with hybrid languages. Their untranslatability under the usual definitions of ‘translation’ suggests a revival of this avant-garde practice, as the mainstream aesthetic of the moment invests in ‘convergence’ and the subsumption of all media into digital code.

Computational and experimental studies of the strength of full-scale samples of pipes with defects "metal loss" and "dent with groove"

2020 ◽  
Vol 10 (3) ◽  
pp. 226-233
Author(s):  
Dmitry A. Neganov ◽  
◽  
Victor M. Varshitsky ◽  
Andrey A. Belkin ◽  
◽  
...  
Keyword(s):  
Internal Pressure ◽  
Experimental Studies ◽  
Full Scale ◽  
The Other ◽  
Metal Loss ◽  
Calculation Methods ◽  
Reliable Operation ◽  
Sufficient Stability ◽  
Comparative Results ◽  
The Moment

The article contains the comparative results of the experimental and calculated research of the strength of a pipeline with such defects as “metal loss” and “dent with groove”. Two coils with diameter of 820 mm and the thickness of 9 mm of 19G steel were used for full-scale pipe sample production. One of the coils was intentionally damaged by machining, which resulted in “metal loss” defect, the other one was dented (by press machine) and got groove mark (by chisel). The testing of pipe samples was performed by applying static internal pressure to the moment of collapse. The calculation of deterioration pressure was carried out with the use of national and foreign methodical approaches. The calculated values of collapsing pressure for the pipe with loss of metal mainly coincided with the calculation experiment results based on Russian method and ASME B31G. In case of pipe with dent and groove the calculated value of collapsing pressure demonstrated greater coincidence with Russian method and to a lesser extent with API 579/ASME FFS-1. In whole, all calculation methods demonstrate sufficient stability of results, which provides reliable operation of pipelines with defects.

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