Inflation and Compression of Rubber Tubes between Parallel Plates

1971 ◽  
Vol 44 (5) ◽  
pp. 1380-1390
Author(s):  
J. M. Charrier ◽  
A. N. Gent
Keyword(s):  
Internal Pressure ◽  
Pressure Rise ◽  
Compressive Force ◽  
Quantitative Agreement ◽  
Elastic Behavior ◽  
Rubber Tube ◽  
Parallel Plates ◽  
Compression Stiffness ◽  
Theoretical Predictions ◽  
Different Dimensions

Abstract When a thin-walled rubber tube containing an incompressible fluid is compressed between two parallel plates the internal pressure rise depends on the restraints in the contact regions. When there is no friction in the contact zone the pressure rise is lower than when slip is prevented, so that the tube, regarded as a spring, has a compression stiffness which depends on the frictional conditions. The same considerations apply to the inflation of a tube between fixed parallel plates. In this case unstable inflation sets in at a critical pressure when the interfaces are frictionless; the tube develops a pronounced bulge when this pressure is approached. Simple theoretical relations are derived for the internal pressure and compressive force for both these deformations, and for both boundary conditions, assuming that the rubber is neo-Hookean in elastic behavior. Experimental measurements on tubes of different dimensions are shown to be in reasonably good quantitative agreement with these theoretical predictions in all cases.

Dependence of Internal Pressure-rise due to Arc on Current Waveform and Ignition Position

2011 ◽  
Vol 131 (7) ◽  
pp. 574-583 ◽  
Author(s):  
Shin-ichi Tanaka ◽  
Tsukasa Miyagi ◽  
Mikimasa Iwata ◽  
Tadashi Amakawa
Keyword(s):  
Internal Pressure ◽  
Pressure Rise ◽  
Current Waveform

The propagation of gravity currents in a V-shaped triangular cross-section channel: experiments and theory

2014 ◽  
Vol 754 ◽  
pp. 232-249 ◽  
Author(s):  
Marius Ungarish ◽  
Catherine A. Mériaux ◽  
Cathy B. Kurz-Besson
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Viscosity Coefficient ◽  
Gravity Currents ◽  
Quantitative Agreement ◽  
Flat Bottom ◽  
Special Configuration ◽  
Theoretical Predictions ◽  
Speed Of Propagation ◽  
High Reynolds

AbstractWe investigate the motion of high-Reynolds-number gravity currents (GCs) in a horizontal channel of V-shaped cross-section combining lock-exchange experiments and a theoretical model. While all previously published experiments in V-shaped channels were performed with the special configuration of the full-depth lock, we present the first part-depth experiment results. A fixed volume of saline, that was initially of length $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x_0$ and height $h_0$ in a lock and embedded in water of height $H_0$ in a long tank, was released from rest and the propagation was recorded over a distance of typically $ 30 x_0$. In all of the tested cases the current displays a slumping stage of constant speed $u_N$ over a significant distance $x_S$, followed by a self-similar stage up to the distance $x_V$, where transition to the viscous regime occurs. The new data and insights of this study elucidate the influence of the height ratio $H = H_0/h_0$ and of the initial Reynolds number ${\mathit{Re}}_0 = (g^{\prime }h_0)^{{{1/2}}} h_0/ \nu $, on the motion of the triangular GC; $g^{\prime }$ and $\nu $ are the reduced gravity and kinematic viscosity coefficient, respectively. We demonstrate that the speed of propagation $u_N$ scaled with $(g^{\prime } h_0)^{{{1/2}}}$ increases with $H$, while $x_S$ decreases with $H$, and $x_V \sim [{\mathit{Re}}_0(h_0/x_0)]^{{4/9}}$. The initial propagation in the triangle is 50 % more rapid than in a standard flat-bottom channel under similar conditions. Comparisons with theoretical predictions show good qualitative agreements and fair quantitative agreement; the major discrepancy is an overpredicted $u_N$, similar to that observed in the standard flat bottom case.

scholarly journals Continued functions and perturbation series: Simple tools for convergence of diverging series in $O(n)$-symmetric $\phi^4$ field theory at weak coupling limit

2021 ◽  
Author(s):  
Venkat Abhignan ◽  
Sankaranarayanan R.
Keyword(s):  
Field Theory ◽  
Continuous Phase ◽  
Perturbation Series ◽  
Experimental Result ◽  
Unknown Parameters ◽  
Epsilon Expansion ◽  
Theoretical Predictions ◽  
Lambda Point ◽  
Different Dimensions ◽  
Dimensions Of Space

Abstract We determine universal critical exponents that describe the continuous phase transitions in different dimensions of space. We use continued functions without any external unknown parameters to obtain analytic continuation for the recently derived 7-loop $\epsilon$ expansion from $O(n)$-symmetric $\phi^4$ field theory. Employing a new blended continued function, we obtain critical exponent $\alpha=-0.01211$ for the phase transition of superfluid helium which matches closely with the most accurate experimental value. This result addresses the long-standing discrepancy between the theoretical predictions and precise experimental result of $O(2)$ $\phi^4$ model known as "$\lambda$-point specific heat experimental anomaly". Further we have also examined the applicability of such continued functions in other examples of field theories.

The liquid blister test

2008 ◽  
Vol 464 (2099) ◽  
pp. 2887-2906 ◽  
Author(s):  
Julien Chopin ◽  
Dominic Vella ◽  
Arezki Boudaoud
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Vertical Displacement ◽  
Quantitative Agreement ◽  
Elastic Plates ◽  
Blister Test ◽  
Thin Liquid Layer ◽  
Theoretical Predictions ◽  
Thin Elastic Plates ◽  
Adhesive Forces

We consider a thin elastic sheet adhering to a stiff substrate by means of the surface tension of a thin liquid layer. Debonding is initiated by imposing a vertical displacement at the centre of the sheet and leads to the formation of a delaminated region or ‘blister’. This experiment reveals that the perimeter of the blister takes one of three different forms depending on the vertical displacement imposed. As this displacement is increased, we observe first circular, then undulating and finally triangular blisters. We obtain theoretical predictions for the observed features of each of these three families of blisters. The theory is built upon the Föppl–von Kármán equations for thin elastic plates and accounts for the surface energy of the liquid. We find good quantitative agreement between our theoretical predictions and experimental results, demonstrating that all three families are governed by different balances between elastic and capillary forces. Our results may bear on micrometric tapered devices and other systems, where elastic and adhesive forces are in competition.

scholarly journals Indentation into a plastic fluid layer

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180747
Author(s):  
Thomasina V. Ball ◽  
Neil J. Balmforth ◽  
Ian J. Hewitt
Keyword(s):  
Slip Line ◽  
Plastic Material ◽  
Fluid Layer ◽  
Viscoplastic Fluid ◽  
Parallel Plates ◽  
Viscoplastic Material ◽  
Layer Depth ◽  
Glass Spheres ◽  
Theoretical Predictions ◽  
Line Theory

We study the indentation of a rigid object into a layer of a cohesive or non-cohesive plastic material. Existing approaches to this problem using slip-line theory assume that the penetration depth is relatively small, employing perturbation theory about a flat surface. Here, we use two alternative approaches to account for large penetration depths, and for the consequent spreading and uplift of the surrounding material. For a viscoplastic fluid, which reduces to an ideal plastic under the limit of vanishing viscosity, we adopt a viscoplastic version of lubrication theory. For a Mohr–Coulomb material, we adopt an extension of slip-line theory between two parallel plates to account for arbitrary indenter shapes. We compare the theoretical predictions of penetration and spreading with experiments in which a flat plate, circular cylinder or sphere are indented into layers of Carbopol or glass spheres with successively higher loads. We find reasonable agreement between theory and experiment, though with some discrepancies that are discussed. There is a clear layer-depth dependence of the indentation and uplift for the viscoplastic material. For a cylinder indented into a Mohr–Coulomb material, there is a much weaker dependence on layer depth.

Leak Behavior and Prediction of Metal Ring Joint Gaskets in Simplified Leak Test With Grooved Platen

2019 ◽  
Author(s):  
Yuya Omiya ◽  
Masahiro Fujii
Keyword(s):  
Internal Pressure ◽  
Evaluation Method ◽  
Compressive Force ◽  
Metal Ring ◽  
Leak Test ◽  
Tightening Force ◽  
Flange Connection ◽  
Sealing Performance ◽  
Sealing Mechanism ◽  
Very High

Abstract Pipe flange connection with metal gasket is used under high temperature and pressure in place required high sealing performance. It has been known that gasket compressive force, which is closely related the leakage decreases by internal pressure action. Since the pressure is very high in metal gaskets, the sealing performance evaluation in internal pressure action is important. However, there is little research that evaluates a little leakage, metal gasket is empirically used up to the present time. Therefore, evaluated sealing performance of metal gasket, it is necessary to clarify the sealing mechanism. In this study, evaluated effect that decreasing of gasket compressive force affects leakage in both octagonal type and oval type in ring joint gasket by simplified leak test using grooved platen and finite element method stress analysis, evaluation method of leakage in metal gasket is proposed. Based on this evaluation method, decision method of initial tightening force that guaranteed one amount of leakage to design internal pressure is shown in pipe flange connection with metal gasket.

Plastic Loads for Cones Subjected to Internal Pressure and Axial Tension

2017 ◽  
Author(s):  
J. Błachut ◽  
D. Sala
Keyword(s):  
Internal Pressure ◽  
Conical Shell ◽  
Plastic Instability ◽  
Combined Loading ◽  
Elastic Behavior ◽  
The Past ◽  
Axial Tension

The paper discusses envelopes of combined loading corresponding to: (i) first yield (ii) plastic load, and (iii) plastic instability load. The latter two were researched in the past but for a single load, only. The past idea has been expanded in the paper to two, practically relevant, simultaneously acting loads. Conical shell serves here as an example. It is shown that the ratio of area of plastic load envelope to the area associated with the first-yield envelope is 3.2 whilst the similar ratio of plastic instability to the first-yield envelope amounts to 25.8. This indicates ‘a modest’ (320 %) increase of possible range of loading, and a substantial reserve of strength above the end-of-elastic behavior (approx. 26-times).

Interfacial wave theory for oscillatory finger formation in a Hele–Shaw cell: a comparison with experiments

1996 ◽  
Vol 7 (2) ◽  
pp. 169-199 ◽  
Author(s):  
Jian-Jun Xu
Keyword(s):  
Wave Theory ◽  
Quantitative Agreement ◽  
Instability Mechanism ◽  
Interfacial Wave ◽  
Wave Instability ◽  
Viscous Fingers ◽  
Theoretical Predictions ◽  
Finger Tip ◽  
Hele Shaw Cell ◽  
Comparison With Experiments

This paper is devoted to an analysis of the formation of oscillatory viscous fingers in a Hele-Shaw cell on the basis of the interfacial wave theory, previously established for the pattern formation dynamics in dendrite growth, as well as in the classic Saffman–Taylor flow. In particular, we study the problem of selection and persistence of oscillatory fingers with a tiny bubble at the finger tip. We obtain uniformly valid asymptotic solutions for this problem, and derive the linear, global wave instability mechanism for this more complicated system. The global, neutrally stable modes are computed in a large region of parameters, which select the form of oscillatory fingers in the later stage of evolution. We have compared the theoretical predictions with the experimental data by Couder et al. (1986) and by Kopf-Sill & Homsy (1987), and found excellent quantitative agreement.

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