Control of the jet of a pulsed flywheel water cannon

We describe a pulsed water cannon in which the compression of the water occurs as a result of a cam located on a flywheel. We pose and solve the variational problem of optimal control of the spray of the pulsed water cannon. The control is the shape of the cam. We compute a way of finding a pressure pulse that is nearly rectangular, providing a uniform fluid flow. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 107–111.     

Pulsed jet of liquid under water

The Godunov numerical method is used to study the interaction of a pulsed, submerged cylindrical jet of liquid with a plane rigid barrier. The time for the parameters to establish themselves is estimated, as well as their dependence on the distance from the barrier. It is shown that the enhanced pressure zone is localized within a small region with dimensions on the order of the jet diameter near the center of the barrier. The effect of different forms of the finite difference approximation for the equations on the accuracy of the calculations near the axis of symmetry is studied. The effect of nonreflection conditions at fictional boundaries on the flow parameters along the center of the barrier is estimated. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 169–174, 1999.     

The drag force on the grains in a permeable medium subjected to a water jet

Summary A theory for destruction of rock with a high speed water jet is derived on the basis of viscous flow through porous media. The theory yields that a grain in the rock exposed to a water jet is subjected to a hydraulic force proportional to the water pressure gradient in the rock and to the volume of the grain. If a semi-space of a presaturated rock is hit by a water jet of sufficient pressure the theory predicts the initial stage of the crater to be an annular crater the radius of which is twice the radius of the jet. In the case of a dry rock the theory predicts that the typical ring structure of the initial stage of the crater should not occur. The conclusion is that in destruction of rock with a high-pressure water jet the permeability is a very important parameter in contrast to the case of mechanical destruction.

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Zusammenfassung Eine Theorie über Gesteinsdestruktion mit Hochdruckwasserstrahl gründet sich auf die Theorie viskoser Strömung durch poröse Medien. Die Theorie besagt dass eine Partikel im Gestein durch einwirken eines Wasserstrahls einer hydraulischen Kraft ausgesetzt wird die proportional zum Gradienten des Wasserdruckes im eigentlichen Gestein und proportional zum Volumen der Partikel ist. Wenn ein Halbraum eines wassergesättigten Gesteins von einem Wasserstrahl mit ausreichend hohen Druck getroffen wird, sagt die Theorie, so soll das Anfangsstadium des sich bildenden Kraters ringförmig sein mit einem Radius doppelt so gross als der Radius des Wasserstrahls. Im Falle trockenen Gesteins, erklärt die Theorie, soll die typische Ringstruktur im Anfangsstadium des Kraters nich auftreten. Zusammenfassend kann man sagen die Permeabilität ist ein bedeutend wichtiges Parameter bei Gesteinsdestruktion mit Hochdruck wasserstrahl im Gegensatz zum Fall mechanischer Destruktion.

     

The back effect of a wall on a jet

Zusammenfassung Ein ebener Flüssigkeitsstrahl von der Weited wird normal gegen eine Wand geleitet, die von der Quelleh Einheiten entfernt ist. Man nimmt gewöhnlich an, dass, wenn das Verhältnish/d gross ist, die Auswirkung des Hindernisses nicht zur Quelle des Strahles zurückwirkt, so dass im besonderen wichtige Eigenschaften des Strahls, wie sein Impuls und die Massenströmung, dürch den Widerstand unberührt bleiben.An einem einfachen Modell, in dem der Strahl, bestehend aus einer inkompressiblen und reibungslosen Flüssigkeit, von einem Schlitz in der Wand einer unendlichen Kammer ausströmt, zeigen wir, dass, soweit diese Haupteigenschaften betroffen sind, der Strahl durch das Hindernis beinahe ungestört bleibt, selbst für Werte der Verhältniszahlh/d, die nahe an der Einheit liegen.     

The axisymmetric free laminar jet of a power-law fluid

Summary The solution of the boundary-layer equations for an axisymmetric free laminar jet of a power-law fluid is investigated. It is shown that similar solutions are possible only forn1/2, wheren is the exponent in the power-law model. Forn>1/2, the axial velocity decay is proportional to the (–1/2n–1) power of the distance downstream and the jet spreads at a rate proportional to the (1/2n–1) power of the distance. Forn=1/2, the velocity decay and the rate of spread are exponential. Experimental data are presented which demonstrate that the predicted exponential decay occurs in real fluids.

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Zusammenfassung Ähnliche Lösungen der Grenzschichtgleichungen für einen achsensymmetrischen laminaren Strahl von Potenzgesetz-Flüssigkeiten werden gegeben. Diese Lösungen werden mit vorhandenen experimentellen Daten verglichen.

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Nomenclature d orifice diameter - D characteristic length - f preliminary dependent variable - F final dependent variable - J momentum inx-direction - K coefficient in power law model - n exponent in power law model - Re generalized Reynolds number - u x-component of velocity;u _o=characteristic velocity;u _p =initial velocity;=u/u _o;u _m =velocity on centerline of jet. - v y-component of velocity; - x coordinate in axial direction; ; = distance from orifice in experimental jet - y coordinate in radial direction; - function of - function of - parameter in final similarity transformation - preliminary independent variable - final independent variable - fluid density - shear stress - stream function     

The statistical mechanics of a class of dissipative systems

The statistical mechanics of dynamical systems on which only isotropic viscous friction forces act is developed. A non-stationary analogue of the Gibbs canonical distribution, which enables each such system to be made to correspond to a certain thermodynamic system that satisfies the first and second laws of thermodynamics, is introduced. The evolution of non-Gibbs probability distributions with time is also considered.     

The dynamics of a meandering coastal jet in the lee of a cape

In a barotropic model of an oceanic channel, bounded to the north by a straight coast indented by a Gaussian cape, the evolution of a coastal jet is studied numerically. In the absence of the cape, the barotropic instability of the jet is determined. In the presence of the cape, a regular row of meanders develops downstream of this feature, and becomes stationary for a particular range of parameters. The relevant parameters are the velocity and width of the jet, size of the cape, and beta effect. The formation of meanders occurs first via the instability of the jet, then via the generation of vorticity anomalies at the cape, which are advected both downstream by the flow and offshore by the radiation of Rossby waves. Once the meanders are established, they remain stationary features if the propagation velocity of the meanders (due to the dipolar effect at the coast) opposes the jet velocity and the phase speed of the wave on the vorticity front. Finally, a steady state of a regular row of meanders is also obtained via a matrix method and is similar to that obtained in the time-dependent case.     

The varieties of mechanics by 1800

After an exploration of some of the basic categories attending mechanics, Newtonianism, and physics, a survey is given of the range of subjects covered by mechanics at the end of the 18th century, and the three main traditions operative in the subject are stressed. A few major French figures of that time are then noted, and also some views evident in certain other countries. The appendix of the paper is concerned with bibliographical questions; and an extensive bibliography, mostly of secondary literature, is appended.     

The trajectory and stability of a spiralling liquid jet: Viscous theory

We examine a spiralling slender viscous jet emerging from a rapidly rotating orifice, extending Wallwork et al. [I.M. Wallwork, S.P. Decent, A.C. King, R.M.S.M. Schulkes, The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory, J. Fluid Mech. 459 (2002) 43–65] by incorporating viscosity. The effects of viscosity on the trajectory of the jet and its linear instability are determined using a mixture of computational and asymptotic methods, and verified using experiments. A non-monotonic relationship between break-up length and rotation rate is demonstrated with the trend varying with viscosity. The sizes of the droplets produced by this instability are determined by considering the most unstable wave mode. It is also found that there is a non-monotonic relationship between droplet size and viscosity. Satellite droplet formation is also considered by analysing very short wavelength modes. The effects of long wavelength modes are examined, and a wave which propagates down the trajectory of the jet is identified for the highly viscous case. A comparison between theoretical and experimental results is made, with favourable agreement. In particular, a quantitative comparison is made between droplet sizes predicted from the theory with experimental observations, with encouraging agreement obtained. Four different types of break-up are identified in our experiments. The experimentally observed break-up mechanisms are discussed in light of our theory.     

Nonlinear evolution of a column swirling jet

The aim of this work is to study the nonlinear temporal evolution of an alternating swirling streaming jet. According to laboratory observations, the viscous dissipation is simulated by means of a phenomenological damping coefficient included in the equation of motion (Jiang et al. in J Fluid Mech 369:273–299, 1998; Wright et al. in J Fluid Mech 402:1–32, 2000) and added to the Bernoulli equation or to the evolution equation. The multiple scales are used for finding out the evolution equations. The fixed points of the solutions have been determined. Really, the modulation concept is exploited in order to analyze the stability criteria in the possible cases of resonance. While in the non-resonant case, the nontrivial solutions are obtained numerically. Different numerical applications have been considered. The studied cases have showed that the Weber number, the phenomenological number and the streamwise circulation play a significant role in determining the dynamics of the developing interfacial patterns.     

Laminar jet of a compressible pseudo-plastic fluid

Similarity solutions of the boundary layer equations for compressible pseudo-plastic fluids for plane symmetrical jet are obtained in a closed form. Behaviour of velocity component perpendicular to the axis of the jet is discussed in detail.     

Quantum mechanics as the quadratic Taylor approximation of classical mechanics: The finite-dimensional case

We show that in contrast to a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. We consider an approximation based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the second-order term. To escape technical difficulties related to the infinite dimensionality of the phase space for quantum mechanics, we consider finite-dimensional quantum mechanics. On one hand, this is a simple example with high pedagogical value. On the other hand, quantum information operates in a finite-dimensional state space. Therefore, our investigation can be considered a construction of a classical statistical model for quantum information. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 278–291, August, 2007.     

The jet at the switch-on stage in a numerical and physical experiment

We analyze the possibility of predicting the structure of the jet at the formative stage using a comparison of experimental results and compulations carried out for flows beyond an acoustic nozzle. The correspondence of the computational model to the conditions in which the experiments were performed is discussed. It is shown that the question of the degree of reliability of the computational prediction should be decided on the basis of comparison of the approximation relations that describe the experimental and computational data. Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 162–171.     

The coupling problem in polymer mechanics

The present status of the coupling problem in polymer mechanics is discussed. The coupled problems of thermoelasticity and thermoviscoelasticity are formulated and methods of solving them are examined.Presented at the 11th Scientific Conference on Thermal Stresses in Structural Elements, Kanev, June 2, 1970.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 59–65, January–February, 1971.