Showing papers on "Bernoulli's principle published in 1989"

Fluid Flow: A First Course in Fluid Mechanics

Abstract: 1. Introduction. 2. The Basic Equations. 3. The Bernoulli Equation. 4. Momentum Theorems. 5. Similitude. 6. Elements of Potential Flow. 7. Analysis of Flow in Pipes and Channels. 8. Flow over External Surfaces. 9. Compressible Fluids - One-Dimensional Flow. 10. Elements of Two-Dimensional Gas Dynamics. 11. Flow in Open Channels. 12. Turbomachines. CHLIST = 13. Some Design Aspects of Turbomachines. Appendix 1: Dimensions and Units. Appendix 2. Physical Properties of Various Fluids. Appendix 3. Summary of the Properties of Vectors. Appendix 4. Summary of Thermodynamic Relations. Appendix 5. Gas Dynamic Tables. Answers to Selected Problems. Index.

Engineering in Process Metallurgy

Abstract: Part 1 An introduction to transport phenomena and properties in metallurgical operations: including Newton's second law of motion Newton's law of viscosity the Chapman-Enskog equation. Part 2 Fluid statics and fluid dynamics: including Navien-Stokes equation flow past spheres at high Reynold's numbers Prandtl's theory of turbulence for boundary layers the Euler (momentum) and Bernoulli equations for inviscid fluids. Part 3 Dimensional analysis and reactor design: including Rayleigh's method of indices Buckingham's "pi" theorem. Part 4 Heat and mass transfer through motionless media: including the "exact" form of Fick's law of diffusion high and low Biot numbers. Part 5 Heat and mass transfer in convective flow systems: including the Lewis-Whitman two-film theory Danckwerts' surface renewal theory. Part 6 Numerical techniques and computer applications: including the Gauss-Siedel point-by-point method. Further reading. Appendices: 1 - nomenclature 2 - units, dimensions and conversion factors 3 - thermodynamic data, worked examples, physical properties, periodic table, error function. Tables. Index. References.

Mountain‐induced stagnation points in hydrostatic flow

Abstract: The Bernoulli and hydrostatic relations are used to derive an exact diagnostic equation relating wind speed to the integral of vertical displacement aloft. The form of this equation does not support the “kinetic energy” concept of flow stagnation proposed by Sheppard (1956). Linear theory estimates of the displacement integral are used to predict the occurrence of stagnation points as a function of hill shape and ambient shear. For a long ridge perpendicular to a weakly sheared flow, stagnation begins aloft, thus allowing wave breaking and transition to a severe state. For a ridge aligned with the flow, waves dispersively weaken aloft and stagnation occurs first on the surface. This allows density surfaces to intersect the ground and the low-level flow to split around the hill.

Melnikov transforms, bernoulli bundles, and almost periodic perturbations

Abstract: In this paper we study nonlinear time-varying perturbations of an autonomous vector field in the plane R2 . We assume that the unperturbed equation, i.e. the given vector field has a homoclinic orbit and we present a gen- eralization of the Melnikov method which allows us to show that the perturbed equation has a transversal homoclinic trajectory. The key to our generalization is the concept of the Melnikov transform, which is a linear transformation on the space of perturbation functions. The appropriate dynamical setting for studying these perturbation is the concept of a skew product flow. The concept of transversality we require is best understood in this context. Under conditions whereby the perturbed equation admits a transversal homoclinic trajectory, we also study the dynamics of the perturbed vector field in the vicinity of this trajectory in the skew product flow. We show the dynamics near this trajectory can have the exotic behavior of the Bernoulli shift. The exact description of this dynamical phenomenon is in terms of a flow on a fiber bundle, which we call, the Bernoulli bundle. We allow all perturbations which are bounded and uniformly continuous in time. Thus our theory includes the classical periodic perturbations studied by Melnikov, quasi periodic and almost periodic perturbations, as well as toroidal perturbations which are close to quasi periodic perturbations.

Real analytic Bernoulli geodesic flows on S2

Abstract: We obtain a family of metrics on the two-dimensional sphere whose geodesic flow is ergodic and Bernoulli. This family includes real analytic metrics.

On combining the Bernoulli and Poiseuille equation—A plea to authors of college physics texts

Abstract: A generalized form of the Bernoulli equation is presented The assumptions involved in the derivation and its limitations are identified The usual form of the Bernoulli and Poiseuille equations is shown to be a special case of this generalized equation Various implications in the teaching of college physics are discussed

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

Abstract: An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Tangential discontinuities and the optical analogy for stationary fields II. The optical analogy

Abstract: It is shown that any stationary three-dimensional velocity field or magnetic field is a potential field in the two dimensional subspace of the Bernoulli surfaces S(Q) or isobaric surfaces S(p), respectively. From this it is shown that the streamlines and the lines of force follow the optical ray paths in S(Q) and S(p) for indices of refraction v and B, respectively. This formal analogy shows how the lines are refracted by variations of the pressure applied by the fluid and field on either side. In particular, it is shown how continuous variations of the pressure produce discontinuities (bifurcations) in the field, forming tangential discontinuities.

Voice of the Dragon: the rotating corrugated resonator

Abstract: A simple, yet unusual, child's toy illustrates some basic features of the physics of resonance, waves and fluid dynamics. The acoustic modes of a corrugated tube open at both ends and rotating in a plane were examined as a function of rotational frequency and found to be similar but not identical to those of a stationary open-ended organ pipe. Measurements of the pressure difference at resonance across the tube ends as a function of rotational frequency agree well with a simple analysis based on Bernoulli's principle. A mechanism of sound production is proposed whereby the tube resonantly amplifies acoustic perturbations to the axial air flow, engendered by the corrugations, that occur at frequencies equal to the resonant frequencies of the tube. The mechanism is supported by direct measurements of the axial air speed as a function of rotational frequency.

Transient bimodality in interacting particle systems

Abstract: We consider a system of spins which have values ±1 and evolve according to a jump Markov process whose generator is the sum of two generators, one describing a spin-flipGlauber process, the other aKawasaki (stirring) evolution. It was proven elsewhere that if the Kawasaki dynamics is speeded up by a factor e−2, then, in the limit e → 0 (continuum limit), propagation of chaos holds and the local magnetization solves a reaction-diffusion equation. We choose the parameters of the Glauber interaction so that the potential of the reaction term in the reaction-diffusion equation is a double-well potential with quartic maximum at the origin. We assume further that for each e the system is in a finite interval ofZ with e−1 sites and periodic boundary conditions. We specify the initial measure as the product measure with 0 spin average, thus obtaining, in the continuum limit, a constant magnetic profile equal to 0, which is a stationary unstable solution to the reaction-diffusion equation. We prove that at times of the order e−1/2 propagation of chaos does not hold any more and, in the limit as e → 0, the state becomes a nontrivial superposition of Bernoulli measures with parameters corresponding to the minima of the reaction potential. The coefficients of such a superposition depend on time (on the scale e−1/2) and at large times (on this scale) the coefficient of the term corresponding to the initial magnetization vanishes (transient bimodality). This differs from what was observed by De Masi, Presutti, and Vares, who considered a reaction potential with quadratic maximum and no bimodal effect was seen, as predicted by Broggi, Lugiato, and Colombo.

A power balance model for converging and diverging flow junctions

Abstract: The authors propose that pressures across a junction of flows are best described by potential, kinetic, and dissipated (lost) power. It is demonstrated that differences in Bernoulli constants up- and downstream of junctions are not proportional to energy losses even in the trivial case of zero junction losses.

Fluid Physics for Oceanographers and Physicists: An Introduction to Incompressible Flow

Abstract: Mechanical properties of fluids; thermodynamic properties of fluids; dimensional analysis; fluid statics; fluid kinematics; conservation of mass; frictionless momentum equations - Euler and Bernoulli; one dimensional flow and energy conservation; motion with rotation; velocity potential, stream function and solution by superstition; forces on a body submerged in a moving fluid; control volume applications; viscous fluids, boundary layers and turbulence. Appendices: some vector calculus identities; answers to selected exercies.

Accuracy of the simplified Bernoulli relationship in measuring pressure gradients across stenosis.

Abstract: In order to test the validity of the modified Bernoulli equation in predicting pressure gradients across stenotic regions, we have constructed an in-vitro model and studied the influence of the length and of the severity of the stenosis. Under physiological conditions, simultaneous pressure gradients are estimated by both Doppler and direct pressure manometer techniques. Measurements of the pressure gradients (in the range 10-150 mmHg) by the two techniques show that the Doppler estimation using the modified Bernoulli equation underestimated the pressure transducer gradient measurements for every length of stenosis, this underestimation being greater than 45% for very severe stenosis.

On the approach to statistical equilibrium in an infinite‐particle lattice dynamic model

Abstract: A deterministic reversible model dynamic system of infinite interacting particles on a lattice is studied. The model is a modification by de Haan of the Kac ring model. The time evolution of the statistical states can be described by a hierarchy for the reduced distribution functions. It is shown that the system is isomorphic to a Bernoulli shift. The isomorphism is given in terms of the infinite process of observation of the states of one particle in a fixed site. The approach to equilibrium is studied and time‐asymmetric initial states that approach equilibrium are constructed. It is shown that these states contain nonvanishing correlations between infinitely distant particles. The Bernoulli property allows the construction of a Markovian irreversible description of the model, realized by a nonunitary transformation. The action of this transformation on the statistical states, the correlations, and the rate of the approach to equilibrium is studied.

Flexible Optical Drive Technology

Abstract: Application of Bernoulli Principle to optical recording is described. Bernoulli technology stabilizes the flexible disk so that a light, fixed focus optical head can be used.

An application of the linear equivalence method to the postcritical study of a Bernoulli-Euler bar

Abstract: This representation forms the background for the study of criticity and postcriticity of the bar under consideration with respect to certain quantities of interest

Maximum a posteriori estimation of multichannel Bernoulli-Gaussian sequences

Abstract: General problems and solutions are described for maximum a posteriori estimation of multichannel Bernoulli-Gaussian sequences, which are inputs to a linear discrete-time multivariable system. The authors first develop a separation principle, which indicates that one can estimate multichannel Gaussian amplitudes and Bernoulli events separately. They then discuss approaches for estimation of these quantities. >

The Bernoulli Spline and Approximation by Trigonometric Blending Polynomials

Abstract: Using an extension of the notion of Bernoulli spline to a multivariate setting, a Jackson-Favard estimate is derived for approximation of 2π-periodic test functions by trigonometric blending polynomials. Techniques involved in the proof include properties of periodic distributions and of their Fourier transforms. The usual Jackson-Favard estimates from the literature can be derived from our result if limits of test functions are considered.

From Bernoulli scaling to turbulent diffusion

Abstract: The scaling found in Bernoulli's St. Petersburg Paradox was perhaps not properly understood until Levy's theory of probability limit distributions with infinite integer moments was developed. We use a generalization of these ideas involving a non-local stochastic equation with a coupled space-time memory to formulate a picture of turbulent diffusion.

Risk attitude and metric Bernoulli-decision-rule

Abstract: The paper is based on the metric Bernoulli-decision-rule developed by Reichel [5]. Under certain conditions, this principle defines preference orderings of “probability games” and support decisions in evaluating economic processes.

Spectral and asymptotic properties of linear elastic systems with internal energy dissipation

Abstract: In this article we consider the problems inherent in developing mathematical models replicating observed damping phenomena in simple linear elastic systems. The Euler — Bernoulli and Timoshenko beam equations are used as the principal examples. We indicate the pitfalls attendant upon the use of dissipation mechanisms based only upon their mathematical convenience and discuss alternatives which originate from more fundamental physical considerations. The last section introduces two mechanisms, namely; thermoelastic damping and shear diffusion damping, which, to our knowledge, have not been discussed previously in this context.