Showing papers on "Bernoulli's principle published in 1996"
Book•
17 Oct 1996
TL;DR: The Bernoulli Equation of Fluid Kinematics as discussed by the authors is used in the analysis of fluid flow in Pipes and open-channel flow in Turbomachines.
Abstract: Fluid Statics. Elementary Fluid DynamicsThe Bernoulli Equation. Fluid Kinematics. Finite Control Volume Analysis. Differential Analysis of Fluid Flow. Similitude, Dimensional Analysis, and Modeling. Viscous Flow in Pipes. Flow Over Immersed Bodies. Open-Channel Flow. Turbomachines. Appendices. Answers. Index.
322 citations
TL;DR: In this paper, the authors derived surface order large deviation estimates for the volume of the largest cluster and the largest region surrounded by a cluster of a Bernoulli percolation process restricted to a big finite box.
Abstract: We derive surface order large deviation estimates for the volume of the largest cluster and for the volume of the largest region surrounded by a cluster of a Bernoulli percolation process restricted to a big finite box, with sufficiently large parameter. We also establish a useful version of the isoperimetric inequality, which is the main tool of our proofs.
132 citations
TL;DR: In this article, it was shown that non-uniformly hyperbolic maps and flows with singularities enjoy the K-property of the Lorentz gas and are Bernoulli properties.
Abstract: We prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space
97 citations
Journal Article•
TL;DR: In this article, a simple well-posed system (P-vector method) is proposed in which the conservation of mass and potential vorticity leads to the condition that the velocity vector is perpendicular to both density (ρ) and potential Vorticity (q = f∂ρ/∂z) gradients.
Abstract: Several major techniques (Stommel-Schott method, Wunsch method, and Bernoulli method) that have been developed to quantitatively estimate the geostrophic velocity at the reference level, have the same order of dynamical sophistication (geostrophy, hydrostatic, and density conservation.) From a technical point of view, the Stommel-Schott method is an overdetermined system (the number of equations is much larger than the number of variables), however, the Wunsch method is an underdetermined system (the number of equations is much smaller than the number of variables). Based on the same dynamical and thermodynamical framework, a simple, well-posed system (P-vector method) is proposed in this study. Consistent with geostrophy, the system is assumed non-dissipative. The conservation of mass and potential vorticity leads to the condition that the velocity vector is perpendicular to both density (ρ) and potential vorticity (q = f∂ρ/∂z) gradients, and that the velocity can be represented as V(x, y, z) = r(x, y, z)P (x, y, z), where P = (⊇ρ x ⊇q)/|⊇ρ x ⊇q|. The unit vector, P, is computed from the density field, and the parameter r(x, y, z) is determined by the thermal-wind relation. Furthermore, an error reduction scheme is also proposed in this study.
65 citations
TL;DR: In this article, the stability and controllability of Euler-Bernoulli beams with intelligent constrained layer damping treatments was investigated and shown on three cantilever beams with displacement or slope feedback at the free end.
Abstract: This paper studies the stability and controllability of Euler-Bernoulli beams whose bending vibration is controlled through intelligent constrained layer (ICL) damping treatments proposed by Baz (1993) and Shen (1993, 1994). First of all, the homogeneous equation of motion is transformed into a first order matrix equation in the Laplace transform domain. According to the transfer junction approach by Yang and Tan (1992), existence of nontrivial solutions of the matrix equation leads to a closed-form characteristic equation relating the control gain and closed-loop poles of the system. Evaluating the closed-form characteristic equation along the imaginary axis in the Laplace transform domain predicts a threshold control gain above which the system becomes unstable. In addition, the characteristic equation leads to a controllability criterion for ICL beams. Moreover, the mathematical structure of the characteristic equation facilitates a numerical algorithm to determine root loci of the system. Finally, the stability and controllability of Euler-Bernoulli beams with ICL are illustrated on three cantilever beams with displacement or slope feedback at the free end.
57 citations
TL;DR: In this article, a three-section model for air bending is presented, assuming that a state of plane strain exists and that Bernoulli's law is valid, and the material behaviour is described with Swift's equation, and Young's modulus under deformation is addressed.
55 citations
TL;DR: In this paper, a comparison of the partial sums associated with two sequences of n exchangeable Bernoulli random variables is presented, where such partial sums are obtained through an iterative procedure of branching type stopped at the first-passage time in a linearly decreasing upper barrier.
Abstract: The paper is first concerned with a comparison of the partial sums associated with two sequences of n exchangeable Bernoulli random variables. It then considers a situation where such partial sums are obtained through an iterative procedure of branching type stopped at the first-passage time in a linearly decreasing upper barrier. These comparison results are illustrated with applications to certain urn models, sampling schemes and epidemic processes. A key tool is a non-standard hierarchical class of stochastic orderings between discrete random variables valued in {0, 1,..., n}.
51 citations
TL;DR: In this article, a finite element method coupled with analysis of a noncavitating lifting surface was used to assess the performance of a marine propeller, including the thrust, torque, efficiency coefficients, and deflections.
Abstract: A finite-element method coupled with analysis of a noncavitating lifting surface was used to assess the performance of a marine propeller, including the thrust, torque, efficiency coefficients, and deflections. The formulation used displacements as unknowns in the structural part and the strength of the vortex as unknowns in the fluid part. A coupled matrix derived from the Bernoulli equation and hydrostatic pressure in terms of the strength, of the vortex enforced coupling between the fluid and the structure. The resulting matrix equation was unsymmetric and nonlinear; a Newton-Raphson procedure was used to solve this equation. The numerical results were compared with test data; computed and measured values agreed satisfactorily. We also investigated the effect of blade thickness on the performance and strength of the propeller. We did not consider the fatigue strengh of the propeller in this analysis.
51 citations
TL;DR: The results show that the simplified Bernoulli equation, despite of its simplicity, provides a good estimation of the pressure drop between the UV and the DV outlet section, and attention must be paid to the velocity measurement sites, as discussed in this paper.
Abstract: The simplified Bernoulli equation is currently used to evaluate pressure gradients on the basis of Doppler velocity measurements when direct pressure data require highly invasive procedures. Recently, this method was applied to the ductus venosus (DV) in order to estimate the fetal central venous pressure. The complex geometry- and consequently hemodynamics-of this fetal region suggests caution in automatically converting Doppler velocity measurements to pressure data. To investigate the reliability of the Bernoulli equation for this practice, we simulated the hemodynamics of the branching between the umbilical vein (UV) and the DV on the basis of ultrasonographic data from a normal fetus, using a simplified parametric 3D numerical model of a bent tube with varying cross section (UV) and a smaller trumpet-shaped branch (DV). A finite element formulation has been adopted to solve the governing Navier-Stokes equations. The results show that the simplified Bernoulli equation, despite of its simplicity, provides a good estimation of the pressure drop between the UV and the DV outlet section (with an error of about 0.25 mmHg, equal to 15%, compared with the model results). Nevertheless, attention must be paid to the velocity measurement sites, as discussed in this paper. In turn, the error becomes notable (2.8 mmHg, i.e., 34%) for high velocity values, thus suggesting that the error in evaluating the pressure drop with the simplified Bernoulli equation during fetal inspiratory movements may be substantial.
45 citations
TL;DR: In this paper, a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term is considered and the main result is that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially.
Abstract: We consider a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially The method we use is a combination of multiplier techniques and of a compactnessuniqueness argument
42 citations
01 Jan 1996
TL;DR: In this article, the relative entropy of the microscopic state of the actual system with respect to a local equilibrium state is estimated by adapting the gradient replacement method devised by Varadhan for the study of the Ginzburg-Landau model of non-gradient type.
Abstract: The hydrodynamic limit for the class of lattice gases that are reversible under the Bernoulli measures is studied by estimating the relative entropy of the microscopic state of actual system with respect to a local equilibrium state (the method of H.T. Yau). The model discussed in this article is of non-gradient type and this forces us to introduce the local equilibrium state of second order approximation that is made according to the variational formula (an equivalent of the Green-Kubo formula) for the diffusion coefficient due to S.R.S. Varadhan. The estimation of the relative entropy is carried out by adapting the “gradient replacement” devised by Varadhan for the study of the Ginzburg-Landau model of non-gradient type. Because of the method adopted we do not need tightness argument nor two-block estimate, but do need to assume that the solution of the limiting nonlinear diffusion equation is smooth.
TL;DR: In this article, the authors considered low energy photon-photon scattering in arbitrary-dimensional space-time and the interaction was widened to include scattering events involving an arbitrary number of photons, and determined the effective interaction Lagrangian for these processes in QED in a manifestly invariant form.
Abstract: The subject of low energy photon-photon scattering is considered in arbitrary-dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalization resolves the structure of the weak field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related not only to the space-time dimension but also to the coefficients of the Bernoulli polynomial.
TL;DR: In this article, a conformal mapping function from a unit circle to the exterior of the bubble has a specific polar decomposition, and the pole locations and corresponding residues are determined numerically, while, in specific limits, their values are determined asymptotically.
Abstract: We consider some analytical properties for a steadily translating two-dimensional bubble in an inviscid irrotational flow when surface tension effects are included but gravity neglected. For a general value of the Bernoulli constant, we show that a conformal mapping function from a unit circle to the exterior of the bubble has a very specific polar decomposition. The pole locations and corresponding residues are determined numerically, while, in specific limits, their values are determined asymptotically.
TL;DR: A long-standing conjecture on the optimal Bernoulli routing policy is proven to be true, and it is shown that splitting equally among the queues minimizes the departure times in a stochastic pathwise sense.
Abstract: A long-standing conjecture on the optimal Bernoulli routing policy is proven to be true. For the case of equal exponential service times it is shown that splitting equally among the queues minimizes the departure times in a stochastic pathwise sense. A new technique is used, showing that certain distributional properties related to Schur convexity propagate forward in time.
TL;DR: In this paper, an efficient method of constructing inviscid Batchelor-model flows is developed based on an analytic continuation of the potential part of the flow into the closed-streamline vortex region.
Abstract: An efficient method of constructing inviscid Batchelor-model flows is developed. The method is based on an analytic continuation of the potential part of the flow into the closed-streamline vortex region. Numerical solutions are presented for Batchelormodel flows past airfoils with cavities. With the airfoil and dividing streamline shape, the eddy vorticity, and the jump in the Bernoulli constant across the eddy boundary given, the program calculates the corresponding cavity shape and the entire flow.
TL;DR: Two policies that maximize the almost sure average reward over an infinite horizon are presented and e-optimal stationary policies that require no information about the distribution of the Bernoulli parameter are developed.
Abstract: We consider a bandit problem with infinitely many Bernoulli arms whose unknown parameters are i.i.d. We present two policies that maximize the almost sure average reward over an infinite horizon. Neither policy ever returns to a previously observed arm after switching to a new one or retains information from discarded arms, and runs of failures indicate the selection of a new arm. The first policy is nonstationary and requires no information about the distribution of the Bernoulli parameter. The second is stationary and requires only partial information; its optimality is established via renewal theory. We also develop e-optimal stationary policies that require no information about the distribution of the unknown parameter and discuss universally optimal stationary policies.
TL;DR: In this article, the authors show how the Hausdorff dimension of the set where the Bernoulli measure has a power law singularity of strength α is related to the large deviation function given in Part I.
Abstract: We show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved Bernoulli measures νγ for γ the golden mean. In this second part we show how the Hausdorff dimension of the set where the measure has a power law singularity of strength α is related to the large-deviation function given in Part I.
TL;DR: In this paper, the authors show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved Bernoulli measures νγ, for γ the golden mean.
Abstract: We show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved Bernoulli measures νγ, for γ the golden mean. In this first part we establish some large-deviation results for random products of matrices, using perturbation theory of quasicompact operators.
TL;DR: In this paper, a general formulation for steady field-aligned magnetohydrodynamic (MHD) equilibrium flows with isotropic or gyrotropic pressures is presented, which allows self-consistent solutions to be constructed numerically in a way similar to the static case; examples of such MHD equilibria are shown.
Abstract: A general formulation is presented for steady field‐aligned magnetohydrodynamic (MHD) equilibrium flows with isotropic or gyrotropic pressures. Closure to the anisotropic MHD model is provided by a pair of double‐polytropic energy equations, for which double‐adiabatic and double‐isothermal conditions are special limits of the model. For the latter case, a MHD counterpart of Bernoulli’s equation is derived. The study is then focused on the two‐dimensional (∂/∂y=0 but By≠0) problems, for which a generalized Grad–Shafranov equation is developed for field‐aligned MHD flow equilibria with isotropic or gyrotropic pressures. The formulation is put in a form that allows self‐consistent solutions to be constructed numerically in a way similar to the static case; examples of such MHD equilibria are shown. An asymptotic formulation is also developed for stretched gyrotropic plasma configurations, which, however, is not applicable to two‐dimensional planar configurations with regions of weak magnetic field strength, ...
TL;DR: In this paper, the direct Kepler problem is solved, where given a curve (e.g. an ellipse) and the center of attraction, the law of this attraction holds if Kepler's second law holds.
Abstract: Newton solved what was called afterwards for a short time “the directKepler problem” (“le probleme direct”): given a curve (e.g. an ellipse) and the center of attraction (e.g. the focus), what is the law of this attraction ifKepler's second law holds?
TL;DR: In this paper, the authors compared observations of a laboratory model of a western boundary current, and its separation and subsequent meandering, with a theoretical model of all three aspects of the current: the structure of the attached current, the process of separation, and the dynamics and path of the meandering jet.
Abstract: Observations of a laboratory model of a western boundary current, and its separation and subsequent meandering, are described The current is established by pumping fluid through a rotating channel that contains a topographic β effect and continental slope topography The observations are compared with a theoretical model of all three aspects of the current: the structure of the attached current, the process of separation, and the dynamics and path of the meandering jet This model includes a viscous boundary layer for the attached current, with a thickness of order [ν/(dvI/dy)]1/2, where ν is kinematic viscosity and dvI/dy is the velocity gradient of the inviscid (free slip) flow along the boundary Comparison between the observations and the model show that the attached boundary current is governed by potential vorticity conservation and the Bernoulli equation, and the pressure decreases along its length The separation of this current from the sidewall is then caused by the minimum pressure le
TL;DR: The Horton-Strahler number H n is studied, and it is shown that formula math.
Abstract: We consider random tries constructed from n i.i.d. sequences of independent Bernoulli (p) random variables, 0 < p < 1. We study the Horton-Strahler number H n , and show that formula math. in probability as n → ∞.
TL;DR: In this paper, a new pressure law is proposed to replace the modified Bernoulli equation of Tate in 1967 and 1969, which is achieved by decomposing the equation of motion into two parts and incorporating the kinematic equation by Wilson et al.
TL;DR: In this article, the authors considered the problem of bending a piano wire and bending the resulting ring so that the wire is held in some configuration described by an immersion of the circle into R3.
Abstract: 1. INTRODUCTION. One of the most classical topics in the Calculus of Varia- tions was proposed by James Bernoulli in 1691: The problem of the bent beam, elastic rod or simply elastica. This problem has to do with the following situation: join smoothly the ends of a piano wire and bend the resulting ring so that the wire is held in some configuration described by an immersion of the circle into R3. Now release the ring and suppose it moves so as to decrease its "bending energy". How does the wire evolve and what will happen ultimately as time goes to infinity? It was Daniel Bernoulli who suggested a model for an elastic rod in equilibrium. Following his model all kinds of elastica should minimize total squared curvature functional, F (also called bending energy functional) among curves of the same length and first order boundary data. In 1743, Euler determined all forms the plane elastic rods may take (see (T) for details). Recently Bryant-Griffiths (BG) and Langer-Singer (LS1, 2), have generalized the notion of elastica and studied them from a geometrical point of view. An elastica is a curve in a Riemannian manifold which is a critical point for FA(^y) = I(k2 + A), where k is the geodesic curvature of Sy, A is real number and Sy is supposed either to be closed or to satisfy given first order boundary data. Geometrically the closed elastica and their global behavior have special interest. In his analysis of the plane elasticae, Euler had already described the closed plane elastica: The circle and the
TL;DR: The stochastic Bernoulli equation with nonlinearly coupled dichotomous noise is exactly solved by direct averaging and the evolution of the mean value from the initial states located close to the equilibrium state is found to be nonmonotonic.
Abstract: The stochastic Bernoulli equation with nonlinearly coupled dichotomous noise is exactly solved by direct averaging. The similar system driven by the periodic perturbation with a random phase is also considered. The results concerning the kinetic and stationary properties in both cases are compared. The evolution of the mean value from the initial states located close to the equilibrium state is found to be nonmonotonic.
TL;DR: In a cycle of Bernoulli servers in discrete time the equilibrium distribution for a customer's round-trip time is shown to be of product-form and is given in explicit formulas.
Abstract: In a cycle of Bernoulli servers in discrete time the equilibrium distribution for a customer's round-trip time is shown to be of product-form and is given in explicit formulas. The results are used to obtain the equilibrium flow time distribution for an open tandem of queues.
Journal Article•
TL;DR: In this paper, the second law of thermodynamics and the generalized engineering Bernoulli equation (GEBE) are derived from the Cauchy momentum equations and a combined equation by subtracting the two is derived which is referred to as the mechanoenergy balance.
Abstract: In this work we thoroughly explore the meanings of dissipation (sometimes referred to as viscous dissipation) and stress power. To do this we utilize the Cauchy momentum equations and the first and second laws of thermodynamics. First, the generalized engineering Bernoulli equation (GEBE) is derived from the Cauchy momentum equations and it is clearly shown to have nothing to do with a balance of energy. Next, the first law of thermodynamics or energy balance is discussed and a combined equation by subtracting the two is derived which we refer to as the mechanoenergy balance (sometimes referred to as the ‘‘equation of thermal energy’’). The fact that a difference exists further reinforces that the GEBE is not related to a balance of energy. Finally, the second law of thermodynamics is presented and the concept of dissipation introduced. An example is presented to demonstrate the utility of these equations which will hopefully eliminate some confusion in the literature.
Book•
29 Aug 1996
TL;DR: In this paper, Newton's Laws are applied to Rotating bodies to measure acceleration and momentum acceleration in a two-dimensional (2D) model of a force and its interaction with other forces.
Abstract: PROBLEM SOLVING AND BASICS Aims Mechanical Engineering Problem Solving Drawing a Diagram Newton's Laws Units MOTION OF BODIES Aims Introduction to Motion Equations of Motion Falling Bodies Relative Velocity Angular Motion NEWTON'S LAWS, IMPULSE, AND MOMENTUM Aims Newton's Laws Newton's Laws Applied to Rotating Bodies Impulse and Momentum STATICS Aims Statics Vector Representation of a Force (Two-Dimensional) Equilibrium Analysis of Forces Moments Contact Forces WORK, ENERGY, AND POWER Aims Work Energy Power DRY FRICTION Aims Introduction to Friction Lubrication and fluid Friction Stiction Friction on a Horizontal Plane Friction on an Inclined Plane Application of Friction to a Screw Thread INTRODUCTION TO VIBRATIONS AND SIMPLE HARMONIC MOTION Aims Introduction to Vibration Harmonic Motion Simple Harmonic Motion Calculation of Natural Frequency Glossary of Terms STRESSES AND STRAINS Aims Behaviour of materials Direct Loading Factor of Safety Thin Cylinders Lateral Strain Shear Loading LOADING OF BEAMS Aims Simply Supported Beams and Cantilevers Sign Conventions Shear Forces and Shear Force Diagrams Bending Moments and Bending Moment Diagrams The Principle of Superposition The Significance of Bending Moments Shear Force and Bending Moment Diagrams STRESSES IN BEAMS AND SHAFTS Aims Beams and Shafts Bending of Beams Theory of Bending Second Moment of Area Stresses in Circular Shafts THERMOFLUID SITUATIONS Aims Thermofluid Mechanics Fluids Pressure Pressure Measurement Closed Thermofluid System Closed System Undergoing a Cycle PROPERTIES OF FLUIDS Aims Properties to be Considered Ideal Gases Specific Heats of Gases Non-Flow Processes for an Ideal Gas Liquids and Vapours Use of Vapour Tables STEADY FLOW OF FLUIDS Aims Open Thermofluid System Continuity Equation Momentum Equation Energy Equation Steady Flow Thermofluid Devices The Steady Flow Energy Equations as a Rate Equation Bernoulli's Equation Flow Measurement FLOW WITH FRICTION Aims Limitations of Frictionless Flow Viscosity Journal Bearing Flow Behaviour with Friction Reynolds Number Pressure Drop in Pipes Flow in Pipeline Systems BASIC HEAT TRANSFER Aims Modes of Heat Transfer Overall Heat Transfer Coefficient Thermal Resistance APPENDICES Mechanical Properties of Metals Second Moment of Area of a Rectangle Saturated Water-Steam Properties Superheated Steam Properties Answers References and Suggested Reading INDEX Each chapter also contains Summary and Problems sections.