Showing papers on "Bernoulli's principle published in 1997"
Proceedings Article•
01 Jun 1997TL;DR: An historical review of the development of optimal control from the publication of the brachystochrone problem by Johann Bernoulli in 1696 can be found in this paper, where ideas on curve minimization already known at the time are briefly outlined.
Abstract: An historical review of the development of optimal control from the publication of the brachystochrone problem by Johann Bernoulli in 1696. Ideas on curve minimization already known at the time are briefly outlined. The brachystochrone problem is stated and Bernoulli's solution is given. Bernoulli's personality and his family are discussed. The article then traces the development of the necessary conditions for a minimum, from the Euler-Lagrange equations to the work of Legendre and Weierstrass and, eventually, the maximum principle of optimal control theory.
233 citations
Abstract: An historical review of the development of optimal control from the publication of the brachystochrone problem by Johann Bernoulli in 1696. Ideas on curve minimization already known at the time are briefly outlined. The brachystochrone problem is stated and Bernoulli's solution is given. Bernoulli's personality and his family are discussed. The article then traces the development of the necessary conditions for a minimum, from the Euler-Lagrange equations to the work of Legendre and Weierstrass and, eventually, the maximum principle of optimal control theory.
225 citations
Journal Article•
TL;DR: In this article, the implicit Neumann scheme for the interior and exterior Bernoulli's free-boundary problem has been proposed, and super linear convergence of a semi discrete variant is proved under a natural non-degeneracy condition.
Abstract: Bernoulli's free-boundary problem arises in ideal fluid dynamics, optimal insulation and electro chemistry. In electrostatic terms we design an annular condenser with a prescribed and an unknown boundary component such that the electrostatic field is constant in magnitude along the free boundary. Typically the interior Bernoulli problem has two Solutions, an elliptic one close to the fixed boundary and a hyperbolic one far from it. Previous results mainly deal with elliptic Solutions exploiting their monotonicity s discovered by A. Beurling. Hyperbolic Solutions are more delicate for analysis and numerical approximation. Nevertheless we derive a second order trial free-boundary method, the implicit Neumann scheme, with equally good performance for both types of Solutions. Super linear convergence of a semi discrete variant is proved under a natural non-degeneracy condition. Numerical examples computed by this method confirm analytic predictions including questions of uniqueness, connectedness, elliptic and hyperbolic limits. 1. Interior and exterior Bernoulli problem The interior Bernoulli problem is the following. Given a connected domain in (T and a constant Q > 0, find a subset A c Ω and a potential u: Ω\Α -* i such that -Δι/ = 0 in Ω\Α, u = Ο οη ΘΩ, u = l on dA , du „ Λ . — = on dA. ov The potential u lives on the domain Ω\Α, typically an annulus (Fig. 1). The exterior unit normal of this domain is denoted by v. In the classical setting the free-boundary condition means 166 (1) Flucher and Rumpf , Bernoulli's free-boundary problem
139 citations
TL;DR: In this paper, a theory for the determination of the effects of a flowing fluid on the vibration characteristics of an open, anisotropic cylindrical shell submerged and subjected simultaneously to an internal and external flow is presented.
91 citations
TL;DR: It is proved that the convolution of two ultra-logconcave sequences isUltra-log-conc Cave and implies that a natural negative dependence property is preserved under the operation of “joining” families of exchangeable Bernoulli random variables.
72 citations
TL;DR: In this article, the governing equations and boundary conditions of laminated beam-like components of smart structures are reviewed, and two mathematical models, namely the shear-deformable (Timoshenko) model and the Euler-Bernoulli model, are presented.
Abstract: In this paper, the governing equations and boundary conditions of laminated beamlike components of smart structures are reviewed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two mathematical models, namely the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model, are presented. The differential equations of the continuous system are approximated by utilizing finite element techniques for both models. A cantilever laminated beam with and without a tip mass is investigated to assess the validity and the accuracy of the two models when used for vibration suppression. Comparison between the two models is presented to show the advantages and the limitations of each of the models. Since the Timoshenko beam theory is higher order than the Euler Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio...
59 citations
Journal Article•
TL;DR: In this article, the governing equations and boundary conditions of laminated beam-like components of smart structures are reviewed, and two mathematical models, namely the shear-deformable (Timoshenko) model and the Euler-Bernoulli model, are presented.
Abstract: In this paper, the governing equations and boundary conditions of laminated beamlike components of smart structures are reviewed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two mathematical models, namely the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model, are presented. The differential equations of the continuous system are approximated by utilizing finite element techniques for both models. A cantilever laminated beam with and without a tip mass is investigated to assess the validity and the accuracy of the two models when used for vibration suppression. Comparison between the two models is presented to show the advantages and the limitations of each of the models. Since the Timoshenko beam theory is higher order than the Euler Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio...
58 citations
09 Jun 1997
TL;DR: In this paper, the collector current of the npn bipolar junction transistor (BJT) is shown to have the form of Bernoulli's general non-linear differential equation and this configuration is termed a Bernoull cell.
Abstract: In this paper a powerful analog circuit building block is identified, composed of a suitably biased npn bipolar junction transistor (BJT) with a grounded capacitor connected to the emitter. The collector current of the BJT is shown to have the form of Bernoulli's general non-linear differential equation and this configuration is termed a Bernoulli cell. By means of a suitable change of variables, Bernoulli's equation may be converted to a linear form and hence the Bernoulli cell can be exploited as a basic element for the synthesis of linear circuits.
54 citations
TL;DR: In this paper, the authors used the Bernoulli equation to predict elongation flow properties of a polymer melt and polymer solution, and showed that Cogswell's technique is adequate at high elongation rates.
Abstract: The minimisation technique proposed by Binding (J. Non-Newtonian Fluid Mech., 27 (1988) 173) was used in our Generalised Engineering Bernoulli Equation framework to relate the entry pressure and stress power. We arrived at a final result similar to Binding's using assumed kinematics. Through subsequent assumptions to the kinematics we finally arrive at a result exactly equivalent to Cogswell's technique (Trans. Soc. Rheol., 16 (1972) 383). Thus, these two techniques are related in this general framework. The techniques were used to predict elongation flow properties of a polymer melt and polymer solution. The results for the polymer melt clearly show Cogswell's technique is adequate at high elongation rates. All these techniques require minimisation of the stress power with respect to the flow volume and discussion is given as to the validity of this minimisation technique. In addition, the approximate variational technique we propose gives clears limits as to when a technique, such as Cogswell's, can be applied.
47 citations
TL;DR: In this article, the problem of finding the minimum-time path of a particle between two points in a uniform gravitational field when motion of the particle is resisted by a force proportional to the normal force exerted on the particle by the path is formulated as a singular control problem.
Abstract: This paper formulates and solves in closed form the problem of finding the minimum-time path of a particle between two points in a uniform gravitational field when motion of the particle is resisted by a force proportional to the normal force exerted on the particle by the path. This resistance to motion is the common mathematical form for Coulomb friction. The problem solution involves the reformulation of the classical brachistochrone of Bernoulli in terms of a singular control problem in which the time derivative of the heading angle of the particle is the control parameter. As such, this solution provides a unique approach to the solution of minimum-time path problems.
45 citations
TL;DR: In this paper, it was shown that the T, T -1-process is not Bernoulli when α ≥ 2, and it is not weak when 3/2 ≤ α < 2 and 1 < α < 3 2.
Abstract: Consider a general random walk on ℤd together with an i.i.d. random coloring of ℤd. TheT, T
-1-process is the one where time is indexed by ℤ, and at each unit of time we see the step taken by the walk together with the color of the newly arrived at location. S. Kalikow proved that ifd = 1 and the random walk is simple, then this process is not Bernoulli. We generalize his result by proving that it is not Bernoulli ind = 2, Bernoulli but not Weak Bernoulli ind = 3 and 4, and Weak Bernoulli ind ≥ 5. These properties are related to the intersection behavior of the past and the future of simple random walk. We obtain similar results for general random walks on ℤd, leading to an almost complete classification. For example, ind = 1, if a step of sizex has probability proportional to l/|x|α
(x ⊋ 0), then theT, T
-1-process is not Bernoulli when α ≥2, Bernoulli but not Weak Bernoulli when 3/2 ≤α < 2, and Weak Bernoulli when 1 < α < 3/2.
TL;DR: A low-level large-signal continuous-time operator, governed by the Bernoulli nonlinear differential equation is proposed, and is shown to formalise in a convenient manner, signal-processing in the log-domain.
Abstract: A low-level large-signal continuous-time operator, governed by the Bernoulli nonlinear differential equation is proposed. This cell consists of a suitably biased bipolar junction transistor and an emitter-connected grounded capacitor, and is shown to formalise in a convenient manner, signal-processing in the log-domain.
TL;DR: In this paper, a finite element formulation of finite deformation static analysis of plane elastic-plastic frames subjected to static loads is presented, in which the only function to be interpolated is the rotation of the centroid axis of the beam.
Abstract: The equation of the vibrating beam, together with some appropriate boundary conditions, can be viewed as an eigenvalue problem for the operator L given by where the functions a and are strictly positive, and correspond to physical characteristics of the beam. In this work we examine how a given spectral datum determines whether If this equation holds, L becomes a `perfect square'.
TL;DR: In this article, a nonlinear problem for an Euler - Bernoulli beam with an adaptive stiffness is formulated on the basis of maximal energy flux criteria, and the technique of direct separation of fast and slow motion coupled with a Green function method is used to analyse the dynamics of the beam with high-frequency modulation of the stiffness.
Abstract: The dynamics of an Euler - Bernoulli beam with a time- and space-dependent bending stiffness is studied. The problem is considered in connection with the application of noise control using smart structures. It is shown that an effective control for the vibrations of the beam can be achieved by varying the bending stiffness. A nonlinear problem for the beam with an adaptive stiffness is formulated on the basis of maximal energy flux criteria. The technique of direct separation of fast and slow motion coupled with a Green function method is used to analyse the dynamics of the beam with high-frequency modulation of the stiffness. By means of such a modulation, it is demonstrated that the radiation frequency can be tuned away from the sound range thus improving substantially the acoustical properties of the structure.
TL;DR: In this paper, a single server two-queue model with Bernoulli schedules is analyzed and a Riemann boundary value problem with shift is solved by exploring a Fredholm integral equation around the unit circle.
Abstract: In this paper we analyze a single server two-queue model with Bernoulli schedules. This discipline is very flexible and contains the exhaustive and 1-limited disciplines as special cases. We formulate the queueing system as a Riemann boundary value problem with shift. The boundary value problem is solved by exploring a Fredholm integral equation around the unit circle. Some numerical examples are presented at the end of the paper.
TL;DR: In this article, a simple procedure for finding a small-sample confidence interval with minimum interval width is given, and a geometric interpretation of the minimization problem is also given for Bernoulli and Poisson distributions.
Abstract: To find an interval estimate for the parameter of the Bernoulli or the Poisson distribution usually requires the sample size to be large so that the normal approximation may be used. Small-sample intervals have been proposed earlier, but the procedures have required tables and are inexact. In this note we give a simple procedure for finding a small-sample confidence interval with minimum interval width. We also give a geometric interpretation to the minimization problem.
TL;DR: In this article, the authors construct smooth surfaces with ergodic, and indeed Bernoulli, geodesic flow that are isometrically embedded in R3, and these surfaces can have arbitrary genus and can be made analytic.
Abstract: Following ideas of Osserman, Ballmann and Katok, we construct smooth surfaces with ergodic, and indeed Bernoulli, geodesic flow that are isometrically embedded in R3. These surfaces can have arbitrary genus and can be made analytic.
TL;DR: In this paper, a notion of weak Bernoulli in all dimensions was proposed, which generalizes the usual definition in dimension 1. The key idea is the concept of a coupling surface.
Book•
13 Nov 1997
TL;DR: In this paper, the Bernoulli Equation is used to describe the energy and pressure of a flow of viscous fluid in a pipeline, as a function of temperature (SI Units).
Abstract: 1 Introduction to Fluid Mechanics 2 Properties of Fluids 3 Fluids at Rest: Pressure Considerations 4 Fluids at Rest: Force Considerations 5 Fluids in Motion: The Bernoulli Equation 6 Fluids in Motion: The Energy Equation 7 Flow of Viscous Fluids in Pipelines 8 Series and Parallel Piping Systems 9 Open Channel Flow 10 Forces Due to Change in Fluid Motion 11 Pumps: Operating Features and Applications 12 Gas Flow: Fans, Blowers, and Compressors 13 Flow Over Immersed Bodies: Drag and Lift Appendix A Properties of Water Appendix B Properties of Air Appendix C Dynamic Viscosity of Common Fluids as a Function of Temperature (SI Units) Appendix D Kinematic Viscosity of Common Fluids (at Atmospheric Pressure) as a Function of Temperature (SI Units) Appendix E Unit Conversion Factors Appendix F References Appendix G Answers to Selected Odd-Numbered Exercises Index
TL;DR: In this article, a distributed parameter system consisting of two Euler-Bernoulli beams coupled in parallel is considered and it is shown that the system is uniformly exponentially stabilizable by an appropriate application of either distributed or boundary control.
Abstract: A distributed parameter system consisting of two Euler-Bernoulli beams coupled in parallel is considered. It is shown that the system is uniformly exponentially stabilizable by an appropriate application of either distributed or boundary control. Strong stability is also established in both cases, although in the case of boundary control, the strong stability result is only proved for the situation in which both beams have identical dynamics.
TL;DR: In this paper, the authors considered steady potential hydrodynamic-Poisson systems with a dissipation term (viscosity) proportional to a small parameter v in a two- or three-dimensional bounded domain.
Abstract: We consider steady potential hydrodynamic-Poisson systems with a dissipation term (viscosity) proportional to a small parameter v in a two- or three-dimensional bounded domain. We show here that for any smooth solution of a boundary value problem which satisfies that the speed, denoted by |∇φ v |, has an upper coarse bound , uniform in the parameter v , then a sharper, correct uniform bound is obtained: the viscous speed |∇φ v | is bounded pointwise, at points x 0 in the interior of the flow domain, by cavitation speed (given by Bernoulli's Law at vacuum states) plus a term of that depends on . The exponent is β = 1 for the standard isentropic gas flow model and β = 1/2 for the potential hydrodynamic Poisson system. Both cases are considered to have a γ-pressure law with 1 In addition, we consider a two-dimensional boundary value problem which has been proved to have a smooth solution whose speed is uniformly bounded. In this case, we show that the pointwise sharper bound can be extended to the section of the boundary ∂Ω\∂ 3 Ω, where ∂ 3 Ω is called the outflow boundary. The exponent β varies between 1 and 1/8 depending on the location of x 0 at the boundary and on the curvature of the boundary at x 0 . In particular, our estimates apply to classical viscous approximation to transonic flow models.
TL;DR: Bernoulli's tree as mentioned in this paper is a binary tree generated by simple arithmetic operations that can be used to generate the Bernoulli numbers, i.e., the even numbered B's.
Abstract: which defines just the even numbered B's. Bernoulli numbers appear in connection with a variety of topics, including sums of powers of integers and the Riemann zeta function. In this note we display a binary tree generated by simple arithmetic operations that can be used to generate the Bernoulli numbers. We call the tree Bernoulli's tree. Each node of Bernoulli's tree is an expression of the form + l/a!b!.... Two operations, 00 and 01, are applied to a node to generate the node's children. The operations are defined as follows
TL;DR: Pressure recovery has been well demonstrated to exist in a variety of pathophysiological states and interpretation of the flow velocity across the valve might make the difference between recommendations to replace or to retain the valve.
Abstract: The Bernoulli equation relates the pressure exerted on a fluid to its flow velocity and its density, in addition to its flow acceleration and its viscous friction loss. When flow velocity increases at a narrowing, the local pressure decreases proportionally. It has been wrongfully assumed that pressure lost distal to a stenosis can never recover. It is, however, the energy content of the fluid, equal to the kinetic plus the potential energy, which can not increase. When flow slows distal to a narrowing and little energy is lost to friction, pressure does actually increase. Pressure recovery has been well demonstrated to exist in a variety of pathophysiological states. Bicuspid aortic valve prostheses such as the St. Jude valves can produce quite remarkable pressure recovery. This causes a great discrepancy between pressure drop calculations based on continuous wave doppler on the one hand and true pressure drop across the prosthesis on the other. Reliance on doppler measurements only might wrongfully lead one to conclude that the prosthesis was malfunctioning. Less extreme pressure recovery is possible across a stenotic native aortic valve, but interpretation of the flow velocity across the valve might make the difference between recommendations to replace or to retain the valve. When interpreting doppler signals across narrowings the phenomenon of pressure recovery should be kept in mind.
04 Jun 1997
TL;DR: In this paper, the authors derived the nonlinear integro-differential equations describing the transverse and rotational motions of a nonuniform Euler-Bernoulli beam with end mass attached to a rigid hub, and investigated the effects of both the linear and nonlinear elastic rotational couplings.
Abstract: The nonlinear integro-differential equations, describing the transverse and rotational motions of a nonuniform Euler-Bernoulli beam with end mass attached to a rigid hub, are derived. The effects of both the linear and nonlinear elastic rotational couplings are investigated. The linear couplings are exactly accounted for in a decoupled Euler-Bernoulli beam model and their effects on the eigensolutions and response are significant for a small ratio of hub-to-beam inertia. The nonlinear couplings with a resultant stiffening effect are negligible for small angular velocities. A discretized model, suitable for the study of large angle, high speed rotation of a nonuniform beam, is presented. The optimal control moment for simultaneous vibration suppression of the beam at the end of a prescribed rotation is determined. Influences of the nonlinearity, nonuniformity, maneuvering time, and inertia ratio on the optimal control moment and system response, are discussed.
TL;DR: In this paper, an inverse method which starts with assuming a displacement function is used to solve structural problems, and the rigorous solution is obtained by requiring all fundamental relations to be satisfied which uniquely determines unknown constants in the displacement function.
TL;DR: In this article, the inclination of this line relative to the bisector of the two colliding streams is expressed as a function of the parameters of the incoming streams, and it is shown that the angle between the jet and the incoming stream supplying momentum at the greater rate increases with the size of the angle, until it reaches a maximum value.
Abstract: A particular problem in the field of shaped charge jet formation modeling concerns the collision of two fluid streams of different widths and speeds. It is commonly assumed that the flow is incompressible, and that the velocity of the fluid in any of the streams is constant across and normal to its cross section. Then the well-known classically indeterminate mathematical problem arises. In the shaped charge context the indeterminacy of the problem has been addressed by making three assumptions about the flow. Several models have assumed that conservation of kinetic energy holds, and have applied Bernoulli’s Law to equate the speeds of the jet and slug in a frame moving with the collision point. One natural choice for the third and final assumption is that the jet and slug lie in a straight line when viewed in this frame, the so-called straight line hypothesis. In this article the inclination of this line relative to the bisector of the two colliding streams is expressed as a function of the parameters of the incoming streams. It is shown that the angle between the jet and the incoming stream supplying momentum at the greater rate increases with the size of the angle between the incoming streams until it reaches a maximum value. It then decreases to zero. It is known that the straight line hypothesis is a good approximation for low values of the angle between the incoming streams, but becomes increasingly inaccurate as this angle increases. The above maximum appears to correspond to the limit of validity of the straight line hypothesis. Recommendations for the utilization of the existing formation models to achieve best accuracy are made, based on this limit.
Patent•
24 Sep 1997
TL;DR: In this article, the utility model of a bernoulli equation experimental apparatus is characterized in that the water can be circularly utilized through an overflow device (1, 2, 3, 3-1), a submersible pump (17), and a water supply pipe (18).
Abstract: The utility model relates to a bernoulli equation experimental apparatus, belonging to the field of the physics educational apparatus. The utility model is characterized in that the water can be circularly utilized through an overflow device (1, 2, 3, 3-1), a submersible pump (17) and a water supply pipe (18). A correction horizontal regulating screw (16), a voltage stabilizing water tank (4) which can discretionally regulate the water level, a flow guiding tube for precisely correcting the zero position of the water level potential energy and an optional supporting post (10) are arranged on a marble pedestal (13) to enhance the accuracy of the experiment. Simultaneously, the utility model is convenient to assemble and disassemble.