Showing papers on "Bernoulli's principle published in 1983"

Variational Principles in Mechanics

Abstract: The recognition that minimizing an integral function through variational methods (as in the last chapters) leads to the second-order differential equations of Euler-Lagrange for the minimizing function made it natural for mathematicians of the eighteenth century to ask for an integral quantity whose minimization would result in Newton’s equations of motion. With such a quantity, a new principle through which the universe acts would be obtained. The belief that “something” should be minimized was in fact a long-standing conviction of natural philosophers who felt that God had constructed the universe to operate in the most efficient manner—but how that efficiency was to be assessed was subject to interpretation. However, Fermat (1657) had already invoked such a principle successfully in declaring that light travels through a medium along the path of least time of transit. Indeed, it was by recognizing that the brachistochrone should give the least time of transit for light in an appropriate medium that Johann Bernoulli “proved” that it should be a cycloid in 1697. (See Problem 1.1.) And it was Johann Bernoulli who in 1717 suggested that static equilibrium might be characterized through requiring that the work done by the external forces during a small displacement from equilibrium should vanish. This “principle of virtual work” marked a departure from other minimizing principles in that it incorporated stationarity—even local stationarity—(tacitly) in its formulation. Efforts were made by Leibniz, by Euler, and most notably, by Lagrange to define a principle of least action (kinetic energy), but it was not until the last century that a truly satisfactory principle emerged, namely, Hamilton’s principle of stationary action (c. 1835) which was foreshadowed by Poisson (1809) and polished by Jacobi (1848) and his successors into an enduring landmark of human intellect, one, moreover, which has survived transition to both relativity and quantum mechanics. (See [L], [Fu] and Problems 8.11 8.12.)

Internal Pressure of Multi‐Room Buildings

Abstract: The Bernoulli equation approach for predicting the variation of internal pressure induced by wind in a single‐room building with a single opening is extended to multi‐room buildings of any number of openings. Examples are given to illustrate this new general approach. The result shows that following the breakage of a windward window during a windstorm, the internal pressure of a multi‐room building oscillates in a manner similar to that in a set of interconnected Helmholtz oscillators.

On the general behavior of acceleration waves

Abstract: A systematic study is made of the general behaviour of solutions to the Bernoulli equation which governs the evolution of acceleration waves in nonlinear systems. The theorems obtained contain all the known results and, in some instances, when specialized to the case of an existing theorem they provide a sharper results obtained here for the Bernoulli equation, and the corresponding results for the propagation of weak discontinuity in a general quasilinear hyperbolic system

A Composite Velocity Procedure for the Incompressible Navier-Stokes Equations.

Abstract: A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Subsonic panel method for designing wing surfaces from pressure distribution

Abstract: An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Equal probability of correct selection for bernoulli selection procedures

Abstract: The problem of selecting the Bernoulli population which has the highest "success" probability is considered. It has been noted in several articles that the probability of a correct selection is the same, uniformly in the Bernoulli p-vector (P1,P2,….,Pk), for two or more different selection procedures. We give a general theorem which explains this phenomenon. An application of particular interest arises when "strong" curtailment of a single-stage procedure (as introduced by Bechhofer and Kulkarni (1982a) )is employed; the corresponding result for "weak" curtailment of a single-stage procedure needs no proof. The use of strong curtailment in place of weak curtailment requires no more (and usually many less) observations to achieve the same.

Strong approximation of very weak Bernoulli processes

Abstract: Very weak Bernoulli processes with values in a separable metric space are introduced. An estimate for the Prohorov distance in the central limit theorem is obtained. This estimate is used to establish a strong (almost sure) approximation of the partial sums of a very weak Bernoulli process by a Brownian motion where the error term is of the order O(t1/2−γ). The proofs are based on a new version of the Berkes-Philipp approximation theorem.

Calculation of afterbody flows with a composite velocity formulation

Abstract: A recently developed technique for numerical solution of the Navier-Stokes equations for subsonic, laminar flows is investigated. It is extended here to allow for the computation of transonic and turbulent flows. The basic approach involves a multiplicative composite of the appropriate velocity representations for the inviscid and viscous flow regions. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli equation for the pressure, while the continuity equation reduces to the familiar potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary layers. The velocity components are computed with a coupled strongly implicity procedure. For transonic flows the artificial compressibility method is used to treat supersonic regions. Calculations are made for both laminar and turbulent flows over axisymmetric afterbody configurations. Present results compare favorably with other numerical solutions and/or experimental data.

Codes and Bernoulli partitions

Abstract: We associate to a maximal codeX on an alphabetA a dynamical system Ω; our main result proves that the property of unique decipherability implies that the partition of Ω associated to the letters ofA is a Bernoulli partition. Surprisingly it is possible to give two very different proofs of this result: the first one uses probability measures on monoids together with methods from automata theory; the other is based on results of entropy theory.

The first repetition of a pattern in a symmetric Bernoulli sequence

Abstract: In a symmetric sequence of Bernoulli trials we define each successive 1 outcomes as a pattern, and look at the first time that any pattern repeats. Asymptotic expressions, as 1-+oo, of the distribution and the expectation of this waiting time are derived. REPEATED PATTERNS; BIRTHDAY PROBLEM

Superpotential Solution for Jet-Engine External Potential and Internal Rotational Flow Interaction

Abstract: For flows with prescribed parallel shear far upstream, the vorticity generation term in the disturbance stream-function (Ψ) equation and the Bernoulli “constant,” both of which vary from stream surface to stream surface, are explicitly evaluated as power series in Ψ with curvature-dependent coefficients, for axisymmetric flows using some invariant properties of vorticity. By casting the linearized stream-function equation in conservation form, extended Cauchy-Reimann conditions are obtained, implying a “superpotential” φ* satisfying a “Laplace-like” equation useful for solving flows past prescribed shapes; the corresponding tangency and Kutta conditions, interestingly, take a “potential form,” so that simple changes to existing potential flow algorithms extend their applicability to strong oncoming shears with arbitrary curvature. The theory, which applies to duct flows behind actuator disks generating shear, is sketched for both “analysis” and “design” formulations; here, we address the interaction between external potential and internal rotational jet-engine flows occurring through both an assumed actuator disk and a trailing edge slipstream, and provide representative numerical calculations.

A mixing T for which T-T −1 is Bernoulli

Abstract: We show that if σ is the Bernoulli shift on sequences of {−1, 1} with equiprobable product measure andT is a suitable mixing entropy zero trnsformation then the skew product defined byS(x,y)=(σx,T x0 y) is Bernoulli.

Mixed flow of an ideal fluid on a plane containing a recess

Abstract: In the exact formulation, a study is made of the solution to the problem of the flow of an ideal incompressible fluid on a flat surface in a recess in the form of a half-cylinder in the direction at right angles to the flow. In the recess, the flow is assumed to have uniform vorticity, while in the exterior unbounded flow it is irrotational. On the separating streamline, the Bernoulli constant has a discontinuity of a given magnitude.

Bernoulli effect and contact potential difference in superconductors

Abstract: An expression is derived for the Bernoulli potential that arises in superconductors with an inhomogeneous current distribution. The expression is valid for arbitrary temperatures and superfluid velocities. In the superconductor--dielectric--superconductor system we consider the Bernoulli effect, which manifests itself in a contact potential difference between the superconductors. The potential difference is determined by the currents flowing through one plate of the contact and can be measured with a voltmeter in the quasi-stationary regime.

Bayes, Bernoulli, and BEIR

Abstract: Bayes's paper represents the first attempt to quantify to what degree repeated experiments confirm a hypothesis. In his essay, Bayes defines the problem as follows: \"Given the number of times in which an unknown event has happened and failed: Re¬ quired the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named.\" Stated in modern language, Bayes asks the scientist to quantify his personal knowledge about an unknown event on the basis of past experience or the lack of it in the form of a \"prior\" distribution of characteristic parameters. \"Prior\" simply means that the analyst uses information available before a particular experiment. \"Distribution\" indicates that each parameter used to characterize a phenomenon, instead of having a single value, is assigned various values, each with a certain pro¬ bability. For example, we might say that the rate of core damage accidents in reactors instead of being a single definite number (like 1 accident per 1000 reactor years) can assume different values within a certain range, and each of these values is assigned a different probability.