Topic

# Bernoulli's principle

About: Bernoulli's principle is a research topic. Over the lifetime, 4039 publications have been published within this topic receiving 57236 citations. The topic is also known as: Bernoulli's equation.

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TL;DR: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.

Abstract: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c.560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered. This started the science of acoustics, a term coined by Joseph Sauveur (1653-1716) who showed that strings can vibrate simultaneously at a fundamental frequency and at integral multiples that he called harmonics. Isaac Newton (1642-1727) was the first to calculate the speed of sound in his Principia. However, he assumed isothermal conditions so his value was too low compared with measured values. This discrepancy was resolved by Laplace (1749-1827) when he included adiabatic heating and cooling effects. The first analytical solution for a vibrating string was given by Brook Taylor (1685-1731). After this, advances were made by Daniel Bernoulli (1700-82), Leonard Euler (1707-83) and Jean d’Alembert (1717-83) who found the first solution to the linear wave equation, see section (3.2). Whilst others had shown that a wave can be represented as a sum of simple harmonic oscillations, it was Joseph Fourier (1768-1830) who conjectured that arbitrary functions can be represented by the superposition of an infinite sum of sines and cosines now known as the Fourier series. However, whilst his conjecture was controversial and not widely accepted at the time, Dirichlet subsequently provided a proof, in 1828, that all functions satisfying Dirichlet’s conditions (i.e. non-pathological piecewise continuous) could be represented by a convergent Fourier series. Finally, the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt (Lord Rayleigh, 1832-1901) in his treatise Theory of Sound. The science of modern acoustics has now moved into such diverse areas as sonar, auditoria, electronic amplifiers, etc.

1,428 citations

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20 Dec 2004

TL;DR: This chapter discusses the development of flow systems for EES and some of the techniques used to develop these systems are currently used in the oil and gas industry.

Abstract: 1 Introduction and Basic Concepts2 Properties of Fluids3 Pressure and Fluid Statics4 Fluid Kinematics5 Bernoulli and Energy Equations6 Momentum and Analysis of Flow Systems7 Dimensional Analysis and Flow Systems8 Flow in Pipes9 Differential Analysis of Fluid Flow10 Approximations of the Navier-Stokes Equation11 Flow Over Bodies: Drag and Lift12 Compressible Flow13 Open-Channel Flow14 Turbomachinery15 Computational Fluid Dynamics (CFD)Appendices1 Property Tables and Charts (SI Units)2 Property Tables and Charts (English Units)3 Introduction to EES

1,257 citations

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TL;DR: In this article, the dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of modified couple stress theory and Hamilton's principle, and the difference between the natural frequencies predicted by the newly established model and classical beam model is very significant when the ratio of characteristic sizes to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio.

560 citations

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01 Jan 1927

TL;DR: In this paper, the authors extend Bernoulli's method to evaluate all the roots of an algebraic equation, whether real, complex, or repeated, by an arithmetical process well adapted to mechanical computation, and without any preliminary determination of the nature or position of the roots.

Abstract: The aim of the present paper is to extend Daniel Bernoulli's method of approximating to the numerically greatest root of an algebraic equation. On the basis of the extension here given it now becomes possible to make Bernoulli's method a means of evaluating not merely the greatest root, but all the roots of an equation, whether real, complex, or repeated, by an arithmetical process well adapted to mechanical computation, and without any preliminary determination of the nature or position of the roots. In particular, the evaluation of complex roots is extremely simple, whatever the number of pairs of such roots. There is also a way of deriving from a sequence of approximations to a root successive sequences of ever-increasing rapidity of convergence.

522 citations

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29 Oct 2012TL;DR: The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem is answered positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret.

Abstract: The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.

521 citations