scispace - formally typeset

Bernoulli's principle

About: Bernoulli's principle is a(n) research topic. Over the lifetime, 4039 publication(s) have been published within this topic receiving 57236 citation(s). The topic is also known as: Bernoulli's equation. more


Open accessBook
20 Dec 2004-
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 more

Topics: Fluid mechanics (68%), Fluid dynamics (63%), Fluid parcel (61%) more

1,221 Citations

Open accessJournal ArticleDOI: 10.4249/SCHOLARPEDIA.4308
09 Jul 2009-Scholarpedia
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. more

Topics: Fourier series (58%), Superposition principle (55%), Nonlinear acoustics (52%) more

1,171 Citations

Journal ArticleDOI: 10.1016/J.IJENGSCI.2007.10.002
Shengli Kong1, Shenjie Zhou1, Zhifeng Nie1, Kai Wang1Institutions (1)
Abstract: The dynamic problems of Bernoulli–Euler beams are solved analytically on the basis of modified couple stress theory. The governing equations of equilibrium, initial conditions and boundary conditions are obtained by a combination of the basic equations of modified couple stress theory and Hamilton’s principle. Two boundary value problems (one for simply supported beam and another for cantilever beam) are solved and the size effect on the beam’s natural frequencies for two kinds of boundary conditions are assessed. It is found that the natural frequencies of the beams predicted by the new model are size-dependent. 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. more

Topics: Boundary value problem (58%), Beam (structure) (54%), Bernoulli's principle (53%) more

524 Citations

Journal ArticleDOI: 10.1017/S0370164600022070
01 Jan 1927-
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. more

Topics: Bernoulli differential equation (61%), Algebraic solution (61%), Bernoulli polynomials (58%) more

477 Citations

Open accessBook
16 Apr 2009-
Abstract: Stability.- Biology.- Bernoulli's equation.- Chemistry.- Mechanical vibrations.- Lasers.- Phase equations. more

470 Citations

No. of papers in the topic in previous years

Top Attributes

Show by:

Topic's top 5 most impactful authors

Taekyun Kim

20 papers, 308 citations

Yadollah Ordokhani

18 papers, 492 citations

Dae San Kim

18 papers, 109 citations

Hasan Bulut

9 papers, 159 citations

Parisa Rahimkhani

8 papers, 230 citations

Network Information
Related Topics (5)
Random variable

29.1K papers, 674.6K citations

90% related
Laplace transform

17.1K papers, 284.3K citations

89% related
Markov chain

51.9K papers, 1.3M citations

89% related
Probability theory

5.5K papers, 280.2K citations

88% related
Exponential function

12.6K papers, 197.1K citations

87% related