2011
DOI: 10.1088/0143-0807/32/2/022
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The Bernoulli equation in a moving reference frame

Abstract: Unlike other standard equations in introductory classical mechanics, the Bernoulli equation is not Galilean invariant. The explanation is that, in a reference frame moving with respect to constrictions or obstacles, those surfaces do work on the fluid, constituting an extra term that needs to be included in the work-energy calculation. A quantitative example is presented here for a horizontal tapered pipe. A frame-independent expression for the pressure drop in the pipe is obtained. The concepts discussed in t… Show more

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Cited by 13 publications
(8 citation statements)
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(11 reference statements)
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“…Bernoulli's equation has become one of the most important theories in fluid dynamics with wide variety of applications in many areas of science and engineering [18]. The formulation in its original form is only applicable to viscous fluid and it is non-Galilean invariant [19,20,21,22]. Bernoulli's equation in energy form,…”
Section: Bernoulli's Equationmentioning
confidence: 99%
“…Bernoulli's equation has become one of the most important theories in fluid dynamics with wide variety of applications in many areas of science and engineering [18]. The formulation in its original form is only applicable to viscous fluid and it is non-Galilean invariant [19,20,21,22]. Bernoulli's equation in energy form,…”
Section: Bernoulli's Equationmentioning
confidence: 99%
“…The unsteady Bernoulli equation, supplemented by the abovementioned formulation of the stagnation pressure, yields the expression describing the pressure field inside the balloon, given in appendix A. It should be noted that Bernoulli equation holds only in a fixed reference frame (Mungan 2011). Therefore, (2.2) was formulated in terms of a fixed coordinate system, whose origin is located at the middle of the connection between the channel and the balloon, followed by returning to the original, non-inertial spherical system.…”
Section: Formulating the Flow Velocity Fieldmentioning
confidence: 99%
“…In mechanics, energy methods can be utilized to solve solid mechanics problems without differential equations. The concept of energy methods has been put forward by Huygens [1], Leibniz [2], Bernoulli [3], and Lagrange [4]. From the 19th century, the available approaches for structural engineers basically followed the energy principles and the equilibrium equation of forces as well as strain.…”
Section: Introductionmentioning
confidence: 99%