Experimental study of Bernoulli’s equation with losses

Saleta, M. E.; Tobia, Dina; Gil, Salvador

doi:10.1119/1.1858486

Cited by 39 publications

(32 citation statements)

References 7 publications

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“…This result was recently questioned [2] [3] in the light of experimental evidence that at any nonzero h the average discharge velocity is zero. The reason is that Bernoulli's equation, which is a macroscopic mechanical balance of energy of an ideal, non-viscous liquid, cannot strictly be applied in the case of real flow due to the various dissipation effects [4] [5], which Equation (1) does not include.…”

Section: Introductionmentioning

confidence: 98%

“…These two effects have to be considered together, therefore we have ( ) 3 A V r γ γ ∂ ∂ = . However, since the shape of the jet is not a perfect cylinder, we introduce in this expression the shape factor 1…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The reason is that Bernoulli's equation, which is a macroscopic mechanical balance of energy of an ideal, non-viscous liquid, cannot strictly be applied in the case of real flow due to the various dissipation effects [4] [5], which Equation (1) does not include. Nevertheless, taking into account the energy losses, Bernoulli's equation was used [3] to modified Equation (1) as follows:…”

Section: Introductionmentioning

confidence: 99%

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Experimental Evidence of Capillary Interruption of a Liquid Jet

Massalha¹,

Digilov²

2014

OJAppS

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We observe the gravity discharge of liquid through the short cylindrical tube of diameter of 2 mm and aspect ratio 2.5 and 10 attached to the underside of Mariotte bottle. When the hydrostatic head is reduced and approaches to a certain value, a laminar jet escaped from the nozzle is interrupted and the discharge is drop wise. The plot of the discharge rate as a function of hydrostatic head does not pass through the origin as predicted by Torricelli law for an ideal liquid. We attribute this feature to the energy losses related with creating a new free surface area of the jet. The measurements for water and aqueous ethanol solution are compared with theoretical predictions based on the modified Bernoulli equation with the interfacial energy density correction and good agreement is observed.

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Section: Introductionmentioning

confidence: 98%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Experimental Evidence of Capillary Interruption of a Liquid Jet

Massalha¹,

Digilov²

2014

OJAppS

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“…The topic was chosen because it potentially brings out students misconceptions regarding to the width of container used [4]. The form of Torricelli principle is described as a cylindrical container filled by water and it has a small leakage in its wall.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Torricelli Effluent Flow by Using Visual Basic for Application (VBA) on Microsoft Excel

Fajar¹,

Kurniasih²,

Khairurrijal³

2015

Advances in Social Science, Education and Humanities Research

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-Simulation of Torricelli effluent flow was created by using Visual Basic for Application (VBA) on Microsoft Excel. It describes a container with a cross sectional area A 1 filled by water with a certain level h 1 . At the container's wall, there is a small leakage with a leakage height h 2 and a cross sectional area A 2 . If the quantity of water in the container is very large (A 1 >> A 2 ), the speed of water is constant, and the effluent distance of water out from leakage (x) can be simply determined by applying the Bernoulli principle, the equation of continuity, and the formula of free-fall motion. However, if the cross sectional area of container is proportional to the leakage's cross sectional area, then the speed of effluent water decreases with time and the formula of effluent distance is revisited. The simulation program was generated by the Euler method and analytical calculation. The manipulated variables are water level, leakage height, buffer height, container cross sectional area, and leakage cross sectional area. The simulation presents idealized condition by ignoring the air resistance, adhesion force, and surface tension of water so that it deviates from experimental results.

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“…In another paper 5 , an experiment is suggested to demonstrate the importance of considering viscous effects for real fluids (such as water draining out of a cylindrical vessel). In this case, the analysis is so particular that it cannot be applied to other flow situations.…”

Section: In Contrast With Bernoulli's Equation Pressure Losses Due Tmentioning

confidence: 99%

Bernoulli correction to viscous losses: Radial flow between two parallel discs

Armengol

Calbó

Pujol

et al. 2008

American Journal of Physics

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For a massless fluid (density = 0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first order in density. This method has been applied to the particular case of a duct, defined by two plane-parallel discs. For this case, the first-order approximation results in a simple analytical solution which has been favorably checked against numerical simulations. Finally, an experiment has been carried out with water flowing between the discs. The experimental results show good agreement with the approximate solution.2

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Experimental study of Bernoulli’s equation with losses

Cited by 39 publications

References 7 publications

Experimental Evidence of Capillary Interruption of a Liquid Jet

Experimental Evidence of Capillary Interruption of a Liquid Jet

Simulation of Torricelli Effluent Flow by Using Visual Basic for Application (VBA) on Microsoft Excel

Bernoulli correction to viscous losses: Radial flow between two parallel discs

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