Flow of A Liquid

Stephens, R.C.; Ward, James J.

doi:10.1007/978-1-349-00870-4_15

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“…Figure 1 depicts a U-tube whose cross-sectional area A[s] varies smoothly as a function of a coordinate s running counter-clockwise around the axis. (If the area changed discontinuously, then pressure and kinetic energy losses would occur due to turbulent eddies near those points, as is modeled using empirical coefficients [2][3][4]. In contrast, the flow in the present article is assumed to be everywhere laminar.)…”

Section: Description Of the U-tubementioning

confidence: 99%

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Liquid oscillating in a U-tube of variable cross section

Mungan¹,

Sheldon-Coulson²

2021

Eur. J. Phys.

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A liquid is set into oscillations in a vertical manometer of smoothly varying cross-sectional area open at both ends to the atmosphere. Ignoring viscous damping, the displacement of either free surface and the pressure at any point in the liquid can be calculated using the unsteady Bernoulli equation which is shown to be consistent with conservation of mechanical energy. If the cross section is constant, the equations are analytically solvable; simple harmonic motion is found for the surface displacement as a function of time, and the pressure variation as a function of depth is in accordance with Newton’s second law. More generally, however, numerical solution of the equations is necessary, as illustrated for the example of a U-tube whose radius is linearly tapered from one end to the other. The level of presentation is appropriate for an upper level undergraduate course in fluid mechanics.

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Section: Description Of the U-tubementioning

confidence: 99%

“…For example, at the instant shown in figure 1, s A = −y A and s B = L + y B . The amplitude of oscillation is assumed to be small enough that the free surfaces always remain in the vertical necks of the tube 3 . The pressure and (signed) velocity of the liquid at point P are denoted p and υ, respectively.…”

Section: Description Of the U-tubementioning

confidence: 99%

Liquid oscillating in a U-tube of variable cross section

Mungan¹,

Sheldon-Coulson²

2021

Eur. J. Phys.

View full text Add to dashboard Cite

show abstract

Flow of A Liquid

Cited by 1 publication

References 0 publications

Liquid oscillating in a U-tube of variable cross section

Liquid oscillating in a U-tube of variable cross section

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