Liquid oscillations in a U-tube

Aguilar, Horacio Munguía; Maldonado, Rigoberto Franco; Navarro, Luis Barba

doi:10.1088/1361-6552/aa8d21

Cited by 3 publications

(6 citation statements)

References 3 publications

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“…which is incorrect except at the instant when the free surfaces pass through the equilibrium level 4 so that y A = 0 = y B . (The pressure difference between points A and B is always zero, in contrast to what Hageseth claims [11][12][13].) Equation ( 1) reduces to the familiar formula for the variation in hydrostatic pressure with depth and so it should not be surprising that it does not apply to a dynamically oscillating liquid column.…”

Section: Analytic Solution For a U-tube Of Uniform Cross-sectional Areamentioning

confidence: 98%

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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: Analytic Solution For a U-tube Of Uniform Cross-sectional Areamentioning

confidence: 98%

“…According to equation(12), the acceleration of the fluid is zero at that instant and so the unsteady Bernoulli equation happens to reduce to equation (1) as the free surfaces pass through their equilibrium positions.…”

mentioning

confidence: 99%

Liquid oscillating in a U-tube of variable cross section

Mungan¹,

Sheldon-Coulson²

2021

Eur. J. Phys.

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“…A first approximation of the motion described by the fluid in a U-tube is given by considering only gravity and the so-called viscous frictional resistance between the fluid and the walls of the tube and neglecting the surface tension force at the upper surface of the liquid [13]. In this case, the total force on a small element of liquid ∆m is caused by the weight (see figure 1) and the damping term, parameterized by b, that can be described as proportional to the velocity 8 .…”

Section: Theoretical Descriptionmentioning

confidence: 99%

“…In this case, the total force on a small element of liquid ∆m is caused by the weight (see figure 1) and the damping term, parameterized by b, that can be described as proportional to the velocity 8 . The equation of motion can be written as follows [13] ρSL…”

Section: Theoretical Descriptionmentioning

confidence: 99%

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A comprehensive modelling and experimental approach for damped oscillations in U-tubes via Easy JavaScript Simulations

Orjuela,

García-Farieta,

Hortúa

et al. 2023

Phys. Educ.

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In recent years, science simulations have become popular among educators due to their educational usefulness, availability, and potential for increasing the students’ knowledge on scientific topics. In this paper, we introduce the implementation of a user-friendly simulation based on Easy Java/JavaScript Simulations (EJS) to study the problem of damped oscillations in U-tubes EJS. Furthermore, we illustrate various advantages associated with the capabilities of EJS in terms of design and usability in order to encourage teachers to use it as an educational supplement to physics laboratories .

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A generalized mathematical model for the damped free motion of a liquid column in a vertical U-tube

Kannaiyan,

Sarno

et al. 2024

Physics of Fluids

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A one-dimensional mathematical model is developed to analyze the unsteady characteristics of arbitrary damped free motion, denoted as Z(τ), in a rigid, constant-diameter vertical column of a U-tube filled with an incompressible Newtonian liquid, where τ represents time. This model utilizes a simplified unsteady momentum equation derived from the Navier–Stokes equations in a circular coordinate system. Moreover, it incorporates assumptions about the periodicity of arbitrary damped free oscillations and employs the Fourier series representation to characterize the damped free motion. The combination of assumptions made for periodicity, the simplified momentum equation, and the Fourier series representation makes the current mathematical model unique and novel compared to prevailing models in the literature. In this model, the governing partial differential equation contains two dependent variables: Z(τ) is the known variable, as one can measure from experiments, and the instantaneous velocity uz is the unknown variable. Fitting the experimental data into the Fourier series provides the Fourier coefficients associated with the specific experiment. The Laplace transform method is used to determine the analytical solution for uz corresponding to the known Z(τ). The analytical expressions for instantaneous flow characteristics of practical importance, including area-averaged velocity, wall shear stress, and acceleration/deceleration, are deduced from uz. The analytical solutions presented are valid for generalized unsteady motions, including underdamped oscillations with varying amplitudes and periods, underdamped oscillations with varying amplitudes and constant period, and overdamped motion that does not exhibit a single oscillation. The findings from the present model offer insights for formulating a new friction model.

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Liquid oscillations in a U-tube

Cited by 3 publications

References 3 publications

Liquid oscillating in a U-tube of variable cross section

Liquid oscillating in a U-tube of variable cross section

A comprehensive modelling and experimental approach for damped oscillations in U-tubes via Easy JavaScript Simulations

A generalized mathematical model for the damped free motion of a liquid column in a vertical U-tube

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