The Bernoulli equation in a moving reference frame

Mungan, Carl E.

doi:10.1088/0143-0807/32/2/022

Cited by 13 publications

(8 citation statements)

References 8 publications

(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%

The Study of Electrical Energy Consumption in Cascaded Pumps for Pipeline Operations

Audu

2021

JENRR

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Pumps are critical infrastructure in the Oil and Gas industry, and have been widely used in pipeline transportations of petroleum products. The electrical energy needed by a pump to meet the minimum pipeline operational requirement plays an important role in the overall cost and evaluation of pumping systems performance, which has become an important issue in pump energy management and pump station designs. This paper provides a quantitative and analytical method using Bernoulli’s equation for studying energy dependence between two pumps (Booster and Mainline pumps) in series within a pump station as a function of pump’s head, flow-rate, and density. Using actual parameters from a pump station, the derived equations are validated on four different products. The densities of products are 1000 kg/cm3, 835 kg/cm3, 800 kg/cm3 and 660 kg/cm3 for Water, Automotive Gas Oil (AGO), Dual Purpose Kerosene (DPK), and Premium Motor Spirit (PMS) respectively. The results show that the energy requirement of the Booster pump is determined by the energy demand of the Mainline pump as a function of flowrate, density and pump’s head. The study is essential for developing energy saving strategy in pipeline operations and in electrical consideration when selecting the right electric motors for pumps in pump station design.

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Section: Bernoulli's Equationmentioning

confidence: 99%

The Study of Electrical Energy Consumption in Cascaded Pumps for Pipeline Operations

Audu

2021

JENRR

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“…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%

On the inflation and deflation dynamics of liquid-filled, hyperelastic balloons

Ilssar

Gat

2020

Journal of Fluids and Structures

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We derive a reduced-order model describing the inflation and deflation dynamics of a liquid-filled hyperelastic balloon, focusing on inviscid laminar flow and the extensional motion of the balloon. We initially study the flow and pressure fields for dictated motion of the solid, which throughout deflation are obtained by solving the potential problem. However, during inflation, flow separation creates a jet within the balloon, requiring a different approach. The analyses of both flow regimes lead to a simple piecewise model, describing the fluidic pressure during inflation and deflation, which is then verified by finite element computations. We then use a variational approach to derive the equation governing the balloon's dynamics, yielding a nonlinear hybrid oscillator equation, describing the interaction between the extensional mode of the balloon, and the entrapped fluid. Analytical and graphical investigations of the suggested model are presented, shedding light on its static and dynamic behaviour under different operating conditions. Our suggested model and its underlying assumptions are verified utilizing a fully coupled finite element scheme, showing excellent agreement.

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“…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%

Applications of common energy variability methods for establishing the equilibrium equation in mechanics

Dao,

Mai

2023

IOP Conf. Ser.: Mater. Sci. Eng.

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The principles of the energy variation method are commonly utilized in mechanics. Energy is a scalar variable, so these are more convenient and simple to establish the equilibrium equations compared to vector-based approaches (i.e. using forces and displacements). The present article applied the theorem of the energy variation method in order to set the equilibrium equations for various complicated problems. Four examples of applying the energy variation method include the differential equation of the Euler – Bernoulli beam based on the energy method, the system of Equilibrium Equations of the Euler–Bernoulli beam with the theorem of Least Work, the principle of maximum work to establish the equation of motions for the Euler–Bernoulli beam and the equation of motion for the Euler–Bernoulli beam by the virtual work theorem, have been implemented. The results obtained from this study open up further research directions on the application of the energy variation method in mechanics as well as in the analysis theory of beam bridges.

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The Bernoulli equation in a moving reference frame

Cited by 13 publications

References 8 publications

The Study of Electrical Energy Consumption in Cascaded Pumps for Pipeline Operations

The Study of Electrical Energy Consumption in Cascaded Pumps for Pipeline Operations

On the inflation and deflation dynamics of liquid-filled, hyperelastic balloons

Applications of common energy variability methods for establishing the equilibrium equation in mechanics

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