scholarly journals Governing equations for acid water in canals

1994 ◽  
Vol 16 (4) ◽  
pp. 21-27
Author(s):  
Nguyen Tat Dac
Keyword(s):  
Governing Equation ◽  
Chemical Equilibrium ◽  
Water Movement ◽  
Equation System ◽  
Acid Water ◽  
Governing Equations ◽  
Kinetic Treatment

It is given in this study governing equation system formulation for acid water movement in canals, especially, in the Plain of Reeds of Vietnam where the urbanite equilibrium is found dominant. It is assumed in the model a chemical equilibrium, however a kinetic treatment is also used to deal with dissolution of precipitates and sedimentation.

scholarly journals Generalized diffusion theory of non-rotational, rigid spherical particle sedimentation in viscous fluid

2001 ◽  
Vol 23 (3) ◽  
pp. 159-166
Author(s):  
Nguyen Hong Phan ◽  
Nguyen Van Diep
Keyword(s):  
Viscous Fluid ◽  
Spherical Particle ◽  
Governing Equation ◽  
Diffusion Theory ◽  
Equation System ◽  
Spherical Particles ◽  
Characteristic Form ◽  
Governing Equations ◽  
Particle Sedimentation ◽  
Mathematical Properties

This paper is devoted to application of Generalized Diffusion Theory for solving a sedimentation problem of rigid spherical particles in viscous fluid. The governing equations have been obtained. It is shown that, in this case the governing equation system is a hyperbolic one, and the equations in the characteristic form have been derived. The mathematical properties of the obtained equation system and the solution for stationary sedimentation where investigated numerically.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

Sensitivity Analysis and Optimization of Mechanical System Design

1988 ◽  
Author(s):  
W. J. Langner
Keyword(s):  
Linear Equation ◽  
Mechanical System ◽  
Numerical Integration ◽  
Equation System ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Governing Equations ◽  
Integration Algorithm ◽  
Linear Equation System ◽  
The Matrix

Abstract The paper follows studies on simulation of three-dimensional mechanical dynamic systems with the help of sparse matrix and stiff integration numerical algorithms. For sensitivity analyses and the application of numerical optimization procedures it is substantial to calculate the effect of design parameters on the system behaviour by means of derivatives of state variables with respect to the design parameters. For static and quasi static analyses the computation of these derivatives from the governing equations leads to a linear equation system. The matrix of this set of linear equations shows to be the Jacobian matrix required in the numerical integration process solving the system of governing equations for the mechanical system. Thus the factorization of the matrix perfomed by the numerical integration algorithm can be reused solving the linear equation system for the state variable sensitivities. Some example demonstrate the simplicity of building the right hand sides of the linear equation system. Also it is demonstrated that the procedure proposed neatly fits into a modular concept for simulation model building and analysis.

Parametric Stability of Axially Accelerating Viscoelastic Beams With the Recognition of Longitudinally Varying Tensions

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Li-Qun Chen ◽  
You-Qi Tang
Keyword(s):  
Governing Equation ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Finite Support ◽  
Governing Equations ◽  
Parametric Stability ◽  
Stability Boundaries ◽  
Axial Acceleration ◽  
The Stability ◽  
Longitudinally Varying Tension

In this paper, the parametric stability of axially accelerating viscoelastic beams is revisited. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was approximately assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite support rigidity is also considered. The generalized Hamilton principle and the Kelvin viscoelastic constitutive relation are applied to establish the governing equations and the associated boundary conditions for coupled planar motion of the beam. The governing equations are linearized into the governing equation in the transverse direction and the expression of the longitudinally varying tension. The method of multiple scales is employed to analyze the parametric stability of transverse motion. The stability boundaries are derived from the solvability conditions and the Routh-Hurwitz criterion for principal and sum resonances. In terms of stability boundaries, the governing equations with or without the longitudinal variance of tension are compared and the effects of the finite support rigidity are also examined. Some numerical examples are presented to demonstrate the effects of the stiffness, the viscosity, and the mean axial speed on the stability boundaries. The differential quadrature scheme is developed to numerically solve the governing equation, and the computational results confirm the outcomes of the method of multiple scales.

Scaling Analysis for the Liquefaction Phenomena Induced by Water Waves

2016 ◽  
Author(s):  
E. Arcos ◽  
E. Bautista ◽  
F. Méndez
Keyword(s):  
Governing Equation ◽  
Analytical Solutions ◽  
Water Waves ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Scaling Analysis ◽  
Governing Equations ◽  
Order Of Magnitude ◽  
Characteristic Scales

In this work an scaling analysis of the liquefaction phenomena is presented. The characteristic scales are obtained by balancing term by term of the well known partial dynamics governing equations (approximation U – P). The order of magnitude of the horizontal displacement are very smaller compared with the vertical displacement and therefore the governing equation are only a function of the dependent vertical variables. The U – P approximation is reduced and presented in its dimensionless version. This scaling analysis can be used to obtain analytical solutions of the liquefaction phenomena under the action of the water waves.

The Effect of Wall Motions on the Governing Equations of Contained Fluids

1990 ◽  
Vol 57 (3) ◽  
pp. 783-785 ◽  
Author(s):  
Roger Ohayon ◽  
Carlos A. Felippa
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Governing Equation ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Displacement Potential ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Acoustic Fluid

The equations of motion for an acoustic fluid enclosed in a moving or flexible container are studied. It is shown that the determination of the reference state must account for the surface-integrated effect of the wall motions. The governing equation of transient motions about this state in the displacement potential does not generally reduce to the classical wave equation unless special adjustments are made. The results are relevant to finite elements formulations based on the displacement potential.

Establishment and solution of governing equation for plana-grooved liquid seals based on three-control-volume theory

2019 ◽  
Vol 72 (3) ◽  
pp. 257-266
Author(s):  
Xiumin Zhang ◽  
Mingfu Yin ◽  
Huilai Sun
Keyword(s):  
Coordinate System ◽  
Governing Equation ◽  
Control Volume ◽  
Order Equation ◽  
Theoretical Research ◽  
Fluid Distribution ◽  
Governing Equations ◽  
Rectangular Coordinate System ◽  
Labyrinth Seals ◽  
Content Type

Purpose This paper aims to study the dynamic characteristics of the straight-through labyrinth seals, which is applied on an oil sealing belt of hydrostatic support system (HSS) oil pocket, the establishment and solution process of seal governing equation is deduced. Design/methodology/approach The three-control-volume model theory is an efficient approach that is applied well. This paper starts with three relative governing equations for the flow characteristics of straight-through labyrinth seals in the plane direction. Referring to the establishment process of governing equations for circumferentially-grooved liquid seals, the governing equation based on space rectangular coordinate system is established, which are transformed into dimensionless equations through a nondimensionalized process and solved by a perturbation method. It contains a zeroth-order equation, through which a steady fluid distribution is determined, and a first-order equation, through which the seal’s dynamic coefficients can be acquired. Findings The governing equation for plane-grooved straight-through labyrinth seals can be established and solved by the three-control-volume theory. Practical implications This study have important guiding significance for further theoretical research and structural design of the straight-through labyrinth seals on the oil sealing belt of HSS oil pocket. Originality/value In this paper, a straight-through labyrinth seal is installed in an oil sealing belt. The three-control-volume governing equations is established in space rectangular coordinate system, and the shear force of the fluid Y-direction is different from the previous model.

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