Finite

In this post, we are dealing with a linear plane rectangular element that has four nodes, and the issue at hand involves calculating the forces acting on each node when there is a uniform surface tension. The thickness of the element is 0.25cm, as follows. First, the formula for calculating the surface traction needed to solve the problem is as follows. To calculate the surface tension for edge ..

Although the total energy equation has been covered in a previous post, there's a section in another book that explains it in a more understandable manner, prompting me to write about the same topic again. When considering the energy of compressible media in the Bernoulli equation, the total energy equation should be used instead of the mechanical energy equation. The total energy equation can b..

Today, I plan to solve a problem related to finite elements, something I haven't done in a while. The problem is as follows. Here, the goal is to fine the nodal displacements and element stresses. $E$ is $210GPa$, and Poission's ratio is 0.3. First, discretize the plate into two elements and simplify the tensil surface traction into nodal forces for calculation. Applying $\left[ F \right] = \lef..

In this post, I aim to explain the modifications of the momentum equation based on the stream tube theory used in fluid mechanics to solve flow problems. When analyzing fluid flow, the momentum equation can be used to determine the fluid's velocity, pressure, density, and other properties. The basic form of the general momentum equation is as follows. The equation represents the change in moment..

The continuity equation in fluid mechanics mathematically represents the principle of mass conservation within fluids. Physically, it asserts that the mass inflow and outflow through any given control volume remains constant over time. Therefore, the continuity equation is critical for analyzing fluid flow, applicable to both incompressible and compressible fluids alike. In this post, I aim to e..

The Bernoulli equation is one of the fundamental principles in fluid mechanics, used to describe the flow of incompressible fluids. It applies the principle of energy conservation to the flow of a fluid, representing the relationship among the fluid's velocity. pressure, and potential energy due to its position. The Bernoulli equation is derived under the ideal conditions of steady flow, incompr..

The Cauchy momentum equation is a partial differential equation presented by Cauchy that describes the transport of momentum in all continua, and it can be represented as follows. Using the point particle accerlation ${\bf{a}}$ and the hydrodynamic volume force $\sum \equiv \nabla \cdot {\bf{\sigma }}$ in the Cauchy momentum equation simplifies it as follows. Here, through the vector form of flu..

Continuum mechanics assumes that a material, even when infinitely divided into smaller elements, retains the properties of the oiginal whole in each element. To consider something as a continuum means to consider it mathematically continous, implying that there are no discontinuities in derivatives and that the continuous properties of the material evident in the original element are maintained...

Hyrodstatics deal with the physics of fluids at rest, meaning fluids that are not in motion. It covers how fluids transmit forces and pressure, and how they affect the surrounding environment structures. Primarily, it involves analyzing the static states of fluids like water or air to study properties such as pressure, buoyancy, density, and their interactions within the fluid. For an ideal gas,..

There are various forms of the energy equation, one of which is the total energy equation in its simplest form. Since the total energy per unit volume consists of internal energy, denoted as $\rho e$, and kinetic energy, denoted as $\rho {w^2}/2$, the rate of change of total energy in the material volume $V$ can be calculated as follows. The fluid within volume $V$ experiences heat transfer with..