1 Stress in a loaded deformable material body assumed as a continuum. 2 Axial stress in a prismatic bar axially loaded. The stress fundamentals of flu
1 Stress in a loaded deformable material body assumed as a continuum. 2 Axial stress in a prismatic bar axially loaded. The stress fundamentals of fluid mechanics wiley pdf force distribution in the cross section of the bar is not necessarily uniform.
4 Shear stress in a prismatic bar. These internal forces are a reaction to the external forces applied on the body that cause it to separate, compress or slide. Stress is the average force per unit area that a particle of a body exerts on an adjacent particle, across an imaginary surface that separates them. F is the force and A is the surface area. So, these internal forces are distributed continually within the volume of the material body.
Some models of continuum mechanics treat force as something that can change. Other models look at the deformation of matter and solid bodies, because the characteristics of matter and solids are three dimensional. Each approach can give different results. Classical models of continuum mechanics assume an average force and do not properly include “geometrical factors”.
The geometry of the body can be important to how stress is shared out and how energy builds up during the application of the external force. The volume of the material stays constant. When equal and opposite forces are applied on a body, then the stress due to this force is called tensile stress. Therefore in a uniaxial material the length increases in the tensile stress direction and the other two directions will decrease in size. All real objects occupy three-dimensional space. However, if two dimensions are very large or very small compared to the others, the object may be modelled as one-dimensional. One-dimensional objects include a piece of wire loaded at the ends and viewed from the side, and a metal sheet loaded on the face and viewed up close and through the cross section.
Practical Stress Analysis in Engineering Design”. 3rd edition, CRC Press, 634 pages. Volume 1 of Advanced series in engineering science. You can change this page.
Please use the preview button before saving. The list of new changes in the wiki. This page was last changed on 31 August 2017, at 12:36. Fluids are composed of molecules that collide with one another and solid objects. However, the continuum assumption assumes that fluids are continuous, rather than discrete. The fact that the fluid is made up of discrete molecules is ignored. The equations can be simplified in a number of ways, all of which make them easier to solve.
Some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. A control volume is a discrete volume in space through which fluid is assumed to flow. The integral formulations of the conservation laws are used to describe the change of mass, momentum, or energy within the control volume. The rate of change of fluid mass inside a control volume must be equal to the net rate of fluid flow into the volume. The left-hand side of the above expression is the rate of increase of mass within the volume and contains a triple integral over the control volume, whereas the right-hand side contains an integration over the surface of the control volume of mass convected into the system. Mass flow into the system is accounted as positive, and since the normal vector to the surface is opposite the sense of flow into the system the term is negated.
Often coordinates can be chosen so that only two components are needed, momentum is conserved in both reference frames. So the total change in momentum is zero. This should not be read as a statement of the modern law of momentum, a control volume is a discrete volume in space through which fluid is assumed to flow. Some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. They cannot be measured using an aneroid, motion will result”. As in the figure.
In the above integral formulation of this equation, the term on the left is the net change of momentum within the volume. The first term on the right is the net rate at which momentum is convected into the volume. The second term on the right is the force due to pressure on the volume’s surfaces. The following is the differential form of the momentum conservation equation. The equation above is a vector equation in a three-dimensional flow, but it can be expressed as three scalar equations in three coordinate directions. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted to heat. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible.
This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0. All fluids are viscous, meaning that they exert some resistance to deformation: neighbouring parcels of fluid moving at different velocities exert viscous forces on each other. Newtonian fluids, it is a fluid property that is independent of the strain rate. An accelerating parcel of fluid is subject to inertial effects. Bernoulli’s equation can completely describe the flow everywhere.