Rate of stress versus velocity gradient

In summary, the conversation discusses the meaning of the equation \int\dot{s}_{ij}\frac{\partial v_{j}}{\partial x_{i}} dV, where \dot{s} is the rate of change of stress and v_{j} is velocity. The equation is used to determine the uniqueness of a body based on its stress and velocity. V represents the volume of the body and the equation can be found in a journal article.
  • #1
maros522
15
0
Hello,
I don't understand the meaning of equation
[tex]\int\dot{s}_{ij}\frac{\partial v_{j}}{\partial x_{i}}[/tex] dV
where [tex]\dot{s}[/tex] is rate of change of stress, [tex]v_{j}[/tex] is velocity.

Can anybody describe the meaning of this equation? Thank you.
 
Last edited:
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  • #2
I don't remember that equation. vj is the velocity of the element under stress? What's V (on dV)?
 
  • #3
Hello, thanks fo posting. vj is the velocity of the element under stress and V is volume of the body. If you have access to journal you can check it

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TXB-46G508Y-H8&_user=10&_coverDate=06%2F30%2F1959&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1226210839&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=62860f8f06fe35bfce725cc38553669a

It is in the equation 4 and 5. And the main meaning is that it is criterion of uniqueness.
 

1. What is the rate of stress versus velocity gradient?

The rate of stress versus velocity gradient is a measure of how much stress a material experiences when it is subjected to a change in velocity. It is a key concept in the study of fluid mechanics and is used to understand the behavior of fluids under different conditions.

2. How is the rate of stress versus velocity gradient calculated?

The rate of stress versus velocity gradient is calculated by dividing the stress (force per unit area) by the velocity gradient (change in velocity over a certain distance). This gives a measure of how much stress is generated in the fluid as it moves.

3. What is the relationship between the rate of stress and the velocity gradient?

The rate of stress and the velocity gradient have a direct relationship - as the velocity gradient increases, the rate of stress also increases. This means that a higher velocity gradient will result in a higher rate of stress, and vice versa.

4. How does the rate of stress versus velocity gradient affect fluid flow?

The rate of stress versus velocity gradient has a significant impact on fluid flow. It determines the resistance or friction experienced by the fluid, which can affect the overall flow rate and behavior of the fluid. Understanding this relationship is crucial in designing and analyzing fluid systems.

5. What factors can influence the rate of stress versus velocity gradient?

Several factors can influence the rate of stress versus velocity gradient, including the properties of the fluid (such as viscosity and density), the geometry of the system, and the velocity of the fluid. Additionally, the presence of boundaries or obstacles can also affect the rate of stress and velocity gradient in a fluid.

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