Can Circulation be Computed in a System with an Open Path of Integration?

  • Thread starter Jhenrique
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In summary: The line integral of a vector field over a closed curve has name: "circulation"But the line integral of a vector field over a open curve hasn't name...Is that a fundamental problem you think?
  • #1
Jhenrique
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Exist circulation in a system/circuit/vector field/anything where the path of circulation is open?

Is possible to compute the circulation of a system/circuit/vector field/anything with an open path of integration?
 
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  • #2
Do you have a specific mathematical definition of circulation in mind? Usually circulation is defined only for closed paths. If paths are open, one would no longer call it circulation.
 
  • #3
  • #4
If that's the definition, then "circulation" the word should only mean for closed paths. Of course you can take a line integral over an open path, that's perfectly well defined, but you just don't call it "circulation".

Are you having trouble with the definition of the word "circulation"? Or is there a math problem you're confused about?
 
  • #5
Matterwave said:
If that's the definition, then "circulation" the word should only mean for closed paths. Of course you can take a line integral over an open path, that's perfectly well defined, but you just don't call it "circulation".

Are you having trouble with the definition of the word "circulation"? Or is there a math problem you're confused about?

The surface integral of a vector field over a open surface has name: "flux"
The surface integral of a vector field over a closed surface has name: "flux"

The line integral of a vector field over a closed curve has name: "circulation"
But the line integral of a vector field over a open curve hasn't name...
 
  • #6
Is that a fundamental problem you think? Say you have a straight line integral, would you still like to call this integral "circulation" even though it has nothing to do with anything circular?
 

What is circulation?

Circulation refers to the movement of fluids, such as blood, throughout the body. This process is essential for delivering oxygen and nutrients to cells and removing waste products.

What organs are involved in circulation?

The main organs involved in circulation are the heart, blood vessels, and lungs. The heart pumps blood through the blood vessels, and the lungs oxygenate the blood before it is distributed throughout the body.

How does blood circulate through the body?

Blood circulates through the body in a continuous loop. It is pumped from the heart into the arteries, which carry it to the organs and tissues. The blood then travels through smaller vessels called capillaries, where gas exchange and nutrient/waste exchange occurs. Finally, the blood is carried back to the heart through veins.

Why is circulation important?

Circulation is important for maintaining overall health and functioning of the body. It ensures that all cells receive the necessary nutrients and oxygen, and it helps remove waste products. Proper circulation also plays a role in regulating body temperature and immune system function.

What factors can affect circulation?

Several factors can affect circulation, including heart health, blood pressure, cholesterol levels, physical activity, and diet. Certain medical conditions, such as diabetes and obesity, can also impact circulation. Lifestyle choices, such as smoking and excessive alcohol consumption, can also have a negative effect on circulation.

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