Fluid circulation around a closed curve

In summary, circulation is a term used in fluid mechanics to describe the counter-clockwise integral around a closed curve of the flow velocity component along the curve. This concept is related to Bernoulli's principle, which states that higher fluid velocity corresponds to lower pressure. It is often seen in the context of lift-generating airfoils and can be used to calculate lift using the Kutta-Joukowski theorem. The relationship between streamlines and the closed curve is arbitrary, as the streamlines simply show that the flow over the airfoil is still moving in one direction despite the presence of circulation.
  • #1
influx
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I know that the circulation is defined as the counter clock wise integral around the closed curve of the flow velocity component along the curve but what is its meaning in real life? I mean what does circulation actually refer to in real life? Also could someone explain the above image? What is the relationship between stream lines and the closed curve? Sorry for the lack of working out but it's just an issue that is baffling me at the moment and I'm unsure of how to proceed
 
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  • #2
I feel that this is related to Bernoulli's principle. For example check out this video:

Bernoulli's principle basically states that a higher velocity of fluid means lower pressure and lower velocity means higher pressure.
 
  • #3
First of all, that YouTube video posted by @Stefan2015 is awful and is filled with half-truths.

Anyway, @influx, the circulation in this sense essentially means that if you were to subtract off the free stream component of the velocity, you'd be left with a disturbance flow that tends to circulate the wing. This is a feature of lift-generating airfoils and can even be used to calculate lift (the Kutta-Joukowski theorem).

There isn't really an important relationship between the streamlines and the closed curve. The closed curve is arbitrary. The author of your book used the streamlines to show that the flow over the airfoil is still moving entirely in one direction yet has a nonzero circulation.
 
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1. What is fluid circulation around a closed curve?

Fluid circulation around a closed curve refers to the movement of a fluid along a closed path or loop. This phenomenon is commonly observed in fluids such as water or air, and is governed by principles of fluid dynamics.

2. How is fluid circulation related to Bernoulli's principle?

Bernoulli's principle states that an increase in the speed of a fluid results in a decrease in pressure. In the context of fluid circulation around a closed curve, this means that as the fluid moves along the path, its speed will vary, causing changes in pressure along the curve.

3. What factors affect fluid circulation around a closed curve?

Several factors can affect fluid circulation around a closed curve, including the shape and size of the curve, the viscosity and density of the fluid, and the speed at which the fluid is moving. Other factors such as external forces and turbulence can also play a role.

4. How is fluid circulation around a closed curve measured?

Fluid circulation can be measured by calculating the circulation function, which is the integral of the fluid velocity around the closed curve. This can be done using mathematical equations or by using specialized instruments such as flow meters.

5. What are some real-world applications of fluid circulation around a closed curve?

Fluid circulation around a closed curve has various practical applications, such as in the design of airplane wings, the study of ocean currents, and the operation of pumps and turbines. It is an important concept in many engineering and environmental fields.

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