Rotating fluid, curl and suspended object rotation

In summary, the conversation discusses the angular velocity of a ball placed in a perfectly rotating fluid with a velocity field of yi - xj and a curl of -2k. The speaker suggests that the ball's angular velocity would be -1rad/s, similar to an object placed on a spinning disc. However, they also mention that the spinning object should have an angular velocity equal to the curl of the fluid, which in this case is -2. The tl;dr from Wikipedia's explanation of curl states that the angular velocity of the ball should be half of the curl, leading to some confusion and discrepancy in the calculations.
  • #1
luca-deltodesco
2
0
I'm trying to figure this out.

Say you have a cylinder of perfectly rotating fluid, so that it's velocity field is:
F(x,y,z) = yi - xj
which has curl -2k

assuming there is 'infinite' fluid drag and you have an 'infinitely' light ball which you place into the fluid at any point (let's say it's centre).

then how fast would the ball be rotating?

In my head I equate this to having a ball cemented into a rotating cylinder of concrete (or simply an object sat ontop of a spinning disc) and it would have an angular velocity of -1rad/s.

but at the same time, it would seem to me that the spinning object should have an angular velocity equal to the curl of the fluid at that point, and of course -1 =/= -2
 
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  • #2
... okay nevermind:

tl;dr from wikipedia's 'intuitive interpretation' of curl:

ang. velocity of the ball is 'half' the curl >.>
 

1. What is a rotating fluid?

A rotating fluid is a type of fluid motion in which the fluid particles move in a circular or spiral pattern around a central axis of rotation. This type of motion is often observed in natural phenomena such as hurricanes and tornadoes, as well as in man-made devices such as turbines and centrifuges.

2. What is curl in relation to fluid motion?

Curl is a mathematical concept that describes the rotational behavior of a fluid. It is a measure of how the fluid particles rotate around a given point in the fluid. A high curl value indicates a strong rotational motion, while a low curl value indicates a more linear flow.

3. How does a rotating fluid affect suspended objects?

A rotating fluid can have a significant impact on suspended objects within the fluid. This is due to the forces exerted by the fluid's rotation, which can cause the objects to spin or move in circular paths. This effect is commonly seen in ocean currents and can also be harnessed in technologies such as hydroelectric power.

4. What are some real-world applications of rotating fluids and curl?

Rotating fluids and curl have a wide range of applications in various industries. One of the most well-known uses is in weather forecasting, where the study of rotating fluids helps predict the formation and movement of storms. They are also used in the design and operation of airplanes, ships, and other vehicles that rely on fluid dynamics for movement. In addition, rotating fluids are utilized in the production of energy, such as in wind turbines and hydroelectric power plants.

5. How do scientists study rotating fluids and curl?

Scientists use a combination of mathematical models, computer simulations, and laboratory experiments to study rotating fluids and curl. These methods allow them to observe and analyze the behavior of rotating fluids in controlled environments and make predictions about their real-world applications. They also use advanced tools such as fluid flow visualization techniques and computational fluid dynamics to gain a deeper understanding of these complex phenomena.

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