Fluids in Rigid Body Rotation

[SmileyBG313]

I have found many cases of fluids entering rigid body motion where the gravity vector is purely down the rotation vector. I am curious if there is a soultion for where the gravity vector is in another direction.

I've attempted to solve this myself for a particular rotation, but it is so fast my parabola's vertex is below 0. This itself presents additional problem as most vertical solutions don't even account for this.

If anyone has seen soultions for either of these problems (non-vertical gravity fields and very fast rotations), please let me know. I'd greatly appreciate being pointed in the correct direciton.

 

[eljose79]

Hello,

Thank you for sharing your findings and questions with us. It is always exciting to see new developments and challenges in the field of fluid dynamics.

In response to your first question, there are indeed solutions for cases where the gravity vector is not purely down the rotation vector. These solutions take into account the direction of the gravity vector and the rotation vector, as well as the magnitude and direction of the fluid velocity. These solutions are often used in simulations and experiments to study the behavior of fluids in non-uniform gravity fields.

As for your second question, I understand that fast rotations can present a challenge in accurately predicting the behavior of fluids. In these cases, it is important to use numerical methods, such as computational fluid dynamics, to accurately capture the complex dynamics of the fluid. These methods take into account all the relevant parameters, including the speed of rotation, and can provide accurate solutions even for very fast rotations.

I would suggest looking into the work of researchers who specialize in fluid dynamics and numerical methods, as they may have solutions or insights that can help you with your specific case. Additionally, consulting with colleagues or experts in the field can also provide valuable insights and potential solutions.

I hope this helps and wish you all the best in your research.

 

[charng]

There are indeed solutions for fluids in rigid body rotation where the gravity vector is not purely down the rotation vector. This is known as non-vertical fluid rotation and has been extensively studied in fluid mechanics.

One approach to solving this problem is to use the Navier-Stokes equations, which describe the motion of fluids, and include the effect of gravity. These equations can be solved numerically to obtain solutions for non-vertical gravity fields and very fast rotations.

Another approach is to use the Euler equations, which are simplified versions of the Navier-Stokes equations and are often used for inviscid fluids. These equations also account for the effect of gravity and can be solved analytically for certain cases.

Some solutions for non-vertical fluid rotation have been found for specific geometries, such as rotating cylinders or spheres. However, for more complex geometries, numerical methods are often required.

In terms of the parabola's vertex being below 0, this could be due to the fast rotation causing the fluid to experience centrifugal forces, which can significantly affect the fluid's behavior. This can be accounted for in the equations used to solve the problem.

I would recommend consulting with a fluid mechanics expert or looking into published literature on the topic for more specific solutions and guidance on how to approach this problem.