Force on a rigid body inside a liquid flow

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Discussion Overview

The discussion revolves around calculating the force acting on a rigid body submerged in a fluid when a second liquid of different density is introduced into the system. The context includes fluid dynamics, particularly during the process of pouring the second liquid, and the complexities involved in understanding the forces at play during this dynamic scenario.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to understand the force on a rigid body submerged in a fluid when a second liquid of greater density is added, highlighting the need for clarity in the scenario.
  • Another participant requests more specifics about whether the inquiry pertains to the force after the system has settled or during the pouring process, noting that the latter is complex and not easily expressible.
  • A participant emphasizes the challenges of calculating forces during the pouring, suggesting that it involves turbulent flow and randomness, drawing a comparison to the unpredictability of throwing dice.
  • One participant proposes approximating the movement of the fluid based on its direction and inquires about applying randomized forces in a simulation context, expressing familiarity with advanced mathematics and seeking resources on computational fluid dynamics (CFD).
  • Another participant mentions the necessity of solving the Navier-Stokes equations for the specific geometry and conditions, indicating that computer simulations may be a viable approach.
  • A participant suggests that if the scenario is simplified, such as having two immiscible fluids with a significant density difference, the object may rise as the denser fluid fills the tub from the bottom.

Areas of Agreement / Disagreement

Participants express differing views on the complexity of the problem, with some acknowledging the challenges of calculating forces during the dynamic process while others suggest simplified scenarios. No consensus is reached on a definitive method for calculating the forces involved.

Contextual Notes

The discussion highlights the dependence on various parameters and the potential for randomness in fluid behavior, as well as the need for specific boundary conditions in simulations. Limitations in the clarity of the initial question and the complexity of fluid dynamics are acknowledged.

Orochi663
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TL;DR
Looking for force change over a rigid body that is completely in a liquid and another liquid is pushed into the container from a direction
Hi,
I am trying to find out Force on a rigid body when it is completely inside a fluid with density p, i.e. the body is completely drowned in the liquid and then another liquid is pushed into the container with different density 'r' (such than r > p).
Thanks.
 

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Your question is not specified sufficiently to provide a reasonable answer. Can you be more specific in your description?
 
@Orodruin not sure what is missing in here. Let me try to give example

Consider you have a bath tub full of water and there is (some thing that is rigid i.e. maintain its original shape when a force is applied over it, like e.g a toy, with some mass that is greater than the buoyant force, i.e. it does not float over the water but is inside the tub completely submerged) and then you pour in some other liquid like oil inside tub in large quantity like e.g: 500 ml , you see the that rigid toy will get disturbed i.e. some force has been applied over it through the disturbance of water when oil is poured into it. How the force acting on rigid body in such case will be calculated.

I have also added the figure in the original question.

Please do let me know what exactly is missing, and i will try to add it.
 
Do you want
(i) the force once everything has settled?
(ii) the force during the pouring?
In case (i) you need to specify the situation afterwards, ie, do the liquids mix? Do they form layers? How much of the object is covered in either liquid in the second case?
Case (ii) is a highly non-trivial hydrodynamics problem and you will not be able to find an easily expressable answer.
 
@Orodruin
Yeh i am looking for (ii) that is what is happening to the rigid body during the phenomena. Can you please point me to some book or paper that i can refer to.

Thanks.
Regards,
 
Orochi663 said:
@Orodruin
Yeh i am looking for (ii) that is what is happening to the rigid body during the phenomena. Can you please point me to some book or paper that i can refer to.

Thanks.
Regards,
There is no simple and easily expressable solution to that. It is going to depend on so many parameters and likely a turbulent flow involving a certain amount of randomness will develop as well. Compare with throwing dice - the dice follow classical mechanics yet the parameters involved in the throw makes the result essentially random. This case is similar, but with stronger dependence on input.

In general, forces on objects immersed in fluids would be within the realm of fluid dynamics, but you would need significant experience in advanced fluid dynamics to even come close to a solution.
 
@Orodruin, hmm thanks. What about if i try to approximate the movement, as we know the direction of fluid being poured ?

Can there be some kind of randomness we can define in the movement so that it can approximate the result. I am trying to do it in liquidfun (https://google.github.io/liquidfun/) i think thay have implemented Navier stokes solution so we don't have to calculate details; so i am wondering how to apply randomize force in such scenario.

Also, I am quite familiar with mathematics and advaned calculus, so in order to understand it all, if you can direct me to a resource on CFD or any paper, i will be grateful.
 
You would have to actually solve the Navier m-Stokes equations for your particular geometry and boundary conditions. This may be done to a certain degree by computer simulation, but I am not an expert in fluid dynamics. Somebody else may be able to help you further.
 
If the scenario is simple - say, the green fluid is much denser than the yellow, and the two are imiscible. If the tub is large and the pour-in point is far from the object, then the green will simply fill the tub from the bottom and the object will rise.

Otherwise, I think the numerical approach (e.g., some CFD variant) would be needed. Or even a test (actually build the tub and perform the fluid addition).

If this is for school or just for fun you might be able to get a free "student edition" software package.
 

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