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Maximum Acceleration Due to Buoyancy


arkie87

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2 hours ago, mikegarrison said:

OK, so what you're asking is how to calculate form drag in water?

If so, I don't know. I'm an aero guy, and we do funny stuff like ignore the mass of the fluid we're moving through, something the hydrodynamics guys can't do. (But they ignore compressibility, which more than makes up for it.)

Not quite. The form drag force is zero (presumably) when the object isnt moving. I am asking about the acceleration obtained at the start. The quora answer @Nightside  gave was pretty useful, and explains the answer to my question. TL;DR: there is a concept of "added/virtual mass" (it is basically the mass of fluid that gets dragged along with the rocket) that limits its acceleration at the start (when velocity and all forms of drag are zero). 

2 hours ago, natsirt721 said:

As a fellow aero guy, cut the hydro guy some slack - water is nearly incompressible, at least under practical pressures.

Form drag is proportional to velocity, just like skin drag. My original answer still stands.

See @Nightside's answer, which directly conflicts with yours. maximum acceleration is 2g, even when velocity is zero (where form drag would be zero). 

Edited by arkie87
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@Nightside Thanks again for your reply. Very often, just knowing what something is called provides a huge breakthrough in being able to learn about it i.e. knowing it is called "added mass" or "virtual mass" allowed me to find much more references out there.

And interestingly, @Scotius, the navy has studied it way before ballistic missiles, to be able to predict acceleration of a submarine underwater, for instance (concept of added mass applies even without buoyancy). See these references below:

https://core.ac.uk/download/pdf/36709212.pdf

So, for a sphere, added mass is 1/2 of the mass of the displaced fluid, but for more streamlined bodies, added mass can approach 0, as shown here:

https://www.researchgate.net/publication/233581794_Translational_Added_Mass_of_Axisymmetric_Underwater_Vehicles_with_Forward_Speed_Using_Computational_Fluid_Dynamics

Edited by arkie87
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Ok, so if we assume an extremely streamlined body, to the extent that drag can be ignored... I'm going to assume a shape like <> ... except much more elongated, and rotated 90 degrees

You asked: "However, it is unclear to me whether this water rushing in underneath can accelerate faster than g. While the water directly below the rocket must accelerate at 1 g, the surrounding water and above would be accelerating significantly slower than 1 g,"

I'm going to have ti disagree right away with you. Assuming the shape I described, the bottow will be like a V or a cone... water would primarily "rush in" not from the bottom, but from the sides. It would also have to be parted by the top, at the " ^ " shape. There will always be a pressure gradient between the top ^ and the bottom " v ". Now, as the water is coming in from the sides, its going to exert not only a lateral force, but a vertical force, related to the angle of the walls of the buoyant vessel. Now if you take 1/ cos x, it goes to infinity as x approaches 90 degrees. I don't think there'd be a limit to the speed, as it would always experience acceleration, as water could "rush in" from the sides fast enough, provided that the taper is shallow enough.

So I'd think that and arbitrarily long/thin/elongated vessel, could reach an arbitrarily high speed, ignoring friction, heating, deformation, relativistic effects, etc.

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6 hours ago, KerikBalm said:

Ok, so if we assume an extremely streamlined body, to the extent that drag can be ignored... I'm going to assume a shape like <> ... except much more elongated, and rotated 90 degrees

You asked: "However, it is unclear to me whether this water rushing in underneath can accelerate faster than g. While the water directly below the rocket must accelerate at 1 g, the surrounding water and above would be accelerating significantly slower than 1 g,"

I'm going to have ti disagree right away with you. Assuming the shape I described,

Well, dont assume that shape. Assume a cylindrical shape... regardless, even for a cylinder water rushes in from directly below but also from the sides. But it is nearly impossible to know the relative balance of each without doing some sort of CFD.

6 hours ago, KerikBalm said:

 

the bottow will be like a V or a cone... water would primarily "rush in" not from the bottom, but from the sides. It would also have to be parted by the top, at the " ^ " shape. There will always be a pressure gradient between the top ^ and the bottom " v ". Now, as the water is coming in from the sides, its going to exert not only a lateral force, but a vertical force, related to the angle of the walls of the buoyant vessel. Now if you take 1/ cos x, it goes to infinity as x approaches 90 degrees. I don't think there'd be a limit to the speed, as it would always experience acceleration, as water could "rush in" from the sides fast enough, provided that the taper is shallow enough.

So I'd think that and arbitrarily long/thin/elongated vessel, could reach an arbitrarily high speed, ignoring friction, heating, deformation, relativistic effects, etc.

Agreed, that is my opinion. 

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