Quote:Original post by Eelco
since the added mass is due to the mass of boundary layers that get dragged along, i think the most important factor to take into account is surface area.

Not only. Imagine you have large sphere with water and with small sphere inside, at center of large one. If you move small sphere, most of water will move in opposite direction. In case large sphere is very big or infinite, you get that added mass should be proportional to volume of small sphere...
Simple idea: as sphere moves in one direction, center of mass of water moves in opposite direction.
Water dragged along only increases amount of water that have to move in opposite direction...

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Looking at my fluid dynamics notes, the added mass is m* = 1/2*(density of fluid)*(volume of sphere)

that surprises me. what does the inner goemerty have to do with the outside flow?

also, using surface area is plausible cuase it has the desired effect of being significant on small objects whilst being insignificant on large objects.

area*mu*rho*someconstant would most probably do fine.

i believe what you are talking about is called the boundary layer Dmytry and feel is a bit over the top for the original poster's needs. Simple approximations are sufficient. I suppose one cannot neglect buoyancy however.

I will also note that non zero viscosity is in use here and we have laminar flow as well as implied by using Stoke's method. By the first stipulation alone it is obvious that there is no inviscid flow.

Quote:Original post by Daerax
i believe what you are talking about is called the boundary layer Dmytry and feel is a bit over the top for the original poster's needs. Simple approximations are sufficient. I suppose one cannot neglect buoyancy however.

I will also note that non zero viscosity is in use here and we have laminar flow as well as implied by using Stoke's method. By the first stipulation alone it is obvious that there is no inviscid flow.

I believe boundary layer is something very different, if I translated this term correctly.

Indeed, there is some liquid moving along with object, but it's usually not as important as flow in liquid all around object, where most of liquid are moving in opposite direction to direction of body. (i.e. easy to see that center of mass of liquid are moving in direction opposite to direction of body movement [grin])

When object are moving in incompressible liquid with constant velocity, and flow is laminar, looking from object's system of reference, there is some constant flow field all around object. If you change velocity by dV you'll change kinetic energy of flow. F*V=dE/dt so you can use energy conservation to find force that was required to cause certain acceleration. (this is actually quite general thing, it works with other mechanical stuff like gearboxes (if you want to compute rotation inertia of gearbox))

With stuff like bubbles(when this "added mass" accounts for literally entire inertia), it is VERY significant and important, and with other stuff it's significant aswell. "added mass" it's just sort of inertia of water that have to move if object moves*, and it is around ~volume*liquid_density.

For example, if you have submerged submarine with mass about M (and buoyancy M*g), and apply force F, it will have acceleration probably about ~F/(2*M) (at least F/(1.5*M), but I remember that for real water and real sub, it's around 2), that is, about 2 times smaller than one would get ignoring added mass. I'm is not sure in figures for floating ships, but also something similar.

[Edited by - Dmytry on June 5, 2005 12:32:10 PM]

Well the boundary layer is the fluid that seems to "stick" to the surface of our object in viscous flow. The proper simulations of this is no simple thing and involves the use of tensors and the use of concepts from the Navier Stokes equations.

The approximation I gave is valid for resisted motion in the direction of motion and takes into account the "resistive forces" of the surrounding fluids with respect to the nature of our body.

But yes you are right about the importance of the concept of boundary layers, I just dont think it would appropriate to simulate such directly unless you were making some sort of professional ship simulator.

I actually weren't proposing to take just boundary layer into account. "Added mass" is not just mass of boundary layer. It consist of inertial effect of fluid motion around object (which could sort of include boundary layer too, tho in not so simple way).
Most of this inertial effect is due to fluid moving in direction opposite to direction of motion of object.

(Actually, Eelco were talking about boundary layer portion of added mass, that would quite depend to surface of object.)

This added mass concept is just a simple method to approximate inertial effect of liquid, absolutely non computationally expensive, and is conceptually very simple. (you just pretend that object have bigger mass)

not to derail this thread: it's sort of like "inertia" of gearbox. If you want to simulate motor attached to gearbox, you pretend that gearbox have some rotation inertia (if you aren't interesting in simulating each gear (for example if motor with torque I is connected to ideal 10x up gearbox connected to flywheel with inertia I, "inertia of gearbox" is 100*I and rotation acceleration of motor is T/(100*I))). Both things is mechanical systems where velocities of massive parts linearly (in case of liquid, approximately linearly) depends to velocity of some shaft.

[Edited by - Dmytry on June 5, 2005 1:29:07 PM]

Quote:Original post by Dmytry

Quote:Original post by Eelco
since the added mass is due to the mass of boundary layers that get dragged along, i think the most important factor to take into account is surface area.

Not only. Imagine you have large sphere with water and with small sphere inside, at center of large one. If you move small sphere, most of water will move in opposite direction. In case large sphere is very big or infinite, you get that added mass should be proportional to volume of small sphere...
Simple idea: as sphere moves in one direction, center of mass of water moves in opposite direction.
Water dragged along only increases amount of water that have to move in opposite direction...

ah yes thats indeed a good point, didnt think of that. that imfluence is probably more significant for a lot of situations.

although adding the mass of this water to that of the body, whilst it does increase its inertia, is far from physically correct, since this added intertia doesnt move with the same speed or in the same direction at all...

this is all quite complex... probably best to use some empirical motivated formula, with numerical stability as an excuse. :)

Quote:Original post by Eelco

Quote:Original post by Dmytry

Quote:Original post by Eelco
since the added mass is due to the mass of boundary layers that get dragged along, i think the most important factor to take into account is surface area.

Not only. Imagine you have large sphere with water and with small sphere inside, at center of large one. If you move small sphere, most of water will move in opposite direction. In case large sphere is very big or infinite, you get that added mass should be proportional to volume of small sphere...
Simple idea: as sphere moves in one direction, center of mass of water moves in opposite direction.
Water dragged along only increases amount of water that have to move in opposite direction...

ah yes thats indeed a good point, didnt think of that. that imfluence is probably more significant for a lot of situations.

although adding the mass of this water to that of the body, whilst it does increase its inertia, is far from physically correct, since this added intertia doesnt move with the same speed or in the same direction at all...

Actually, it's sorta like gearbox or other similar mechanical system. If speeds of massive parts linearly depend to speed of "shaft"(I mean thing we apply force to) (currently I'm talking about one dimension of motion of thing we apply force to, like rotation around one axis, or motion of ball along straight line(note:water doesn't have to move along straight line)), it will work like there's some inertia added, doesn't really matter how this mechanical system works. It comes from energy conservation, and that F*V=dE/dt. For some dV/dt you find corresponding dE/dt that is nicely proportional to V so you get F.

Of course, everything is more complicated in 3D with general shapes (I think in general case you have something like dV/dt=T*F where T is some tensor). But with spheres everything is simpler, and you really have added mass that (for idealized liquid) is mostly straightforward to compute, you just need to integrate energy of flow and apply energy conservation. (thing higherspeed said about)

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this is all quite complex... probably best to use some empirical motivated formula, with numerical stability as an excuse. :)

Yes, and added mass is such thing(used in simulating ships), but it's not only empirically motivated but theoretically aswell.

first: Yes, that's important question, actually.
To get acceleration you need to divide sum of all these forces by mass + added mass.
But added mass should not affect rotational inertia of ball.

It is important to note that generally speaking fluid forces do not have to apply to this "added mass". Them might have their own inertias. But things like buoyancy, drag, "friction", and similar stuff that absolutely doesn't somehow account for inertia of liquid should apply to this added mass.

Added mass might looks to you like sort of dark voodoo spell. Actually, it's better to think about "added mass" as draglike force that depends to acceleration of object, like F[am]=-A*added_mass , similarly to how drag depends to velocity. So, you have
A=(all_other_forces-A*added_mass)/mass
and to solve for A,
A*mass=all_other_forces-added_mass*A
and
A*mass+A*added_mass=all_other_forces
brackets
A*(mass+added_mass)=all_other_forces
and finally
A=all_other_forces/(mass+added_mass)

Of course it's all approximation, in real hydrodynamics you don't have such separate forces, you have integral of pressure on surface of object, that gives you all this stuff.

second: there's probably no real rules of that (except that there's no liquids with really very small density. ) I don't think that low density liquid can't be very viscosous; it's just not very typical. There's many liquids much more viscosous than water yet having same or lower density.

third:Speaking of turbulence and stuff... it's rather complicated thing, and requirs fluid simulation that simulates grid of cells, or simulates particles, or something similar (i did some for gas with thermal expansion).
There may be some approximations, but I don't sure how correct them may be. Whole thing leaves impression that such things is going to give you atleast twofold errors. (or even tenfold if taken from game physics books.[grin])

[Edited by - Dmytry on June 6, 2005 10:07:09 AM]