[ODE] Demo of buoyancy and ODE

[Jonathan Langridge]

I think the argument of pressure differential you're using may be inaccurate
in the sloping water case. The standard relation of pressure proportional to
depth is based on a flat water surface, because moving water can distribute
its own weight due to its viscosity. (Obviously sloped water cannot be
accurately viewed as static.) Without viscosity, water could be regarded as
a set of independant molecule-diameter columns, each with its pressure
gradient moving exactly in sync with the water surface.

----- Original Message -----
From: Mattias Fagerlund <mattias@cambrianlabs.com>
To: Jonathan Langridge <jon_lgridge@hotmail.com>; ODE <ode@q12.org>
Sent: Saturday, February 08, 2003 6:49 AM
Subject: Re: [ODE] Demo of buoyancy and ODE


> > It might be a fair approximation, but it's worth being aware that the
> > only
> > things determining buoyancy direction are gravity and acceleration of
> > the system.
>
> I would respectfully disagree;
>
> Buoyancy appears because the pressure on the bottom of an object is
> higher than the force at the top, simply because the bottom is deeper.
> These forces acts on the bottom surface area and top surface area of the
> object. Sideways forces are canceled out because they are equal and
> opposite, so the object doesn't move sideways.
>
> However, if the right side is deeper in the water than the left side,
> then the pressure on the right side will be greater, thus creating a
> sideways force that wants to move the object towards the shallow side.
>
> I would direct you to the formula I present at
> http://www.cambrianlabs.com/Mattias/DelphiODE/BuoyancyParticles.htm ;
>
> Sideways force acting on submerged cube
> g = gravity
> a = height on the left side
> b = height on the right side
> h = side of cube
> p = liquid density
>
> Fx = p * g * h2 * (b - a)
>
> Please review the equation and see if you still disagree?
>
> > I suspect the most significant influence on body floating as
> > far as
> > waves are concerned is drag against the moving water, but I could well
> > be wrong.
>
> Well, I don't have a formula that describes the speed of the surface
> water when a wave passes, or indeed, any "strata" of water in a wave.
> Drag is modelled, but since I don't have the speed of the water, that
> particular force eludes me :(
>
> > Just keep in mind that while the surface normal of the water may
> > be a
> > good source for approximation, it doesn't have any real physical effect
> > on
> > the buoyancy of submerged objects.
>
> As stated above, it would seem it does?
>
> > 'Fraid I can't comment on the accuracy of the drag system you're using,
> > but
> > I'm sure drag proportional to r^2 of sphere (surface area presented)
> > times
> > v^2 would be good enough.
>
> Yep, that's the one!
>
> cheers,
> m
>