Buoyancy

Yes. What is to hold it down?

The net upthrust. Volume of can is about 0.4 litre. Flooded density of sand I make 2.15 kg/litre, so upthrust = mass of fluid (sand + water) displaced = 0.4 x 2.15 = 0.86kg. Mass of can = 0.5kg so net upthrust = 0.86 - 0.5 = 0.36kg.

Whether it actually rises depends on the sand characteristics. If it's small, round particles it's more likely than with large, angular stuff.

Cheers......Codey

Codey,

Many thanks,

If the overburden was gravel, 20mm to 50mm, submerged buoyancy 1000kg/cubic meter, would you consider this to be a buoyant media? Would you consider the weight of the overburden to act as a downward force?

chama

Chama

Firstly, I made a mistake in #4, should be flooded density 2.05 kg/litre.

The gravel you're describing now is very different from sand. I'd be very surprised if the can floated up through that. But a test would clinch it.

Cheers......Codey

Codey,

This is the problem. When does the overburden become susceptable to acting like a liquid.

Chama

My guess is, if it's say 0.5 mm round sand the box probably floats, if it's the gravel you described it probably doesn't.

Where the dividing line comes - your guess is likely to be as good as mine. Sounds like some testing is called for.

Cheers........Codey

The mass of your overburden allways acts as a downward force. That is why drillers of deep holes make mud to counterbalance the expected pressures of gas or oil at depth

Garth CR4

It's an important consideration in industrial tanks, be they made of tin, steel, GRP, concrete, whatever. The structure needs to be either heavy enough, or sufficiently anchored down to something that is heavy enough, such that ground water levels don't turn the thing into a boat.

Oops...changed my mind. The volume of the can is 0.0003927m³. Its mass is 0.5 kg. Its mass per unit volume is 1273 kg/m³ which exceeds the submerged density of the liquid. It is too heavy to float. It will be kept down by its own weight.

But the density of the saturated sand is higher, > 2000 kg/m³.

Okay...I was taking the density of the saturated sand as 1050, but that can't be correct. If the density of the saturated sand is 2000 kg/m³ then the can will float to the top, just as it would in quicksand.

Yep, the 1050 kg/m³ is the apparent weight when flooded, i.e. the load on a perforated false floor supporting 1 m³ of sand all under water. The 700 kg difference between that and the dry weight 1750 kg/m³ means 0.7 m³ of water is displaced so sand is 0.7 solid, 0.3 voids.

Cheers.....Codey

This is no ordinary tin can. If placed in water (no sand) it would sink. I originally assumed, without doing any calculations, that it would float in water.

If the sand particles are supported by inter granular contact, then any sand lying over the tin can will add to the weight and the tin can will stay down.

If the sand is in a "quicking" condition, each particle of sand is in a colloidal suspension and the quicksand acts like a dense fluid. Then the tin can will float because the density of the fluid is greater than the net density of the can.

I believe that the answer to the problem as stated is the can stays down.

Codey,

A point to consider. Although the sand is in a submerged condition the sand will not liquify unless it is severely agitated. ie an earthquake of blasting nearby. Check liquefaction. Also if it is compacted the tendency to liquify is much less.

Chama

NO

The volume of the can is 0.001571 metre cube

The weight of the can is o.5 Kg

The Density is weight over volume = 318.3 Kg per metre cube

Water is 1000 kg metre cube

The effective density of sand is 1750 - 1000 ie 750kg metre cube downwards

As 750 down is greater than 318.3 up the can will settle downwards

Planet

The volume of the can is 0.393 litre. I think you used diameter instead of radius.

The effective density (submerged density) was given as 1050 kg/m³ in original post. Not appropriate to subtract 1000 from the dry density, this would only be the case if 1 m³ (bulk) sand displaced 1 m³ water, but it doesn't as some water goes in the voids.

It's the density of the can relative to the flooded sand density (2050 kg/m³) not the submerged sand density that determines whether there's a net upthrust. Whether it actually rises is something else!

Cheers....Codey

Codey,

Sorry another point. To make this more realistic consider the can to weigh 0.1 Kg. This would make it buoyant in water.

Chama

Hello Chama

0.5kg makes density already below that of sand/water mixture, so change to 0.1kg makes no difference of principle. It would alter the sand particle size at which floating occurs.

Ref your #21, this is first mention of the sand being fluidised! Under conditions discussed, the can always floats in that situation (as pointed out by ba/ael). The upflow velocity needed to fluidise depends on particle size. For sand about 1mm dia velocity is around 40m/h (varies with viscosity hence water temperature). Sand filters with that sort of sand size are often backwashed at fluidisation velocity. For gravel 20 - 50mm the required velocity would be huge.

Cheers.......Codey

Codey,

A couple of points.

The sand/ water is not a mixture, it is sand that is submerged in water by pouring water on the dry sand.

Sand that is submerged in water will only liquify if strong vibrations are present. like an earthquake. Otherwise the submerged sand, density 1000 kg/m3, will act as a downward force adding to the negative buoyancy of the can.

There is no upflow velocity.

Gravel will not liquify when submerged.

Chama

Agreed, I just meant it could be fluidised by an upflow of water, as I believe happens in the case of quicksand.

No doubt vibration can also cause fluidisation, I've read about this being a mechanism of earthquake damage. Again, the vibration needed to fluidise would be greater with increasing particle size.

Cheers......Codey

Good spot Codemaster

YES

The volume of the can is 0.000393 metre cube

The weight of the can is o.5 Kg

The Density is weight over volume = 1273 Kg per metre cube (heavy little tin)

Water is 1000 kg metre cube

The effective density of sand is 1750 - 1000 ie 750kg metre cube

(This means the sand will resist a load of 750kg per square metre )

As 1273 down is greater than the 750 that the sand can resist the can will settle downwards

An empty can would collapse and that would stop any flotation!

Water density at 1000 kg/cubic meter would make the temperature of the water at about 4°C, near the freezing point. This would reduce the movement the sand.

Just another point that might be considered.

A further point, given that temperature, is the likelihood of a freeze-thaw cycle. If the frost line in that area is 300mm or greater, frost heave will cause the can to rise, even if the density is greater than that of the saturated sand. This is a continuous headache for landfills in temperate zones.