How to get Buoyancy Force 2

[XinLok]

I am confused with getting the Buoyancy force for a combined footing.

So, please let me know if this is correct:

F = 250 (width) x 100 (depth) x (90 (soil height above footing) + 30 (footing height) - 50 (water table height)) x (62.4/12/12/12 lb/in3) x 32.17 * 12 in / s2

Is this correct?

 

[EireChch]

Buoyant force is the volume of footing below water table times unit weight of water.

 

[XinLok]

what about the gravity? What I did up is wrong?

 

[1503-44]

Much easier like this

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[XinLok]

Thank you @1503-44 for your effort for doing the excel sheet, well appreciated.
but in my example, I should not use the gravity g? F = m x g?

Still I did not understand how to get the Buoyant force

 

[1503-44]

You do not need to multiply by 32.174.
The origins of the "gravitational system units of pounds" is strange. I think Newton did not know at first if he was feeling mass or force. Hence it is confusing. A pound is not always a pound, yet it is. We actually have pounds weight, or force (in place of Newtons), and pounds of mass (in place of Kg). They are same-same, but different. I will try to explain.

Densities are "pounds force". That's already what you need to work out the problem.

As for why, here is why...

1 "lb force" or 1 lbf, is equal to the force exerted by gravity on 1 "lb mass" at the earth's surface
In other words, if you have M =1 lb mass, lbm, in your hand at the Earth's surface, the force you experience is 1 "lb force".

Gravity at the Earth's surface places an acceleration A of 32.174 ft/sec^2 on your M of 1 "lb mass".
Thats what we have. Force = Mass x Acceleration, force F = M * A

So you now have 1 "lb-mass" x 32.174*ft/sec^2 = 1 lbf
Grouping the units = 32.174 lbm*ft/sec^2 That is equal to 1 "lb force" , or 1 lbf.

If you have mass densities for your materials, such as for water with a mass density of
62.4 lbm/ft3, and you put 1 ft3 of it in an acceleration of 32.174 ft/sec2 then you automatically have 62.4 pounds force. On Mars that will be a different force, because Mars' gravity is not 32.174 but our foundation is on Earth, so its 62.4 pounds force of water.

If you do not want to think that you automatically get pounds force, then you need a conversion factor. That conversion factor is
C = 1 lbf / (lbm x gravity) where on Earth g = 32.174 ft/sec2
C = 1 lbf /(lbm x 32.174 ft/sec2)
C = 1/ 32.174 lbf x sec2 /(lbm x ft)

F = M A
F = 10 lbm x 32.174 ft/sec2
F = 10 lbm x 32.174 ft/ sec2 x C
F = 10 lbm x 32.174 ft/ sec2 x 1/ 32.174 lbf x sec2 /(lbm x ft)
F = 10 lbm x 32.174 ft/ sec2 x 1/ 32.174 lbf x sec2 /(lbm x ft)
F = 10 lbf

So you see, 10 lbm is = 10 lbf, if you use the conversion factor of 1/g and multiply mass x gravity to get lbf.

I prefer to think it is automatic. Just keep it in mind when you go to Mars and blame Isaac Newton.

Buoyant force is the weight of water that an object placed in the water would have if its density was the same as water. A 1 ft3 box placed entirely under water would have a buoyant force of 62.4 lbf. If only placed half way into the water, its buoyant force would only be 62.4 x 0.5 ft3 = 32.2 lbf.

Weight of an object in water.
Calculate a dry weight then subtract the weight of the volume of water from it. But only subtract the weight of water from the volume that is below the water line.

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[XinLok]

GREAT EXPLANATION, thank you vey much.

So, F = 250 (width) x 100 (depth) x (90 (soil height above footing) + 30 (footing height) - 50 (water table height)) x (62.4/12/12/12 lb/in3) ???

 

[1503-44]

The water height is (50+ 30) = 80

Water weight (lbf) below the water line is 80 x 100 x 250 / 1728 x 62.4



A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[XinLok]

Thanks a lot, now it is clear

 

[1503-44]

Great. Everything below the water line.

A black swan to a turkey is a white swan to the butcher ... and to Boeing.