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Let me explain: As I remember, Archimedes' principle goes something like upthrust is equal to the weight of the displaced fluid. Archimedes was saying that the force down was being overcome by the force up, which is proportional to the weight of the displaced fluid. Most take the easy route and calculate buoyancy from the standpoint of the displaced fluid.

I can calculate the buoyancy of an object from the standpoint of the displaced fluid, from the standpoint of the object, and from pressure-area calculations of down force versus up force. All three methods give the exact same result - IF the object is suspended in the surrounding fluid.

If the pressure-area method is the real correct scientific method to calculate buoyancy and if the lower surface area is isolated from the surrounding fluid, then what is buoyancy? What is correct? Do we take Archimedes' principle literally or ...?

Real example: running steel casing in a vertical oil well:

14644 feet of 88.2 lbs/ft casing with end surface areas of 25.3 sq in.

the pipe is otherwise smooth

The weight of pipe in air is 1,291,601 lbs, and its buoyant weight in 13.9 ppg drilling mud is 1,017,505 lbs. If the bottom surface area is somehow blocked from the surrounding fluid, what is the pipe's weight?