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Archimedes' Principle, Euler's Equations and Hydrostatic Pressure

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Recall the standard vector identity: {see attachment}.

? A body is immersed in water at rest, under gravity. Show from Euler's equations that the pressure is: {see attachment}

(Hydrostatic pressure)

? Deduce that the buoyancy force on the body is equal to the weight of water displaced by it.
? A boat floats on a pond. A crew member carefully lowers a wooden oar into the pond. What happens to the water level in the pond? What about the waterline of the boat?
? The crew member now gently drops the anchor from the boat into the pond. What happens to the water levels now?

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Solution Summary

Archimedes' Principle, Euler's Equations, Buoyancy and Hydrostatic Pressure are investigated. The solution is detailed and well presented.

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