Sometimes people think the buoyant force increases as an object is brought to deeper and deeper depths in a fluid. But the buoyant force does not depend on depth. It only depends on volume of the displaced.

Archimedes’ derivation of the spherical cap area formula. Archimedes derived a formula for the area of a spherical cap. so Archimedes says that the curved surface area of a spherical cap is equal to the area of a circle with radius equal to the distance between the vertex at the curved surface and the base of the spherical cap. A=π(h2+a2) I want.

Archimedes Principle. A long time ago a Greek scientist named Archimedes discovered an important scientific law related to buoyancy. It can be expressed as ‘Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.’.

Sometimes people think the buoyant force increases as an object is brought to deeper and deeper depths in a fluid. But the buoyant force does not depend on depth. It only depends on volume of the displaced.

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Archimedes’ Principle. The net pressure-times-area force on an object submerged in a fluid, the vector sum of the forces on all the infinite number of infinitesimal surface area elements making up the surface of an object, is upward because of the fact that pressure increases with depth.

(b) Archimedes’ Principle. Archimedes’ Principle state that “ When an object is immersed in a fluid (a liquid or a gas) ,the buoyant force ( upthrust force) on the object is equal in size to the weight of fluid displaced by the object.

Mathematical derivation of Archimedes’ Principle Consider a hydrostatic fluid with a pressure and a closed volume of fluid, drawn with dashed lines in the figure above. The pressure increases with depth according to the following equation:

This discussion on About of Archimedes law and it’s derivation? is done on EduRev Study Group by Class 11 Students.

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Sometimes people think the buoyant force increases as an object is brought to deeper and deeper depths in a fluid. But the buoyant force does not depend on depth. It only depends on volume of the displaced.

The consensus of scholars seems to be that Archimedes considers this to be a postulate, and with it his derivation of the law of the lever is valid, see e.g. Palmieri’s The Empirical Basis of Equilibrium. But where does this assumption come from if not from empirical experience condensed into intuition?

Specifically, I shall present a derivation of Archimedes principle which, though it is based on elementary energy considerations, seems to be largely ignored, at least if one refers to textbooks. Indeed, I have been able to find only one book (Tarasov and Tarasova 1973) in which this derivation is mentioned, and yet this book is virtually unavailable.

Archimedes’ principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. Archimedes’ principle is a law of physics fundamental to fluid mechanics.

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