Question

Derive the mathematical Expression for Floatation.

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Answer 1

HEY!

SOLUTION IS GIVEN IN THE ATTACHMENT

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Answer 2

$<font color=red> The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.</p><p></p><p>The value of thrust force is given by the Archimedes law which was discovered by Archimedes of Syracuse of Greece. When an object is partially or fully immersed in a liquid, the apparent loss of weight is equal to the weight of the liquid displaced by it.$

$<font color=blue>Apparent weight= Weight of object (in the air) – Thrust force (buoyancy)the buoyant force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as:$

$<font color=orange>Fb = ρ x g x V</p><p>Where,</p><p></p><p>Fb is the buoyant force</p><p>ρ is the density the fluid</p><p>V is the submerged volume</p><p>g is the acceleration due to gravity</p><p>$

$<font color=green>The mass of the liquid displaced is.</p><p></p><p>•Mass = Density × Volume = ρ × V</p><p></p><p>•This is because density (ρ) is defined as</p><p></p><p>Density,ρ = MassVolume = MV</p><p></p><p>▪Thus the weight of that displaced liquid is:</p><p></p><p>•Weight = Mass × Acceleration due to gravity</p><p></p><p>•W = M × g = ρ × V × g</p><p></p><p>Thus, from the Archimedes principle, we can write:</p><p></p><p>•The apparent loss of weight = weight of water displaced = ρ×V×g</p><p></p><p>Thus, the Thrust force is,</p><p></p><p>•Thrust = ρ × V × g</p><p></p><p>Where,</p><p></p><p>▪ρ is the density of liquid</p><p>▪V is the volume of liquid displaced</p><p>▪The thrust force is also called the ▪buoyant force because it is responsible for objects to float. Thus, this equation is also called the law of buoyancy.$