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BuoyancyForce

# BuoyancyForce - Buoyancy Overview According to Archimedes...

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Buoyancy Overview According to Archimedes, an object immersed in a fluid displaces the same volume of fluid as the volume of that object, and is consequently buoyed up by a force equal to the weight of the displaced fluid. Hence, if the mass of the liquid displaced is less (greater) than the mass of the object, the object will sink (float). We will show that the buoyant force can be analyzed using the equations of hydrostatics and is a result of two effects: the variation of hydrostatic pressure with depth, and an unbalanced upward force acting on the bottom of a submerged object. Buoyancy is the reason why a heavy ocean liner can float. What matters is not only the weight of an object, but also the amount of fluid it displaces. Analysis The buoyant force is essentially caused by the difference between the pressure at the top of the object, which acts downward, and the pressure at the bottom, which acts upward. Since the pressure at the bottom is always greater than at the top, every object submerged in a fluid necessarily feels an upward buoyant force. Let us use the equations of statics to analysis this phenomenon. Consider a completely submerged aluminum cylinder of length ! , and radius R, is oriented vertically in a fluid bath of depth L (See Figure 1). Figure 1 p 0 z = 0 z = L z x n T n B h 1 ! The top surface of the cylinder is a distance h 1 below the liquid surface. The force acting on the top surface due to hydrostatics is

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(1) F top = A T t H n L A = - A T n T p
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