Buoyancy Equation and Review

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Buoyancy Equation and Review

Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the column than at the top.

Buoyancy is defined as the tendency of a body to float or rise when submerged in a fluid. We all have had numerous opportunities of observing the buoyant effects of a liquid. When we go swimming, our bodies are held up almost entirely by the water. Wood, ice, and cork float on water. When we lift a rock from a stream bed, it suddenly seems heavier on emerging from the water. Boats rely on this buoyant force to stay afloat. The amount of this buoyant effect was first computed and stated by the Greek philosopher Archimedes. When a body is placed in a fluid, it is buoyed up by a force equal to the weight of the water that it displaces.

If a body weighs more than the liquid it displaces, it sinks but will appear to lose an amount of weight equal to that of the displaced liquid, as our rock. If the body weighs less than that of the displaced liquid, the body will rise to the surface eventually floating at such a depth that will displace a volume of liquid whose weight will just equal its own weight. A floating body displaces its own weight of the fluid in which it floats.

Assuming Archimedes' principle to be reformulated as follows,

Aapparent Immersed Weight = Weight - Weight of Displaced Fluid

then inserted into the quotient of weights, which has been expanded by the mutual volume

Density/ (Density of Fluid) = Weight / (Weight- Apparent Immersed Weight)

yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes.:

(Density of Object) / (Density of Fluid) = Weight/ ( Weight - Apparent Immersed Weight)

(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing .)

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