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Buoyancy & Compressibility.

Buoyancy is the tendency of a body to float or rise in a fluid, with the buoyant force equal to the weight of the displaced liquid, as first described by Archimedes. Compressibility measures the volume change of a substance under pressure, with liquids being mostly incompressible and gases being highly compressible. The pressure in a liquid increases with depth and is exerted equally in all directions, with external forces affecting the pressure experienced by pistons in a container filled with liquid.

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20 views2 pages

Buoyancy & Compressibility.

Buoyancy is the tendency of a body to float or rise in a fluid, with the buoyant force equal to the weight of the displaced liquid, as first described by Archimedes. Compressibility measures the volume change of a substance under pressure, with liquids being mostly incompressible and gases being highly compressible. The pressure in a liquid increases with depth and is exerted equally in all directions, with external forces affecting the pressure experienced by pistons in a container filled with liquid.

Uploaded by

Shiju Kp.
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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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.

Compressibility

Compressibility is the measure of the change in volume a substance undergoes when a pressure

is exerted on the substance. Liquids are generally considered to be incompressible. For instance,

a pressure of 16,400 psig will cause a given volume of water to decrease by only 5% from its

volume at atmospheric pressure. Gases on the other hand, are very compressible. The volume

of a gas can be readily changed by exerting an external pressure on the gas

Relationship Between Depth and Pressure

Anyone who dives under the surface of the water notices that the pressure on his eardrums at a

depth of even a few feet is noticeably greater than atmospheric pressure. Careful
measurements

show that the pressure of a liquid is directly proportional to the depth, and for a given depth
the

liquid exerts the same pressure in all directions.

The pressure of the liquids in each of the previously cited cases has been due to the weight of

the liquid. Liquid pressures may also result from application of external forces on the liquid.
Consider the following examples. Figure 2 represents a container completely filled with liquid.

A, B, C, D, and E represent pistons of equal cross-sectional areas fitted into the walls of the

vessel. There will be forces acting on the pistons C, D, and E due to the pressures caused by

the different depths of the liquid. Assume that the forces on the pistons due to the pressure

caused by the weight of the liquid are as follows: A = 0 lbf, B = 0 lbf, C = 10 lbf, D = 30 lbf,

and E = 25 lbf. Now let an external force of 50 lbf be applied to piston A. This external force

will cause the pressure at all points in the container to increase by the same amount. Since the

pistons all have the same cross-sectional area, the increase in pressure will result in the forces

on the pistons all increasing by 50 lbf. So if an external force of 50 lbf is applied to piston A,

the force exerted by the fluid on the other pistons will now be as follows: B = 50 lbf, C = 60

lbf, D = 80 lbf, and E = 75 lbf.

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