Pressure and Buoyancy

Pressure is defined as the force acting per unit area.

Pressure = Force / Area

S.I. unit of pressure is Pascal (Pa) which is equal to 1 N/m2.

Pressure in liquids

Calculate pressure at depth force at depth D = weight of liquid column above D
weight of liquid column above B = mass (m) * gravity (g)
pressure at level D = volume (v) * density (ρ) * gravity (g)
= area (a) * height (h) * density (ρ) * gravity (g)
= force at level B / area
= height (h) * density (ρ) * gravity (g)

Water seeks its own level

Wate seeks its own level

Water pressure depends on depth, so only at equal depths of water will the pressure be equal. Consider a connected section of tubes as shown above. If water is at rest, the pressures at A and B must be equal. Otherwise a flow would occur from the region of higher to the region of lower pressure until the pressures equalize. For this to happen, the depths below the surfaces must be equal.

This is true whatever the density of water or whether or not there is atmospheric pressure.

This principle is used in a hydraulic lift to multiply the force.

Hydraulic lift

Atmospheric pressure

Atmospheric pressure is the force per unit area exerted against a surface by the weight of air above that surface in the Earth's atmosphere.

Atmospheric pressure

Atmospheric pressure decrease with altitude. This can be demonstrated by sealing a plastic bottle at a hill station and bringing it down to sea level. The bottle gets crushed by the increase in atmospheric pressure as it is brought down towards sea level.

Atmospheric pressure and altitude

Buoyancy

Buoyancy is the upward force exerted by a fluid on an object. A fluid is defined as either a gas or a liquid. 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. This difference in pressure results in a net force that tends to accelerate an object upwards.

The magnitude of that force is equal to the difference in the pressure between the top and the bottom of the column, and is also equivalent to the weight of the fluid that would otherwise occupy the column. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink. If the object is either less dense than the liquid or is shaped appropriately (as in a boat), the force can keep the object afloat. The buoyant force an object feels depends only on the weight of the volume of fluid the object displaces.

Eureka episode 26 - Buoyancy

Archimedies Principle

Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

Archimedes principle

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