Understanding Pressure, Density, and Buoyancy in Fluids

Pressure (p) is the ratio of force (F) to the area (S) over which it is applied: P = F / S.

Hydrostatics and Fluid Density

Hydrostatics is a branch of physics that studies fluids at rest. The density (d) of a fluid is its mass per unit volume. The relationship between mass and volume is used to calculate density.

Hydrostatic Equilibrium and Pressure

Hydrostatic equilibrium refers to the pressure within a fluid generated by its weight. The pressure (p) at a point within a fluid is determined by the fluid's density (d), the acceleration due to gravity (g), and the depth (h) of the point: p = dgh. Pressure applied at any point in a fluid is transmitted equally to all points within the fluid.

Surface Tension

Surface tension relates to the strength of the surface and can be understood in two ways:

1. The force multiplied by the strength of the surface.
2. The ratio between the surface and the force.

Communicating Vessels

In a system of communicating vessels, the liquid level is the same in all containers.

Buoyancy (E)

Buoyancy (E) is the vertical upward force exerted by a fluid on an immersed object. An object immersed in a fluid experiences an upward thrust equal to the weight of the fluid displaced.

The buoyant force (E) on a body of volume V immersed in a liquid of density d is given by: E = Vdg, where g is the acceleration due to gravity. Buoyancy is measured in Newtons (N) in the SI system.

Buoyancy and Density Relationships

• If the density of the object (D) is greater than the density of the fluid (d), then the weight (P) is greater than the buoyant force (E), and the object sinks. (D > d, P > E)
• If the density of the object (d) is equal to the density of the fluid (d), then the weight (P) is equal to the buoyant force (E), and the object is in equilibrium within the fluid. (d = d, P = E)
• If the density of the object (d) is less than the density of the fluid (d), then the weight (P) is less than the buoyant force (E), and the object floats. (d < d, P < E)

The ratio of the volume of a solid immersed in a fluid to the total volume of the solid is equal to the ratio of the solid's density to the fluid's density: V_immersed / V_total = d_solid / d_fluid.

Atmospheric Pressure

Atmospheric pressure is commonly measured in several units:

• 760 mm Hg (millimeters of mercury)
• 1 atm (atmosphere)
• 101,300 Pa (Pascal)
• 1.033 at (technical atmosphere)
• 1013 mb (millibar)

Altimeters and Atmospheric Pressure

An altimeter is an instrument used to determine altitude based on changes in atmospheric pressure.

High and Low Pressure Systems

In high-pressure areas, or anticyclones (A), air tends to descend, creating downward air currents and stable, good weather. In low-pressure areas, or cyclones (B), air rises, leading to rising air currents that can cause humidity and rain.