Fundamental Principles of Hydrostatics and Fluid Pressure

Fundamentals of Hydrostatics

Hydrostatics is the branch of fluid mechanics that studies fluids at rest.

Key Concepts and Definitions

Fluid

A fluid is a substance that flows easily and changes its shape under the action of low-magnitude forces. Fluids include both liquids and gases.

• Gases: Molecules vibrate randomly and are compressible.
• Liquids: Take the shape of their container; their vibrating molecules are separated.

Pressure

Pressure (measured in Pascals, Pa, or N/m²) is the quotient resulting from dividing the value of a force acting perpendicularly on a surface by the area over which it is exerted.

• The greater the force, the greater the pressure.
• The greater the area, the lower the pressure.

Any body immersed in a fluid experiences pressure, which increases with depth.

Atmospheric Pressure

This is the pressure exerted by the weight of the atmosphere on the Earth's surface, a concept demonstrated by the Italian physicist Evangelista Torricelli.

Standard atmospheric pressure is equivalent to: 1 atm = 76 cmHg = 760 mmHg = 1.01 x 10⁵ Pa.

• Measurement Instruments: Barometers and manometers.
• Variables Affecting Atmospheric Pressure:
  • Height: The higher the altitude, the lower the atmospheric pressure.
  • Weather: Changes in weather can cause variations in barometric pressure.

Density

Density (ρ) is the quotient obtained by dividing the mass of a body by the volume it occupies. It is commonly measured in kg/m³ or g/cm³.

• Variables Affecting Density:
  • Mass and Volume: The primary components of the density calculation.
  • Temperature: Affects the density of liquids, solids, and gases.
  • Pressure: Significantly affects the density of gases.

Pascal's Principle

Pascal's Principle states that the pressure exerted on an enclosed fluid at rest is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

Applications of Pascal's Principle

• Hydraulic presses
• Car lifts
• Hydraulic brake systems in vehicles

Archimedes' Principle

Archimedes' Principle states that a body immersed in a fluid experiences a vertical upward buoyant force equal to the weight of the fluid it displaces.

Displaced Volume

The displaced volume is the volume of the part of the body that is immersed in the fluid.

• If a body is completely submerged, its volume is equal to the displaced volume.
• If it is only partially submerged, the immersed part of its volume corresponds to the displaced volume.

Why Does a Boat Float?

A boat floats because the buoyant force acting on it is equal to its total weight. The volume of water it displaces is equivalent to the volume of the boat's hull that is submerged.

Application to Gases

Archimedes' principle also applies to gases. For example, a hot air balloon rises because of the upward buoyant force. This occurs because its average density (hot air inside) is less than the density of the surrounding atmospheric air, a state achieved by heating the air inside the balloon.

Apparent Weight

When a body is placed in a fluid, it appears to have less weight (its apparent weight). This is because the upward buoyant force counteracts the object's actual weight.

Boyle's Law

Boyle's Law states that for a fixed amount of gas at a constant temperature (an isothermal process), the product of its initial pressure and volume is equal to the product of its final pressure and volume. In other words, as pressure increases, volume decreases, and vice versa.