Understanding Key Concepts in Fluid Mechanics and Elasticity
Hooke’s Law: Elasticity
When an object is subjected to external forces, it undergoes changes in size or shape, or both. These changes depend on the arrangement of atoms and their bonds in the material. When a weight pulls and stretches another, and when released, this weight returns to its normal size, we say it is an elastic body.
- Elasticity: The property to change shape when a force acts on an object, causing deformation, and the object returns to its original shape when the deformation ceases.
- Inelastic materials: Non-deformable materials are called inelastic (clay, dough, and pastry dough). Lead is also inelastic because it is easily deformed permanently.
Density
Density, usually symbolized by the Greek letter “ρ” and sometimes referred to as specific mass, is a quantity that refers to the amount of mass contained in a given volume and can be expressed in absolute or relative terms. In simple terms, a small, heavy object such as a stone or a piece of lead is denser than a large, light object like a cork or a piece of foam.
Pressure
In physics and related disciplines, pressure is a physical quantity that measures the force per unit area and serves to characterize a given resultant force on a surface.
- In the International System of Units (SI), pressure is measured in a derived unit called Pascal (Pa), which is equivalent to a total force of one newton acting uniformly on a square meter.
Hydrostatic Pressure
Hydrostatic pressure is the pressure due to the weight of a fluid at rest. In a fluid at rest, the only pressure is the hydrostatic pressure. In a moving fluid, additional hydrodynamic pressure related to the speed of the fluid can also appear. It is the pressure that bodies immersed in a liquid or fluid experience through the simple fact of being within it.
Barometer
Atmospheric pressure is the pressure exerted by air at any point in the atmosphere. Usually, it refers to the atmospheric pressure on Earth, but the term is extended to the atmosphere of any planet or satellite.
The atmosphere on Earth has a mean pressure of 1013.25 hectopascals (hPa) or millibars (mbar) at sea level, measured at 45 degrees latitude. The measure of pressure in the International System of Units (SI) is the newton per square meter (N/m²) or Pascal (Pa). The atmospheric pressure at sea level in international units is 101,325 N/m² or Pa.
Pascal’s Principle
In physics, Pascal’s Principle, or Pascal’s Law, is a law formulated by the French physicist and mathematician Blaise Pascal (1623-1662), which is summarized in the phrase: “Increasing pressure applied to a surface of an incompressible fluid (liquid), contained in a non-deformable container, is transmitted with the same value to each of the parties hereto.”
- Pascal’s Principle can be verified using a hollow sphere, perforated in several places and provided with a plunger. By filling the sphere with water and applying pressure through the plunger, it is observed that the water exits through every hole with the same pressure.
Archimedes’ Principle
Archimedes’ Principle is a principle of physics that states that a body wholly or partially submerged in a static fluid will be pushed upward with a force equal to the weight of the volume of fluid displaced by that object. Thus, when a body is submerged in the fluid, it creates hydrostatic pressure resulting from the body’s surface, which always acts upwards through the center of gravity of the displaced fluid and is of a value equal to the weight of the fluid displaced. This force is measured in Newtons (in SI).
Properties of Fluids
Since the study of fluid mechanics typically treats a fluid with a continuous flow or with a small amount of fluid at rest, it is more convenient to relate the mass and weight of the fluid with a given volume of fluid. Thus, the properties of density and specific gravity are defined.