Properties of fluids, buoyancy, and Archimedes' principle

Fluids are substances that can flow and take the shape of their container, including liquids and gases.
Density (ρ) is the mass per unit volume of a fluid, given by the formula ρ = m/V, where m is mass and V is volume.
The SI unit of density is kg/m³.
Pressure (P) is defined as the force exerted per unit area, expressed as P = F/A, where F is force and A is area.
The SI unit of pressure is Pascals (Pa).
Viscosity is the property of a fluid that resists its flow due to internal friction between layers.
Liquids with high viscosity (e.g., honey) flow more slowly than those with low viscosity (e.g., water).
Surface tension is the cohesive force at a liquid's surface that minimizes its surface area, allowing phenomena like water droplets forming spheres.
Buoyancy is the upward force exerted by a fluid on an object submerged in it, countering the force of gravity.
The magnitude of the buoyant force depends on the volume of the fluid displaced and its density.
Archimedes' Principle states that a body submerged in a fluid experiences an upward force equal to the weight of the displaced fluid.
The formula for buoyant force is: F_b = ρ × V × g, where ρ is fluid density, V is displaced volume, and g is acceleration due to gravity.
An object will float if its density is less than that of the fluid it is placed in.
An object will sink if its density is greater than the fluid's density.
Relative density, also known as specific gravity, is the ratio of an object's density to the density of water.
The SI unit of relative density is dimensionless.
The pressure in a fluid increases with depth due to the weight of the fluid above, given by P = ρgh, where h is depth.
The pressure at any point in a static fluid is the same in all directions, a property known as isotropy.
Pascal’s Principle states that a change in pressure at any point in an incompressible fluid is transmitted undiminished to all points in the fluid.
Applications of Pascal’s Principle include hydraulic brakes and hydraulic presses.
Hydraulic systems use fluids to transmit force and multiply mechanical advantages.
Streamline flow occurs when fluid particles move in parallel layers without mixing, while turbulent flow involves chaotic mixing.
The continuity equation, A₁v₁ = A₂v₂, states that the product of cross-sectional area and velocity is constant in an incompressible fluid.
Bernoulli’s Principle states that in a flowing fluid, an increase in velocity leads to a decrease in pressure, and vice versa.
Applications of Bernoulli’s Principle include airplane wings, Venturi meters, and carburetors.
The Reynolds number determines whether a flow is laminar or turbulent, with higher values indicating turbulence.
Capillary action occurs when a liquid rises or falls in a narrow tube due to cohesive and adhesive forces.
Hydrostatic pressure is the pressure exerted by a fluid at rest, depending on its depth and density.
The concept of buoyancy explains why ships float and why helium balloons rise in air.
In gases, buoyancy plays a role in atmospheric phenomena, such as hot air balloons and weather patterns.
The center of buoyancy is the point where the upward buoyant force acts on a submerged object.
Floating equilibrium occurs when the buoyant force equals the object’s weight, ensuring it neither sinks nor rises.
Objects partially submerged displace fluid equal to their weight, as described by Archimedes' Principle.
The specific weight of a fluid is its weight per unit volume, influencing buoyant forces.
Hydrometer devices measure the relative density of liquids using the principles of buoyancy.
The Stoke's law describes the force of viscous drag on small spherical objects moving through a fluid.
The terminal velocity is reached when the downward gravitational force equals the upward drag and buoyant forces on an object falling in a fluid.
The study of fluid mechanics has applications in engineering, meteorology, oceanography, and medicine.
Naval architecture relies on principles of buoyancy and Archimedes' Principle to design stable and efficient ships.
Understanding viscosity is crucial in industries involving lubrication, pipelines, and fluid transport.
Bernoulli’s Principle is the basis for devices like atomizers, spray guns, and chimneys.
Principles of fluid mechanics are used in designing turbines, pumps, and fluid-based energy systems.
Fluid statics deals with fluids at rest, while fluid dynamics focuses on fluids in motion.
Applications of Archimedes' Principle include measuring the volume and density of irregularly shaped objects.
The behavior of fluids under various forces is described using equations of motion, such as the Navier-Stokes equations.
Fluid properties like density, pressure, viscosity, and buoyancy are fundamental to understanding their behavior and practical applications.