The Physics of Fluids
A fluid is any substance that can flow and take the shape of its container (i.e., liquids and gases).
Pressure
Pressure (P) is defined as the force exerted per unit area.
Formula: P = F / A
F is the force acting perpendicular to the surface.
A is the area over which the force is exerted.
The SI unit of pressure is the Pascal (Pa), which is one newton per square meter (N/m²).
Pressure in a fluid increases with depth due to the weight of the fluid above.
Pascal's Principle
This principle applies to a confined, incompressible fluid.
The Principle: A change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel.
Application: Hydraulic Lifts: A small force applied to a small piston (small area) creates a pressure change in the fluid. This pressure is transmitted to a large piston (large area). Since P = F/A is constant, the same pressure acting on a larger area produces a much larger output force (F₂ = F₁ * (A₂/A₁)). This allows a small input force to lift a very heavy object, like a car.
Buoyancy and Archimedes' Principle
Buoyancy is the upward force exerted by a fluid that opposes the weight of an immersed object.
Archimedes' Principle: The buoyant force on a submerged or floating object is equal to the weight of the fluid displaced by the object.
Formula: Fₑ = ρₒₗᵤᵢₐ Vₛᵤᵦₘₑᵣ₉ₑₐ g
ρₒₗᵤᵢₐ is the density of the fluid.
Vₛᵤᵦₘₑᵣ₉ₑₐ is the volume of the object that is submerged in the fluid.
Floating and Sinking:
An object will float if the buoyant force is equal to its weight. This happens when the object's average density is less than the density of the fluid.
An object will sink if its weight is greater than the buoyant force. This happens when the object's average density is greater than the density of the fluid.
An object will be neutrally buoyant (remain suspended) if its weight equals the buoyant force when fully submerged, which occurs when its average density equals the density of the fluid.