Fluid Statics
Fluid static equilibrium, fundamental hydrostatic equation, and Pascal's principle.
General idea of the topic
Fluid statics studies fluids at rest. Without motion there are no shear stresses, and the only force the fluid exerts on a surface is normal, produced by the pressure. The pressure increases with depth because each layer supports the weight of those above it.
The topic derives the hydrostatic pressure and the fundamental equation, which gives the variation of pressure with depth, and from it obtains Pascal's and Archimedes' principles, which explain hydraulic presses and flotation.
What you will truly understand
By the end you will be able to compute the pressure at a given depth, the force on walls and gates, the transmission of pressure in a press and the buoyant force on a submerged body.
You will also be able to decide whether a body floats or sinks by comparing densities.
Recommended learning route
- Hydrostatic Pressure: pressure due to the weight of the fluid and its relation to depth.
- Fundamental Principle of Hydrostatics: fundamental equation, p = p₀ + ρgh, and its assumptions.
- Pascal's Principle: transmission of pressure in an enclosed fluid.
- Archimedes' Principle: buoyant force on a submerged body equal to the weight of the fluid displaced.
- Applications of Hydrostatics: manometers, communicating vessels and flotation.
Physical criterion you must acquire
The essential criterion is that the pressure depends on depth, not on the shape of the container or the total amount of fluid. The buoyant force is computed with the submerged volume and the density of the fluid, not of the body, and a body floats in equilibrium when its weight equals the buoyant force.
Connection with real problems
- dams, tanks and gates.
- hydraulic presses and brakes.
- ships, submarines and balloons.
- manometers and pressure measurement.
Final goal of the topic
The final goal is to solve any problem of fluids at rest, compute pressures, forces and buoyancy and explain flotation rigorously.
Topics in this section
- Hydrostatic Pressure
Hydrostatic pressure variation in stationary fluids as a function of depth, density, and gravity.
- Fundamental Principle of Hydrostatics
Relationship between pressure and vertical elevation in a fluid at rest.
- Pascal's Principle
Transmission of pressure in confined fluids. Theory, formulas, worked examples and interactive graphs.
- Archimedes' Principle
Hydrostatic buoyant force on submerged objects and physical conditions for equilibrium and flotation.
- Applications of Hydrostatics
Manometers, hydraulic presses, communicating vessels, and stability of floating bodies.