Fluids

Hydrostatics and hydrodynamics: ideal and viscous fluids, pressure fields, flow rates, and lift.

General idea of the topic

Fluid mechanics studies liquids and gases, media that have no shape of their own and flow under the action of forces. They are described with continuous quantities such as density, pressure and the velocity field, instead of following individual particles.

The block starts with the basic properties, continues with fluids at rest, moves to ideal fluids in motion, introduces viscosity and flow regimes, treats real fluids and ends with the waves that propagate in them.

What you will truly understand

By the end you will be able to compute pressures and forces in fluids at rest, apply continuity and Bernoulli to ideal flows, estimate viscous losses with the Reynolds number and recognize when an ideal model stops being valid.

You will also be able to relate fluid mechanics to sound and surface waves.

Recommended learning route

1. Fundamentals: fluid, density, pressure, compressibility and surface tension.
2. Fluid Statics: hydrostatic pressure, Pascal's and Archimedes' principles and their applications.
3. Fluid Dynamics: continuity, Bernoulli's equation and its applications, and the equations of motion.
4. Viscosity and Flow Regimes: viscosity, laminar and turbulent flow, Reynolds number and head loss.
5. Real Fluids: pipe flow, basic aerodynamics and hydrodynamics with technical applications.
6. Waves in Fluids: surface waves, longitudinal waves and an introduction to sound.

Physical criterion you must acquire

The essential criterion is to choose the model according to the problem: hydrostatics if the fluid is at rest, Bernoulli if the flow is steady, incompressible and with negligible viscosity, and head loss if there is friction with the walls. The Reynolds number indicates when the ideal model is reasonable.

Connection with real problems

• dams, tanks and water systems.
• aviation and aerodynamics.
• medicine: circulation and blood pressure.
• pipes, pumps and hydraulic networks.

Final goal of the topic

The final goal is to model the behavior of fluids at rest and in motion, choose the appropriate model and compute pressures, flow rates and forces with physical coherence.