# Fluid Mechanics

**Fluid Mechanics** is a branch of physics that deals with the behavior of fluids, both liquids and gases, under various conditions of flow, pressure, and temperature. The field has applications in a wide range of engineering disciplines, including mechanical, aerospace, civil, and chemical engineering, as well as fundamental implications in areas like geophysics, meteorology, and physiology.

## Fundamental Concepts

### Fluid Properties

Key properties of fluids include viscosity, density, and compressibility. Viscosity describes a fluid's resistance to flow, density relates mass to volume, and compressibility measures the change in volume under pressure.

### Flow Regimes

- Laminar Flow: Characterized by smooth, orderly fluid motion.
- Turbulent Flow: Characterized by chaotic, disorderly fluid motion.

## Governing Equations

- Navier-Stokes Equations: These are the fundamental equations of fluid flow and describe how the velocity of a fluid evolves over time. They are a set of non-linear partial differential equations that consider viscosity.
- Euler's Equations: A simplification of the Navier-Stokes equations that applies to ideal, inviscid fluids.
- Bernoulli's Equation: An energy conservation equation useful for inviscid flows along a streamline.

## Types of Fluid Flow

- Steady vs. Unsteady Flow
- Compressible vs. Incompressible Flow
- One, Two, and Three-dimensional Flows
- Internal vs. External Flows

## Methods of Analysis

### Experimental Methods

Wind tunnels, water flumes, and PIV (Particle Image Velocimetry) are some of the methods used to study fluid flows experimentally.

### Computational Fluid Dynamics

Computational methods, often abbreviated as CFD, are used to solve complex fluid flow problems numerically.

## Applications

- Aerospace: Airflow over aircraft
- Civil Engineering: Flow in pipes, dams, and drainage systems
- Environmental Science: Air and water pollution dynamics
- Medicine: Blood flow, respiratory mechanics
- Meteorology: Weather systems and ocean currents

## History

Fluid Mechanics has a long history dating back to ancient civilizations for irrigation and water supply. However, the modern form of the subject took shape in the 18th and 19th centuries with contributions from Euler, Bernoulli, and Navier-Stokes, among others.