Fluid dynamics

Fluid dynamics studies how liquids and gases move and interact with forces, boundaries, and one another. It explains flows ranging from air around wings to water through pipes.

Navier–Stokes equations: A system of partial differential equations describing how a viscous fluid’s velocity changes under forces and pressure. They express the central momentum balance used to model fluid motion.
Velocity field: A function assigning a velocity vector to each position and time in a moving medium. It is the basic description of how fluid motion varies through space and time.
Aerodynamics: The study of air motion and the forces it exerts on moving or stationary bodies. It applies fluid-flow principles to aircraft, vehicles, and structures exposed to wind.
Hydrostatics: The study of fluids at rest and the pressure forces within them. It treats equilibrium rather than the moving flows that define fluid dynamics.
Continuity equation: An equation expressing conservation of mass in a flowing medium. It constrains how fluid speed and density change as flow passes through different areas.
Pressure: Force exerted per unit area by a fluid or other material. Pressure differences drive and redistribute fluid motion.
Hydraulics: The engineering study of liquids at rest and in motion, especially in practical systems. It uses fluid behavior to design pipes, pumps, turbines, and hydraulic machinery.
Potential flow: An idealized, irrotational fluid flow represented by a velocity potential, usually neglecting viscosity. Its simpler equations omit viscous effects that can dominate near surfaces and in wakes.
Reynolds number: A dimensionless ratio comparing inertial forces with viscous forces in a flow. It helps predict whether viscous effects or inertia dominate a particular flow.
Viscosity: A measure of a fluid’s resistance to deformation and internal shearing motion. It determines how strongly neighboring layers of fluid resist sliding past one another.

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