Hydrodynamics

Hydrodynamics is the branch of fluid dynamics that studies the motion of liquids and the forces acting on them. It treats liquids as continuous media and encompasses flows in pipes, channels, around bodies, and in natural water bodies. It distinguishes from gas dynamics by focusing on liquids that are largely incompressible at common speeds, though compressibility can be relevant in high-speed jets and cavitation.

The motion of fluids is governed by conservation laws. The continuity equation expresses mass conservation. For viscous flows, momentum conservation leads to the Navier-Stokes equations; for inviscid flows, the Euler equations apply. In many problems, the velocity field and pressure distribution are unknown and are solved subject to boundary conditions on surfaces such as walls and free surfaces. For steady, inviscid, incompressible flows, Bernoulli's principle relates pressure and velocity along a streamline.

Key concepts include Reynolds number, which characterizes the relative importance of inertial and viscous forces; laminar versus turbulent flow; boundary layers near solid surfaces; vorticity and potential flow; and wave phenomena including surface and internal waves in fluids. Problems may be treated analytically in simple geometries or numerically using computational fluid dynamics (CFD).

Applications span engineering and natural sciences, including ship hydrodynamics and hull design, propeller and turbomachinery analysis, offshore engineering, hydraulics and flood modeling, environmental flows, oceanography, and geophysical flows in rivers and coastal regions.

The subject has a long history, with early work by Euler and Bernoulli, and later foundational developments by Navier and Stokes, who derived the general equations of motion for viscous fluids. Hydrodynamics remains an active field in research and industry, combining theory, computation, and experimentation.