Hydrodynamiikan

Hydrodynamiikan, or hydrodynamics, is the branch of fluid mechanics that studies the motion of liquids and the forces that act on them. It treats phenomena where inertia, pressure, gravity, and viscous stresses influence fluid motion. In many practical problems liquids are approximated as incompressible Newtonian fluids, though compressibility can be important in high-speed flows.

Core equations are conservation of mass (continuity) and momentum, expressed by the Navier–Stokes equations. For inviscid flows these reduce to Euler equations, and, for irrotational motion, potential flow theory applies. Bernoulli's principle relates pressure and velocity along a streamline in steady, incompressible flow. Vorticity and circulation describe rotational aspects of the flow.

Boundary conditions include no-slip at solid surfaces for viscous flows, giving rise to boundary layers described by Prandtl. Dimensionless analysis via Reynolds number, Froude number, and others helps categorize flow regimes into laminar and turbulent.

Applications span engineering and natural systems: pipe networks, hydroelectric and hydraulic machines, naval and aerospace hydrodynamics, oceanography, coastal engineering, and biomedical flows such as blood movement in vessels. Modern analysis relies on computational fluid dynamics (CFD), experimental methods, and analytical solutions.

Historical development: early quantitative studies emerged with Euler and Bernoulli; Navier and Stokes formulated the governing equations in the 19th century; Prandtl introduced boundary layer theory in 1904, enabling practical modeling of viscous flows. The field has since grown to address turbulence, multiphase flows, and complex geometries.