Dictionary:

hydrodynamics

  (hī'drō-dī-năm'ĭks)

1. (used with a sing. verb) The branch of science that deals with the dynamics of fluids, especially incompressible fluids, in motion.
2. (used with a pl. verb) The dynamics of fluids in motion.

The study of fluids in motion. The study is based upon the physical conservation laws of mass, momentum, and energy. The mathematical statements of these laws may be written in either integral or differential form. The integral form is useful for large-scale analyses and provides answers that are sometimes very good and sometimes not, but that are always useful, particularly for engineering applications. The differential form of the equations is used for small-scale analyses. In principle, the differential forms may be used for any problem, but exact solutions can be found only for a small number of specialized flows. Solutions for most problems must be obtained by using numerical techniques, and these are limited by the computer7's inability to model small-scale processes. See also Conservation of energy; Conservation of mass; Conservation of momentum; Fluid flow; Fluid mechanics.

Applications of hydrodynamics include the study of closed-conduit and open-channel flow, and the calculation of forces on submerged bodies.

Flow in closed conduits, or pipes, has been extensively studied both experimentally and theoretically. If the pipe Reynolds number, given by the equation below, where V is the average velocity and D is the pipe diameter, is less than about 2000, the flow in the pipe is laminar. In this case, the solution to the continuity, momentum, and energy equations is readily obtained, particularly in the case of steady flows. If Re_D is greater than about 4000, the flow in the pipe is turbulent, and the solution to the continuity, momentum, and energy equations can be obtained only by employing empirical correlations and other approximate modeling tools. The Re_D region between 2000 and 4000 is the transition region in which the flow is intermittently laminar and turbulent. See also Laminar flow; Reynolds number; Turbulent flow.

Confined flows that have a liquid surface exposed to the atmosphere (a free surface) are called open-channel flows. Flows in rivers, canals, partially full pipes, and irrigation ditches are examples. The difficulty with these flows is that the shape of the free surface is one of the unknowns to be calculated.

In most open-channel flows the bottom slope and the water depth change with position, and the free surface is not parallel to the channel bottom. If the slopes are small and the changes are not too sudden, the flow is called a gradually varied flow. An energy balance between two sections of the channel yields a differential equation for the rate of change of the water depth with respect to the distance along the channel. The solution of this equation, which must be accomplished by using one of many available numerical techniques, gives the shape of the water surface.

Flow over spillways and weirs and flow through a hydraulic jump are examples of rapidly varying flows. In these cases, changes of water depth with distance along the channel are large. Here, because of large accelerations, the pressure distribution with depth may not be hydrostatic as it is in the cases of gradually varied and uniform flows. Solutions for rapidly varying flows are accomplished by using approximation techniques. See also Hydraulic jump; Open channel.

The force exerted by a fluid flowing past a submerged body is calculated by integrating the pressure distribution over the surface of the body. The pressure distribution is determined from the simultaneous solution of the continuity and momentum equations along with the appropriate boundary conditions. In almost all cases, this solution must be accomplished by using an appropriate approximation. See also Boundary-layer flow.

Usually the force exerted on the body is resolved into two components, the lift and the drag. The drag force is the component parallel to the velocity of the undisturbed stream (flow far away from the body), and the lift force is the component perpendicular to the undisturbed stream.

The mathematical study of forces, energy, and pressure of liquids in motion. Compare hydrostatics.

The noun has one meaning:

Meaning #1: study of fluids in motion
  Synonym: hydrokinetics

Hydrodynamics simulation of the Rayleigh-Taylor instability ^[1]

Hydrodynamics, also known as liquid-dynamics in limited academic circles, (literally, "water motion") is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. However, this distinction from fluid dynamics as a whole is not always fully observed.

Blaise Pascal in the 1600s contributed some of the initial theory to this field. The term originates from the work of Daniel Bernoulli, based on the title of his work called Hydrodynamica (1738). He and Leonhard Euler established the general equations of hydrodynamics.

The practice was continued by Joseph Louis Lagrange (1736-1813) with the Euler-Lagrange system, Jean le Rond d'Alembert (1717-1783) discovered the Cauchy-Riemann equations, Pierre-Simon Laplace (1749-1827) with the governing equation in the potential flow named after him, Hermann Ludwig Ferdinand von Helmholtz (1821-1894) and William Thomson, Lord Kelvin (1824-1907) with Kelvin-Helmholtz instability (see also the Rayleigh-Taylor, Plateau-Rayleigh and Richtmyer-Meshkov instabilities) and Helmholtz's work on vortices.

An analogous field of study, the dynamics of electrically conducting fluids in magnetic fields is called magnetohydrodynamics.

Footnotes

1. ^ Shengtai Li, Hui Li "Parallel AMR Code for Compressible MHD or HD Equations" (Los Alamos National Laboratory) [1]

See also

• Dissolution rate
• Convective diffusion theory
• Reynolds number
• Boundary layer
• Ludwig Prandtl
• Benjamin Levich
• Osborne Reynolds
• Magnetohydrodynamics
• Poiseuille's law
• Potential flow
• Plume (hydrodynamics)
• Entrainment (hydrodynamics)be-x-old:Гідрадынаміка

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