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The shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant (see the related section below). The equations are derived [ 2 ] from depth-integrating the Navier–Stokes equations , in the case where the horizontal length scale is much greater than the vertical ...
Leonhard Euler is credited of introducing both specifications in two publications written in 1755 [3] and 1759. [4] [5] Joseph-Louis Lagrange studied the equations of motion in connection to the principle of least action in 1760, later in a treaty of fluid mechanics in 1781, [6] and thirdly in his book Mécanique analytique. [5]
Defining equation (physical chemistry) List of electromagnetism equations; List of equations in classical mechanics; List of equations in gravitation; List of equations in nuclear and particle physics; List of equations in quantum mechanics; List of photonics equations; List of relativistic equations; Table of thermodynamic equations
[3] Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Dye steadily injected into the fluid at a fixed point (as in dye tracing) extends along a streakline. Pathlines are the trajectories that individual fluid particles follow. These can be thought of as ...
Washburn's equation is also used commonly to determine the contact angle of a liquid to a powder using a force tensiometer. [ 5 ] In the case of porous materials, many issues have been raised both about the physical meaning of the calculated pore radius r {\displaystyle r} [ 6 ] and the real possibility to use this equation for the calculation ...
Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell.The law was formulated by Henry Darcy based on results of experiments [1] on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.
For a water-filled glass tube in air at standard conditions for temperature and pressure, γ = 0.0728 N/m at 20 °C, ρ = 1000 kg/m 3, and g = 9.81 m/s 2. Because water spreads on clean glass, the effective equilibrium contact angle is approximately zero. [4] For these values, the height of the water column is
The primitive equations may be linearized to yield Laplace's tidal equations, an eigenvalue problem from which the analytical solution to the latitudinal structure of the flow may be determined. In general, nearly all forms of the primitive equations relate the five variables u, v, ω, T, W, and their evolution over space and time.