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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
By measuring the level of water remaining in the vessel, the time can be measured with uniform graduation. This is an example of outflow clepsydra. Since the water outflow rate is higher when the water level is higher (due to more pressure), the fluid's volume should be more than a simple cylinder when the water level is high.
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 ...
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 Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. [1] It is a quasilinear partial differential equation ; its analytical solution is often limited to specific initial and boundary conditions. [ 2 ]
Then for an ideal gas the compressible Euler equations can be simply expressed in the mechanical or primitive variables specific volume, flow velocity and pressure, by taking the set of the equations for a thermodynamic system and modifying the energy equation into a pressure equation through this mechanical equation of state. At last, in ...