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According to the equations, a basin with high drainage density, the contribution of surface runoff to stream discharge will be high, while that from baseflow will be low. Conversely, a stream in a low drainage density system will have a larger contribution from baseflow and a smaller contribution from overland flow. [8] [9]
Darcy's law is an equation that describes the flow of a fluid flow trough 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.
Solutions that can be formally expanded in this way are known as normal solutions to the Boltzmann equation. [6] This class of solutions excludes non-perturbative contributions (such as /), which appear in boundary layers or near internal shock layers. Thus, Chapman–Enskog theory is restricted to situations in which such solutions are negligible.
Volume velocity, volume flux φ V (no standard symbol) = m 3 s −1 [L] 3 [T] −1: Mass current per unit volume: s (no standard symbol) = / kg m −3 s −1 [M] [L] −3 [T] −1: Mass current, mass flow rate: I m
The amplified drainage equation uses an hydraulic equivalent of Joule's law in electricity. It is in the form of a differential equation that cannot be solved analytically (i.e. in a closed form ) but the solution requires a numerical method for which a computer program is indispensable.
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 ]
In hydrology, discharge is the volumetric flow rate (volume per time, in units of m 3 /h or ft 3 /h) of a stream. It equals the product of average flow velocity (with dimension of length per time, in m/h or ft/h) and the cross-sectional area (in m 2 or ft 2). [1] It includes any suspended solids (e.g. sediment), dissolved chemicals like CaCO
The hyperbolic nature of the equation implies that the solution of the Buckley–Leverett equation has the form (,) = (), where is the characteristic velocity given above. The non-convexity of the fractional flow function f w ( S w ) {\displaystyle f_{w}(S_{w})} also gives rise to the well known Buckley-Leverett profile, which consists of a ...