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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]
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 discharge may also be expressed as: Q = − dS/dT . Substituting herein the expression of Q in equation (1) gives the differential equation dS/dT = A·S, of which the solution is: S = exp(− A·t) . Replacing herein S by Q/A according to equation (1), it is obtained that: Q = A exp(− A·t) .
Dissolved load is the portion of a stream's total sediment load that is carried in solution, especially ions from chemical weathering. It is a major contributor to the total amount of material removed from a river's drainage basin , along with suspended load and bed load .
Results showed that this approximation does not affect the calculated infiltration flux because the diffusive flux is small and that the finite water-content vadose zone flow method is a valid solution of the equation [13] is a set of three ordinary differential equations, is guaranteed to converge and to conserve mass. It requires the ...
Drainage basin of the Ohio River, part of the Mississippi River drainage basin. In hydrology, the drainage basin is a logical unit of focus [clarification needed] for studying the movement of water within the hydrological cycle. The process of finding a drainage boundary is referred to as watershed delineation. Finding the area and extent of a ...
Equation. By modeling Playfair's law in the following mathematical scheme, we can find the incision rate of the stream into the valley by following:
This is an important distinction because, for example, the vertical velocity cannot be zero when the floor changes depth, and thus if it were zero only flat floors would be usable with the shallow-water equations. Once a solution (i.e. the horizontal velocities and free surface displacement) has been found, the vertical velocity can be ...