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The hydraulic radius is one of the properties of a channel that controls water discharge. It also determines how much work the channel can do, for example, in moving sediment. All else equal, a river with a larger hydraulic radius will have a higher flow velocity, and also a larger cross sectional area through which that faster water can travel.
In fluid mechanics and hydraulics, open-channel flow is a type of liquid flow within a conduit with a free surface, known as a channel. [ 1 ] [ 2 ] The other type of flow within a conduit is pipe flow .
This can only occur in a smooth channel that does not experience any changes in flow, channel geometry, roughness or channel slope. During uniform flow, the flow depth is known as normal depth (yn). This depth is analogous to the terminal velocity of an object in free fall, where gravity and frictional forces are in balance (Moglen, 2013). [ 3 ]
The one-dimensional (1-D) Saint-Venant equations were derived by Adhémar Jean Claude Barré de Saint-Venant, and are commonly used to model transient open-channel flow and surface runoff. They can be viewed as a contraction of the two-dimensional (2-D) shallow-water equations, which are also known as the two-dimensional Saint-Venant equations.
The Chézy Formula is a semi-empirical resistance equation [1] [2] which estimates mean flow velocity in open channel conduits. [3] The relationship was conceptualized and developed in 1768 by French physicist and engineer Antoine de Chézy (1718–1798) while designing Paris's water canal system.
Open channel flow describes cases where flowing liquid has a top surface open to the air; the cross-section of the flow is only determined by the shape of the channel on the lower side, and is variable depending on the depth of liquid in the channel. Techniques appropriate for a fixed cross-section of flow in a pipe are not useful in open channels.
[4] [5] [6] A generalized model of the flow distribution in channel networks of planar fuel cells. [6] Similar to Ohm's law, the pressure drop is assumed to be proportional to the flow rates. The relationship of pressure drop, flow rate and flow resistance is described as Q 2 = ∆P/R. f = 64/Re for laminar flow where Re is the Reynolds number.
Computation in flows with free and moving boundaries like the open-channel flow is a difficult task. The position of the boundary is known only at the initial time and its location at later times can be determined as using various methods like the Interface Tracking Method and the Interface Capturing Method.