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Note the location of critical flow, subcritical flow, and supercritical flow. The energy equation used for open channel flow computations is a simplification of the Bernoulli Equation (See Bernoulli Principle), which takes into account pressure head, elevation head, and velocity head. (Note, energy and head are synonymous in Fluid Dynamics.
If more than one formula is applicable in the flow regime under consideration, the choice of formula may be influenced by one or more of the following: Required accuracy; Speed of computation required; Available computational technology: calculator (minimize keystrokes) spreadsheet (single-cell formula) programming/scripting language (subroutine).
The depth of flow is the same at every section of the channel. Uniform flow can be steady or unsteady, depending on whether or not the depth changes with time, (although unsteady uniform flow is rare). Varied flow. The depth of flow changes along the length of the channel. Varied flow technically may be either steady or unsteady.
The Chézy formula concerns the velocity of water flowing through conduits and is widely celebrated for its use in open channel flow calculations. [2] By the definition of open channel, the Chézy formula also applies to partially-full pipe flow.
The Chézy formula describes mean flow velocity in turbulent open channel flow and is used broadly in fields related to fluid mechanics and fluid dynamics. Open channels refer to any open conduit, such as rivers, ditches, canals, or partially full pipes. The Chézy formula is defined for uniform equilibrium and non-uniform, gradually varied flows.
However, this equation is also used for calculation of flow variables in case of flow in partially full conduits, as they also possess a free surface like that of open channel flow. All flow in so-called open channels is driven by gravity .
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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.