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Uniform flow. 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.
In mathematics, potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a ...
The laminar flow through a pipe of uniform (circular) cross-section is known as Hagen–Poiseuille flow. The equations governing the Hagen–Poiseuille flow can be derived directly from the Navier–Stokes momentum equations in 3D cylindrical coordinates ( r , θ , x ) by making the following set of assumptions:
Superposition of uniform flow and source flow yields the Rankine half body flow. A practical example of this type of flow is a bridge pier or a strut placed in a uniform stream. The resulting stream function ( ψ {\displaystyle \psi } ) and velocity potential ( ϕ {\displaystyle \phi } ) are obtained by simply adding the stream function and ...
n = 1: a trivial case of uniform flow, n = 2: flow through a corner, or near a stagnation point, and; n = −1: flow due to a source doublet; The constant A is a scaling parameter: its absolute value | A | determines the scale, while its argument arg(A) introduces a rotation (if non-zero).
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] Typically, this depth is calculated using the Manning formula. Gradually varied flow occurs when the change in flow depth per change ...
Potential flow streamlines for an ideal uniform flow. For steady-state, spatially uniform flow of a fluid in the xy plane, the velocity vector is = + where is the absolute magnitude of the velocity (i.e., = | |);
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.