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A polynomial weir is a weir that has a geometry defined by a polynomial equation of any order n. [11] In practice, most weirs are low-order polynomial weirs. The standard rectangular weir is, for example, a polynomial weir of order zero. The triangular (V-notch) and trapezoidal weirs are of order one. High-order polynomial weirs are providing ...
Hydraulic jump in a rectangular channel, also known as classical jump, is a natural phenomenon that occurs whenever flow changes from supercritical to subcritical flow. In this transition, the water surface rises abruptly, surface rollers are formed, intense mixing occurs, air is entrained, and often a large amount of energy is dissipated.
For channels of a given width, the hydraulic radius is greater for deeper channels. In wide rectangular channels, the hydraulic radius is approximated by the flow depth. The hydraulic radius is not half the hydraulic diameter as the name may suggest, but one quarter in the case of a full pipe. It is a function of the shape of the pipe, channel ...
In rectangular channel, such conservation equation can be further simplified to dimensionless M-y equation form, which is widely used in hydraulic jump analysis in open channel flow. Jump height in terms of flow Dividing by constant and introducing the result from continuity gives
It uses a combination of the energy, momentum, and continuity equations to determine water depth with a given a friction slope (), channel slope (), channel geometry, and also a given flow rate. In practice, this technique is widely used through the computer program HEC-RAS , developed by the US Army Corps of Engineers Hydrologic Engineering ...
The velocity of the surface can by related to the outflow velocity by the continuity equation =, where is the orifice's cross section and is the (cylindrical) vessel's cross section. Renaming v 2 {\displaystyle v_{2}} to v A {\displaystyle v_{A}} (A like Aperture) gives:
The Brezina equation. The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. [n 1] These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is ...
The equation is = / where: Q is the discharge in cubic feet per second over the weir, L is the length of the weir in feet, and h 1 is the height of the water above the top of the weir. [14] [15] [further explanation needed]