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The parameter is known as the Froude number, and is defined as: = where is the mean velocity, is the characteristic length scale for a channel's depth, and is the gravitational acceleration. Depending on the effect of viscosity relative to inertia, as represented by the Reynolds number , the flow can be either laminar , turbulent , or ...
The extended Froude number is defined as the ratio between the kinetic and the potential energy: = + (), where u is the mean flow velocity, β = gK cos ζ, (K is the earth pressure coefficient, ζ is the slope), s g = g sin ζ, x is the channel downslope position and is the distance from the point of the mass release along the channel to the ...
To help visualize the relationship of the upstream Froude number and the flow depth downstream of the hydraulic jump, it is helpful to plot y 2 /y 1 versus the upstream Froude Number, Fr 1. (Figure 8) The value of y 2 /y 1 is a ratio of depths that represent a dimensionless jump height; for example, if y 2 /y 1 = 2, then the jump doubles the ...
The energy equation used for open channel flow computations is a simplification of the Bernoulli Equation ... this depth corresponds to a Froude Number ...
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
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
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.
This number is relevant when gravitational force is predominant in the fluid motion. For example, open channel flow, wave motion in the ocean, forces on bridge piers and offshore structures. [citation needed] The Eötvös number defines the ratio of buoyancy compared with surface tension forces.