Chézy formula
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.
[2][4] Chézy discovered a similarity parameter that could be used for estimating flow characteristics in one channel based on the measurements of another.
[1][5][6][7] Manning's modifications to the Chézy formula allowed the entire similarity parameter to be calculated by channel characteristics rather than by experimental measurements.
Today, the Chézy and Manning equations continue to accurately estimate open channel fluid flow and are standard formulas in various fields related to fluid mechanics and hydraulics, including physics, mechanical engineering, and civil engineering.
The relationship between linear momentum and deformable fluid bodies is well explored, as are the Navier–Stokes equations for incompressible flow.
[2] As long as uniform flow can be assumed, applying the linear momentum equation to a river channel flowing in one dimension means that momentum remains conserved and the forces are balanced in the direction of flow: Here, the hydrostatic pressure forces are F1 and F2, the component (τwPl) represents the shear force of friction acting on the control volume, and the component (ω sin θ) represents the gravitational force of the fluid's weight acting on the sloped channel bottom are held in balance in the flow direction.
[1][2] This can be illustrated in a series of advanced formulas which identify a shear stress similarity parameter characteristic of all turbulent open channels.
[6][7] Manning's modifications to the Chézy formula allowed the entire similarity parameter to be calculated by channel characteristics rather than by experimental measurements.
) was determined to remain constant based on the material of the wetted perimeter, allowing for a standardized table of values to be developed that could reasonably estimate flow velocity.
[2] Additionally, both equations are explicitly used with uniform or "steady-state" flow where the hydraulic depth is constant, due to their derivation from the conservation of momentum.
Both formulas continue to be broadly taught and are used in open channel and fluid dynamics research.
Today, the Manning formula is likely the most globally used formula for open channel uniform flow analysis, due to its simplicity, proven efficacy, and the fact that most open channel studies are concerned with turbulent flow.
[12] Chézy's formula is one of the oldest in the field of fluid mechanics,[1] it applies to a wider range of flows than the Manning equation,[13] and its influence continues to this day.
