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The discharge formula, Q = A V, can be used to rewrite Gauckler–Manning's equation by substitution for V. Solving for Q then allows an estimate of the volumetric flow rate (discharge) without knowing the limiting or actual flow velocity. The formula can be obtained by use of dimensional analysis.
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.
The first term on the right-hand side of the equation is the dimensionless ratio of hydraulic radius to roughness height, commonly referred to as relative roughness. The remaining term, known as the boundary shear velocity, approximates the flow of water downhill under the influence of gravity and has units of velocity, i.e., L/T. [8] [1] [4]
Shear velocity also helps in thinking about the rate of shear and dispersion in a flow. Shear velocity scales well to rates of dispersion and bedload sediment transport. A general rule is that the shear velocity is between 5% and 10% of the mean flow velocity. For river base case, the shear velocity can be calculated by Manning's equation.
Manning equation – Estimate of velocity in open channel flows; Mild-slope equation – Physics phenomenon and formula; Morison equation – Equation for force on an object in sea waves; Navier–Stokes equations – Equations describing the motion of viscous fluid substances
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One roughness coefficient is Manning's n-value. [2] Manning's n is used extensively around the world to predict the degree of roughness in channels. The coefficient is critical in hydraulic engineering, floodplain management, and sediment transport studies. Flow velocity is strongly dependent on the resistance to flow. [3]
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 ...