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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 wall shear stress τ is dependent on the flow velocity u, they can be related by using e.g. the Darcy–Weisbach equation, Manning formula or Chézy formula. Further, equation ( 1 ) is the continuity equation , expressing conservation of water volume for this incompressible homogeneous fluid.
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 following outline is provided as an overview of and topical guide to fluid dynamics: . In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases.
Note that for the case of a circular pipe, D H = 4 π R 2 2 π R = 2 R {\displaystyle D_{\text{H}}={\frac {4\pi R^{2}}{2\pi R}}=2R} The need for the hydraulic diameter arises due to the use of a single dimension in the case of a dimensionless quantity such as the Reynolds number , which prefers a single variable for flow analysis rather than ...
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] From experimental data, Stickler proposed that the dimensionally homogeneous form of the Manning formula could be quantified as: [3]
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Most charts or tables indicate the type of friction factor, or at least provide the formula for the friction factor with laminar flow. If the formula for laminar flow is f = 16 / Re , it is the Fanning factor f, and if the formula for laminar flow is f D = 64 / Re , it is the Darcy–Weisbach factor f D.