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The Chézy formula describes mean flow velocity in turbulent open channel flow and is used broadly in fields related to fluid mechanics and fluid dynamics. Open channels refer to any open conduit, such as rivers, ditches, canals, or partially full pipes. The Chézy formula is defined for uniform equilibrium and non-uniform, gradually varied flows.
The Chézy equation is a pioneering formula in the field of fluid mechanics, and was expanded and modified by Irish engineer Robert Manning in 1889 [1] as the Manning formula. The Chézy formula concerns the velocity of water flowing through conduits and is widely celebrated for its use in open channel flow calculations. [ 2 ]
The discharge is constant throughout the reach of the channel under consideration. This is often the case with a steady flow. This flow is considered continuous and therefore can be described using the continuity equation for continuous steady flow. Spatially-varied flow. The discharge of a steady flow is non-uniform along a channel.
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 is the continuity equation, expressing conservation of water volume for this incompressible homogeneous fluid.
Thus the water discharge of a tap (faucet) can be measured with a measuring jug and a stopwatch. Here the discharge might be 1 litre per 15 seconds, equivalent to 67 ml/second or 4 litres/minute. This is an average measure. For measuring the discharge of a river we need a different method and the most common is the 'area-velocity' method.
The variations of Q/Q (full) and V/V (full) with H/D ratio is shown in figure(b).From the equation 5, maximum value of Q/Q (full) is found to be equal to 1.08 at H/D =0.94 which implies that maximum rate of discharge through a conduit is observed for a conduit partly full.
It is described by the fact that the discharge through a river of an approximate rectangular cross-section must, through conservation of mass, equal Q = u ¯ b h {\displaystyle Q={\bar {u}}bh} where Q {\displaystyle Q} is the volumetric discharge, u ¯ {\displaystyle {\bar {u}}} is the mean flow velocity, b {\displaystyle b} is the channel ...
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.