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The Manning formula or Manning's equation is an empirical ... of a full pipe. It is a function of the shape of the pipe, channel, or river in which the water is ...
, the hydraulic diameter of the pipe (for a pipe of circular section, this equals D; otherwise D H = 4A/P for a pipe of cross-sectional area A and perimeter P) (m); v {\displaystyle \langle v\rangle } , the mean flow velocity , experimentally measured as the volumetric flow rate Q per unit cross-sectional wetted area (m/s);
The Haaland equation was proposed in 1983 by Professor S.E. Haaland of the Norwegian Institute of Technology. [9] It is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation, but the discrepancy from experimental data is well within ...
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 shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant (see the related section below). The equations are derived [ 2 ] from depth-integrating the Navier–Stokes equations , in the case where the horizontal length scale is much greater than the vertical ...
Once the friction factors of the pipes are obtained (or calculated from pipe friction laws such as the Darcy-Weisbach equation), we can consider how to calculate the flow rates and head losses on the network. Generally the head losses (potential differences) at each node are neglected, and a solution is sought for the steady-state flows on the ...
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Defining equation SI units Dimension Flow velocity vector field u = (,) m s −1 [L][T] −1: Velocity pseudovector field ω = s −1 [T] −1: Volume velocity ...