Manning formula

Summary

The Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.e., open channel flow. However, this equation is also used for calculation of flow variables in case of flow in partially full conduits, as they also possess a free surface like that of open channel flow. All flow in so-called open channels is driven by gravity. It was first presented by the French engineer Philippe Gaspard Gauckler in 1867, and later re-developed by the Irish engineer Robert Manning in 1890. Thus, the formula is also known in Europe as the Gauckler–Manning formula or Gauckler–Manning–Strickler formula (after Albert Strickler). The Gauckler–Manning formula is used to estimate the average velocity of water flowing in an open channel in locations where it is not practical to construct a weir or flume to measure flow with greater accuracy. Manning's equation is also commonly used as part of

Official source

https://en.wikipedia.org/wiki/Manning_formula

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Related publications (3)

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Understanding diffusive processes across the sediment-water interface is important for quantifying hyporheic exchanges and related biogeochemical processes (e.g., denitrification, biomass growth). Viscous, turbulent and dispersive effects all contribute to the hydrodynamics of flows over rough permeable beds, although their specific role across the interface remains poorly understood. In order to model mixing processes from the permeable bed to the free surface, we have run experiments on low submergence flows over sloping porous beds made of randomly packed glass beads. Fluid velocities were measured using Particle Image Velocimetry (PIV) and a technique called Refractive Index-Matched Scanning (RIMS) allowing the interior of the bed to be examined. By applying the double averaging methodology, we determined the following mesoscale profiles: porosity, mean velocity, turbulent and dispersive stresses from the subsurface to the free surface. We observed a turbulent boundary layer over the rough bed for at intermediate Reynolds numbers, i.e. Re = O(1000). Under these flow conditions, viscosity played a non-negligible role through the van Driest damping effect. Based on the Prandtl mixing length theory and mechanistic considerations, we propose a new theoretical model to reproduce turbulent and dispersive stress profiles. In contrast to existing boundary layer models, our model takes into account the continuity of the porosity profile and the associated damping effects on flow momentum in the roughness layer. A good agreement is found between the model and classic flow resistance laws employed for low-land and gravel-bed rivers (e.g. Chézy, Manning-Strickler, Keulegan). A 1D vertical effective diffusion model is derived from the hydrodynamic model and should contribute improving our understanding of depth dependent diffusive processes across the sediment-water interface and thus hyporheic exchanges in various settings.

2020

Manning’s empirical formula in conjunction with Strickler’s scaling is widely used to predict the bulk velocity V from the hydraulic radius Rh, the roughness size r and the slope of the energy grade line S in uniform channel and pipe flows at high bulk Reynolds numbers. Despite their importance in science and engineering, both Manning’s and Strickler’s formulations have waited for decades before finding a theoretical explanation. This was provided, for the first time, by Gioia & Bombardelli (Phys. Rev. Lett., vol. 88, 2002, 014501), labelled as GB02, using phenomenological arguments. Perhaps their most remarkable finding was the link between the Strickler and the Kolmogorov scaling exponents, the latter pertaining to velocity fluctuations in the inertial subrange of the turbulence spectrum and presumed to be universal. In this work, the GB02 analysis is first revisited, showing that GB02 employed several ad hoc scaling assumptions for the turbulent kinetic energy dissipation rate and, although implicitly, for the mean velocity gradient adjacent to the roughness elements. The similarity constants arising from the GB02 scaling assumptions were presumed to be independent of r/Rh, which is inconsistent with well-known flow properties in the near-wall region of turbulent wall flows. Because of the dependence of these similarity constants on r/Rh, this existing theory requires the validity of the Strickler scaling to cancel the dependence of these constants on r/Rh so as to arrive at the Strickler scaling and Manning’s formula. Here, the GB02 approach is corroborated using a co-spectral budget (CSB) model for the wall shear stress formulated at the cross-over between the roughness sublayer and the log region. Assuming a simplified shape for the spectrum of the vertical velocity w, the proposed CSB model (subject to another simplifying assumption that production is balanced by pressure–velocity interaction) allows Manning’s formula to be derived. To substantiate this approach, numerical solutions to the CSB over the entire flow depth using different spectral shapes for w are carried out for a wide range of r/Rh. The results from this analysis support the simplifying hypotheses used to derive Manning’s equation. The derived equation provides a formulation for n that agrees with reported values in the literature over seven decades of r variations. While none of the investigated spectral shapes allows the recovery of the Strickler scaling, the numerical solutions of the CSB reproduce the Nikuradse data in the fully rough regime, thereby confirming that the Strickler scaling represents only an approximate fit for the friction factor for granular roughness.

2017

One-Dimensional Numerical Modelling Of Mobile Bed Evolution In A Flume With A Side Weir

Burkhard Rosier, Anton Schleiss

Side weirs are widely used to control flow processes along a channel or river. The lateral loss of water reduces the sediment transport capacity in the main-channel leading to local sediment deposition near the overflow. The design discharge to be diverted is increased in an uncontrolled way by this flow-sediment interaction. The flow-sediment interaction is investigated numerically and compared with results from a flume study. The numerical tool is based on the continuity and momentum equations and performs the coupled hydrodynamic simulation of ID flow behaviour and bed-load transport. The friction head loss is computed according to the Manning formula. The outflow is determined by applying the general equation of weirs. With an appropriate formula for bed-load transport capacity and an adequate roughness function to account for form roughness, the geometry of the sedimentary deposit, as well as the side overflow discharge, is reproduced with reasonable accuracy.

2009

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2017