**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Publication# Manning's Formula and the Strickler Scaling Derived from a Co-spectral Budget Model

Abstract

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 flows at high bulk Reynolds numbers. Despite their importance in science and engineering, both Manning's and Strickler's formulations have awaited decades before finding a theoretical explanation. This explanation was provided using phenomenological arguments by Gioia and Bombardelli (2002) and is hereafter labeled as GB02. The main finding was a link between the Strickler and the Kolmogorov scaling exponents, the latter pertaining to velocity fluctuations in the inertial sub-range of the turbulence spectrum that is presumed to be universal. In this work, the GB02 analysis is revisited showing that GB02 employed some 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 inconsistent with known flow properties in the near-wall region of turbulent wall flows. Because of the dependency of these similarity constants on r/Rh, GB02 requires the validity of the Strickler scaling to cancel the dependency of these constants on r/Rh so as to arrive at the Strickler scaling and thus Manning's formula. Here, the GB02 approach is corroborated using a co-spectral budget (CSB) model for the wall shear stress at the interface between the roughness sublayer and the log-region. Assuming a simplified shape for the spectrum of the vertical velocity (Eww), the proposed CSB model 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 Eww are carried out across a wide range of r/Rh. The results support the simplifying hypotheses used to derive Manning's equation. 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's scaling represents only an approximate fit for the friction factor for granular roughness.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (35)

Turbulence

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent.

Laminar flow

In fluid dynamics, laminar flow (ˈlæmənər) is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface.

Manning formula

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.

Related MOOCs (13)

Related publications (104)

Ontological neighbourhood

Fluid Mechanics

Ce cours de base est composé des sept premiers modules communs à deux cours bachelor, donnés à l’EPFL en génie mécanique et génie civil.

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Véronique Michaud, Jacobus Gerardus Rudolph Staal

Segmented micro-CT images of flow fronts produced by UV-flow freezing. Front morphologies correspond to capilary-dominated, equilibrated and viscous-dominated flow regimes. ...

Mohamed Farhat, Huaiyu Cheng, Mohan Xu

Large eddy simulations of tip vortex cavitation (TVC) around an elliptical hydrofoil is performed to study its scale effect. A satisfying agreement is obtained between the numerical and experimental data. It indicates that the scale effect of TVC is remark ...

In this research, the flow features around a spur dike located in a 90˚ sharp channel bend have been studied experimentally in detail. Results showed that the effects of the spur dike on upstream sections increased by increasing α (spur dike location from ...

2023