Peer Review Board Lee Cesario (Denver Water), Robert M. Clark (U.S. EPA), Jack Dangermond (ESRI), Allen L. Davis (CH2M Hill), Paul DeBarry (Borton-Lawson), Frank DeFazio (Franklin G. DeFazio Corp.), Kevin Finnan (Bristol Babcock), Wayne Hartell (Bentley Systems), Brian Hoefer (ESRI), Bassam Kassab (Santa Clara Valley Water District), James W. Male (University of Portland), William M. Richards (WMR Engineering), Zheng Wu (Bentley Systems ), and E. Benjamin Wylie (University of Michigan)

/pdf/advanced-water-distribution-modeling-and-management-4xc6pded9c.pdf

Advanced Water Distribution Modeling and Management

The historical development of the Darcy-Weisbach equation for pipe flow resistance is examined. A concise examination of the evolution of the equation itself and the Darcy friction factor is presented from their inception to the present day. The contributions of Chezy, Weisbach, Darcy, Poiseuille, Hagen, Prandtl, Blasius, von Karman, Nikuradse, Colebrook, White, Rouse and Moody are described.

http://depa.fquim.unam.mx/ipm/introd_ing_metymat/mat_apoyo/bernoulli/HistoryoftheDarcyWeisbachEq.pdf

The History of the Darcy-Weisbach Equation for Pipe Flow Resistance

New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations

A Rankine vortex model is used as the basis for an equation for critical submergence of intakes. The equation relates critical submergence to Froude number, circulation number, Reynolds number, and Weber number. The Froude and circulation numbers are the major controlling parameters. The model accounts for the effect of eddy viscosity on vortex-core characteristics. The equation for critical submergence is in agreement with experimental results. Criteria for neglect of surface tension and kinematic viscosity are established.

Free‐Surface Air Core Vortex

https://hal.archives-ouvertes.fr/hal-01586547/document

Review of explicit approximations to the Colebrook relation for flow friction

Direct solutions of pipe flow problems are not possible because of the implicit form of Colebrook-White equation which expresses the hydraulic resistancee of commercial pipes. The three basic and major problems encountered in hydraulic engineering practice are the determination of pipe diameter, the discharge and the head loss. The solution of these problems on conventional lines involves many trials and tedious computations. Some research workers have proposed graphical solutions which have their own inherent limitations. Reported herein are explicit and accurate equations for pipe diameter and head loss and a closed form solution for the discharge through the pipe, based on Colebrook-White equation. These explicit equations can also be utilized with advantage in optimization studies of pipelines and water distribution systems.

Explicit Equations for Pipe-Flow Problems

With the object of determining the similarity criterion, experimental studies on vortex formation at pipe intakes were carried out using two geometrically similar circular vortex tanks, circulation in approach flow was generated by means of adjustable guide vanes Transparent pipe intakes of different sizes and liquids of different viscosities and surface tensions were used in a recirculating system Based on the analysis of data, a method has been proposed according to which a geometrically similar model is operated at the same Froude number as in the prototype and the observed critical submergence is corrected for distortion due to change in the model Reynolds number A criterion to determine the type of vortex for known geometric and kinematic conditions has also been proposed

Vortex formation at vertical pipe intakes

The solution of pipe flow problems encountered in engineering practice requires an intermediate step of computation of friction factor. The friction factor of commercial pipes is described by a semi-empirical equation developed by Colebrook. This equation that expresses the friction factor as a function of relative roughness and Reynolds number is an implicit one requiring a trial-and-error procedure for its determination. Wood has pointed out obvious disadvantages of an implicit relationship and recognizing the necessity of an explicit equation proposed one to replace the implicit equation for friction factor. It has, however, been possible to develop a simple and more accurate explicit equation for friction factor, based on the Colebrook-White formula, and is presented herein.

Accurate Explicit Equation for Friction Factor

The aim of this paper was to understand clearly the role of the different parameters on vortex formation. A study was made where the vanes for circulation are radial and thus the approach flow is free from circulation. Air entrainment in radial flow at intakes occurs when the submergence is greatly reduced and the flow is of the gulping type with the liquid surface above the intake pulsating. It was shown by experimentation that the critical submergence is practically independent of the viscosity, as well as the surface tension of the liquid. In radial approach flow towards vertical pipe intakes, the safe submergence to prevent air entrainment must always be greater than the value predicted by the proposed equation, for ranges of the Froude number between 1.1 and 20.

Air Entrainment in Radial Flow Towards Intakes

/pdf/erratum-for-explicit-equations-for-pipe-flow-problems-5dbr514f04.pdf

Akalank K. Jain

Papers

Explicit Equations for Pipe-Flow Problems

Vortex formation at vertical pipe intakes

Accurate Explicit Equation for Friction Factor

Air Entrainment in Radial Flow Towards Intakes

Erratum for “Explicit Equations for Pipe-Flow Problems”