Ecuación de Hazen-williams (Caída de Presión). Uploaded by Estuardo Javier Gan Rodríguez. Ecuación de Hazen Williams para el cálculo de la caída de. en: williams hazen head loss formula equation pressure drop friction loss head; es: williams presión ecuación fórmula para perder la cabeza hazen cabeza del. Friction head loss (ft H2O per ft pipe) in water pipes can be estimated with the empirical Hazen-Williams equation.

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Published on Dec View Download 5. The Hazen-Williams equation is used widely in water supply and sanitary engineering. This equa-tion uses a constant, the Hazen-Williams C, to indicate the roughness of a pipe interior.

Because of the empiricalnature of the equation, its range of applicability is limited.

Hazen–Williams equation

Many textbooks and software manuals give C valuesbased on pipe type, condition, and age but do not give the range of applicability. Historic experimental data isused to demonstrate that C is a strong function of Reynolds number and pipe size and that the Hazen-Williamsequation has narrow applicable ranges for Reynolds numbers and pipe sizes.

The level of error when the Hazen-Williams equation is used outside its data ranges is significant. However, a valid C for a given pipe at a specificReynolds number can be used to estimate a pipe’s relative roughness, which then can be used by the rationalDarcy-Weisbach equation without the range hxzen.

A method for doing so is given. Discussion open until February 1, The manuscript for this paper was submitted for review andpossible publication on July 11, This paper is part of the Joumalof Hydraulic Engineering, Wi,liams. The Hazen-Williams equation empirically relates the slopeof an energy grade line to the hydraulic radius and the dis-charge velocity gazen water flowing full in a pipe. This equationuses a constant to characterize the roughness of the pipe’sinner surface.

Originally hazeen init still is usedwidely in water supply and sanitary engineering. However,being empirical, the Hazen-Williams equation is not dimen-sionally homogeneous and its range of applicability is limited. The well-known Colebrook-White transition formula relatesthe friction factor in the Darcy-Weisbach equation to the Reyn-olds number and the relative roughness of the pipe inner wall.

The Moody diagram Moody facilitates the determina-tion of this friction factor, which is implicit in the Colebrook-White formula. The Darcy-Weisbach equation is rational, di-mensionally homogeneous, and applicable to water as well asto other fluids. Frequently, the Hazen-Williams equation is presented in hy-draulics, water supply, and sanitary engineering texts togetherwith the Darcy-Weisbach equation.


VennardStreeterand WylieStreet et al. Consequently, the Hazen-Williams equation ismisapplied outside its data range. The first objective of thispaper is to show quantitatively bazen limitations of the Hazen-Williams equation.

Despite its limitations, the Hazen-Williams equation hasbeen used for a long time and there exists a valuable databasefor the inner surface roughness of older pipes Hudson For these pipes, validated C values can be used to establishtheir relative roughnesses.

After doing so, the knowledge ofpipe roughness accumulated for the Hazen-Williams equationcan be transformed and used by the Darcy-Weisbach equationfor broader applications. Ecuacoon transformation also allows theerror of a misapplied Hazen-Williams equation to be quanti-fied. The second objective of this paper is to show such atransformation. The C is the Hazen-Williams coefficient.

Daugherty and Franzini and Hwang and Hita suggest that the equation is ap-plicable for the flow of water in pipes larger than 5 cm andvelocities less than 3 mls.

The friction factor is related tothe Reynolds number R and the equivalent roughness e, andthe pipe diameter D by the Colebrook-White formulaI Exuacion 2. In williqms doing, a yo. By introducingthe kinematic viscosity v, yo.

Meanwhile, Rh is replaced by Williamz This, com-bined with Dlv O. I84l introduced earlier, results in a Dl. Let e be the equivalent roughness of the pipeinner wall.

OI8S and rewrite the latteras Dle o. Finally, replace S by HIL. With these ma-nipulations, I is recast in the form of 2 as[ 0. I DVennard introduced a similar equation in U. OI8S dropped because of the small expo-nent. Sim-ilar equations can be found in Streeter and WylieStreetet al.

For personal use only; all rights reserved. The mean C column 6 for data sets 12 evuacion 14 were not stated by Williams and Hazenbut they are obviously the same as those incolumn 5. Selected from Table 1 of Williams and Hazenpp. The data used byWilliams and Hazen for new cast-iron pipes lie entirelywithin the transition zone. For a given pipe inner surface type,the computed C value varies significantly with Hzzen D. Theexperimental data used to establish the C williamw in Williamsand Hazen has limited ranges in Rand D.

For specified D and v for water, C can be plotted as a func-tion of Rand fiD. If C and R are known, which is the casein the database of the Hazen-Williams equation, then ID canbe found from the plot.

To illustrate this process and to dem-onstrate that C varies with D in fiD as well as in D alone,plots with D of 0. Superim-posed on each are the applicable experimental data from Table1. However, the exponents were selected representing “ap-proximately average conditions” so that C is practically con-stant and is viewed as an index of the smoothness of the in-terior of the pipe surface.


This intent of C and the fact thathydraulic radius appears separately in the Hazen-Williamsequation might have motivated many texts, references, andsoftware manuals [e. Some cursory information on the variations of C with pipesize can be found in Babbitt et al.

A portion ofthat table is reproduced in Table 1. The first 14 sets pertainingto new cast iron pipes are used here to demonstrate the vari-ation of C with R and D.

Limitations and Proper Use of the Hazen-Williams Equation

It is seen that the variations in Camong the coated cast-iron pipes mask the difference in Cbetween the coated and the uncoated cast iron pipes. For thepurpose of showing C varying with Rand D, these 14 pipesare assumed to have a common E. Variations of C with E areaddressed later. This common E is 0. Using this E and a v of 1. Each curve inthis figure corresponds to an ID. Because E is fixed, the IDvalues indicate the pipe diameters.

The R and ID ranges coverthe transition zone and the complete turbulence-rough pipezone of the Moody diagram. However, it is awkward to use and an alter-native is provided here.

Several formulas that approximate 3 and are explicit forfexist Barr ; Swamee and Jain ;Round They can be used with 7 to express ElD ex-plicitly. For example, by substituting the f in the explicit ap-proximation formula of Swamee and Jain 0.

Hazen-Williams Equation Module 3c: For SI units, the Hazen-Williams equation for pipes Assume that bazen Hazen-Williams coefficient for the Documents. Hazen-Williams is simpler to use than DArcy-Weisbach where you are solving for flowrate, Hazen-Williams Equation – Toro??

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