Noche Potosi

Noche Potosi
Iglesia San Bernardo

miércoles, 28 de diciembre de 2016


Some times, in Bolivia Rural towns, old serial sysyems of pipes become at time not enough for present water supply requeriments, is a good solution a branches and serial system, this example
show how adding a 4-inch branch improve the whole capacity to 2.78 times.
Many times the high reservoir is a earth dam , no is possible install a parallel pile and the lower tank is a concrete-tank.
Darcy - Weisbach equation for friction losses was ussed, at firts ; Colebrook - White - Prandtl _ Von Karman - NIKURADSE  C-W-P-VK-N) equation was employed; then que Swamee - Jain (1976) equation  was ussed. of course no are difference at 0.0001 L/s.

A veces en los pueblos rurales de Bolivia, los antiguos acueductos deben ser renovados, en muchos casos las tuberías aun están en muy buen estado (tubos PVC superan los 40 años),   y se puede mejorar su capacidad integral añadiendo un ramal, en este caso de 4".  Darcy Weisbach , con  Colebrook - White - Prandtl _ Von Karman - NIKURADSE y luego con Swamee - Jain (1976), Ambas rindieron el mismo resultado. Fueron omitidas ciertas operaciones para centrar la atención en el análisis hidráulico.
PTC (c) - MATHCAD (c) , por supuesto, al final se muestra el enlace para su sitio WEB de donde se puede descargar una version gratis por 30 días-

domingo, 9 de octubre de 2016


Two reservoirs are connected to water supply network.
Using Swamee´s equation  (1993) for friction factor laminar , transition or turbulent flows.
The advantage of this equation is the direct use in EXCEL (c) of MICROSOFT (c), the
powerful spreadsheet without iterative method for friction factor of Darcy-Weisbach´s
equation, and we can copy any times as needed the Inverse Matrix to get the tolerance
level previously asumed.
Usando la ecuación de Swamee (1993) en la poderosa hoja de cálculo EXCEL (c) de
MICROSOFT (c) sin iterar para obtener f, se logra copiando los bloques de matriz inversa
tantas veces como se necesite, un grado de tolerancia previamente asumido.

for absolute rugosity : 0.05 mm; for kinematic viscosity : 1.33*10^-6 m2/s, and g = 9.79 m/s2   
Lesson 15 for the asignature of CIV 338 Ingenieria Sanitaria I, Facultad de Ingenieria,
Universidad Autonoma Tomas Frias; Potosí, Bolivia

sábado, 25 de junio de 2016

Water Network analysis by Cross Method using Darcy_Weisbach and Colebrook-White-Prandtl-Von Karman equation and Swamee (1993)

Analisis de redes de distribución de agua por el Método de Hardy Cross usando  Darcy - Weisbach.
a)  factor  de fricción por Colebrook-White-Prandtl-Von Karman y b) Factor de Friccción por Swamee (1993) con Excel(c) de Microsoft(c).

Este ejemplo muestra la conveniencia de usar la ecuación de Swamee (1993) en planilla Excel (c) porque
evita calculos iterativos adicionales, como los de la primera parte donde se eempleo Mathcad (c) de PTC (c).
This example was solved with Swamee´s (1993) equation that avoid iterative procedure, at the firts was employed Mathcad (c) of PTC (c).

La fórmula mencionada permite todos los tipos de flujo : Laminar, transicional y turbulencia.
The equation fields "f" for laminar , transition and turbulent flow.

In this example both,  Colebrook-White-Prandtl-Von Karman and Swamee´s (1993) gets same flows.

martes, 11 de agosto de 2015

New extraordinary book of Prof. Dr. Prabhata K. Swamee ( Dr. B.R. Chahar, coautor )

  Prof. Dr. Prabhata K. Swamee´s  book 2015 : extraordinary, nice, modern, new and more...

 It is the cover of a very wonderful book, new, published recently : 2015. Editorial Springer (C)

The autors has wrote at


"Huge amounts of money are invested around the world in construction or up gradation
"of canals. Nearly 80–85 % of the cost of a total canal system constitutes
"transmission and the distribution canal networks. Due to the enormous costs
"involved, canal design is an area that has attracted many researchers for a long time.
"The aim of this book is to provide the reader with an understanding of the analysis
"and design aspects of canals. The book covers the topics related to the analysis
"and design of water-carrying as well as sediment-transporting canals. It covers the
"uniform flow principles and their application in the determination of normal depth... "

Prof. Dr. Swamme´s new book include new perspectives for Design of Canals using  Mathematics, Operation Research, Fluid Mechanics, modern graphical tools...

The special focus on Cost, not only hydraulics basis for get a optimal design.

As, Prof. Dr. Swamee and Dr. Chahar has wrote (page 2  - Introduction)

"1.2 Objective Function

" The optimal design of a canal consists of minimization of an objective function
"which is subjected to certain constraints. The known parameters are flow discharge,
"longitudinal bed slope of canal, and the canal surface roughness. There are various
"objective functions such as flow area, earthwork cost, lining cost, seepage loss,
"evaporation loss, and their combinations (Swamee et al. 2000a, b, c, 2001a, b,
"2002a, b; Chahar 2000; Basu 2013). Apart from costs, reliability is another
"important objective of the canal design. However, there has been no attempt in this
"As artificial channels have objective function, natural channels also have objectives.
"A natural channel is a stream in equilibrium, which is neither silting nor
"scouring over a period of time. Obviously, such a stream has developed a crosssectional
"area of flow through natural processes of deposition and scour. Using
"Lacey’s equations for stable channel geometry, and using geometric programming,
"Swamee (2000) synthesized an objective function for stable alluvial channels. On
"the other hand, in a similar manner, Swamee et al. (2008) found an objective
"function for river Brahmaputra. Chapter 2 formulates objective functions."

Circular section was included, too.

Chapter 11, also include :  "Terrain representation by Fourier Series"
 Graphical representations:

 Appendix 1,  has a review of:   Lambert´s W Function.  Appendix 2: Conformal Mapping; Schwarz-Christoffel Transformation; Schwarz-Christoffel Transformation of Semi-infinite Strip; Appendix 3: Solution of Cubic Equation.


1 Introduction
1.1 General.
1.2 Objective Function
1.3 Uniform Flow
1.4 General Principles
1.5 Minimum Area Section
1.6 Minimum Cost Canal Section .
1.7 MinimumWater Loss Section
1.8 Minimum Overall Cost Section
1.9 Canal Transitions
1.10 Transmission Canal
1.11 Canal Route Alignment
1.12 Mathematical Terms.
1.13 Scope of the Book
2 Objective Functions
2.1 Flow Area.
2.2 Lining Cost .
2.3 Earthwork Cost
2.4 AnnualWater Loss Cost .
2.4.1 Seepage Loss.
2.4.2 Evaporation Loss .
2.4.3 Annual Cost of Total Water Loss .
2.5 Unification of Costs .
2.5.1 CapitalizationMethod .
2.5.2 AnnuityMethod .
2.5.3 Cost Function .
2.6 Stable Channel Objective Function. .
3 Basic Canal Hydraulics .
3.1 Resistance Equations .
3.1.1 Viscous Flow in Channels .
3.1.2 Turbulent Flow in Channels .
3.1.3 Sediment-Transporting Canals . .
3.2 Normal Depth .
3.2.1 Viscous Flow in Rectangular Channel .
3.2.2 Turbulent Flow Channels.
3.2.3 Natural Channels .
3.3 Canal Operations .
3.3.1 Normal Sluice Gate.
3.3.2 Side Sluice Gate .
3.3.3 SideWeir .
3.4 Canal DischargeMeasurements .
3.4.1 RectangularWeir .
3.4.2 LinearWeir .
3.5 Critical Flow.
3.5.1 Critical Depth ..
3.5.2 Critical Slope and Limit Slope .
4 General Principles of Canal Design .
4.1 Constraints .
4.1.1 Safety Constraints .
4.1.2 System Constraint .
4.2 Formulation of the Problem.
4.3 Essential Parameters for Canal Design .
4.3.1 Canal Discharge .
4.3.2 Canal Lining andMaterial Selection .
4.3.3 Canal Banks and Freeboard
4.3.4 Longitudinal Slope of Canal .
4.3.5 Canal Section Shape .
4.3.6 Canal Layout .
5 Design for Minimum Flow Area .
5.1 Turbulent Flow Canals .
5.2 Viscous Flow Channels .
5.3 Sediment-Transporting Channels .
6 Minimum Cost Canal Section .
6.1 Construction Cost Minimization .
6.1.2 Minimum Earthwork Cost Section .
6.2 Generalized Equations of Wider Applicability .
7 Minimum Water Loss Canal Section .
7.1 Minimum Seepage Loss Canal Sections .
7.1.1 Channels Having Drainage Layer at Large Depth .
7.1.2 Channels Having Drainage Layer at Shallow Depth.
7.2 Inclusion of Evaporation Loss .
8 Overall Minimum Cost Canal Sections .
8.1 Analytical Considerations.
8.2 Particular Cases .
8.2.1 Minimum Cost Lined Sections.
8.2.2 Minimum Water Loss Sections .
8.3 Design Steps .
Reference .

9.1 Expansion Transitions.
9.1.1 Numerical Algorithm..
9.2 Contraction Transitions .
10 Optimal Design of Transmission Canal .
10.1 Analytical Considerations.
11 Salient Features of Canal Route Alignment .
11.1 Unit Length Costs .
11.1.1 Earthwork Cost .
11.1.2 Unit Length Canal Section Cost .
11.2 Balancing Depth Considerations .
11.3 Balancing Length Considerations .
11.4 Canal Alignment: Costs .
11.5 Terrain Representation by Fourier Series .
11.5.1 Canal Alignment Algorithm .
Appendices .
Appendix 1: Lambert’s W Function
Solutions of Equations .
Selection of Branch of W Function.
Asymptotic Limits .
Reference .
Appendix 2: Conformal Mapping .
Mapping .
Conformal Mapping.
Inverse Mapping Functions .
Velocity Hodograph .
Schwarz  -Christoffel Transformation .
Mapping Example for Seepage from a Canal .

One Real Root Case .
Three Real Roots Case .
Index .

Dr. P.K. Swamee is a distinguished Emeritus Professor of Civil Engineering at
ITM University, Gurgaon, Haryana, India. He was formerly a Professor of Civil
Engineering at the University of Roorkee (now the Indian Institute of Technology
Roorkee), India. He has over fifty years of teaching, research, and industry
experience in water resources engineering and has published numerous articles in
international journals. Dr. Swamee is a Fellow of the Indian National Academy of

The book has a lot of absolute new concepts, of course will be the main reference for DESIGN OF CANALS, and it will be a CLASSIC.

Thanks you Dr. Swamee for let me  know your work and extend it for Bolivia and South America.

Alberto Gonzales Murillo, august 11, 2015  , Potosi , Bolivia

Editor web site:

domingo, 4 de enero de 2015


Ejemplo de diseño de acueducto para caudal dado y que debe cumplir con las dimensiones comerciales , se emplea la norma ISO 2531 o catálogo ACIPCO -USA.
No es posible usar una tubería sencilla, a menos que se instale una válvula de paso; un sistema de tuberías es la solución más económica. Es posible encontrar soluciones para otras combinaciones de dos diámetros, pero serán más costosas en función de la longitud empleada.

Design for presurised pipe line, water flow is know. See ISO 2531 Code for  K9 Cast Iron Pipe  or ACIPCO - USA technical brochure.

System of two pipes , in serie, will be analized, better than single pipe, no control-flow valve at the end of pipeline is required. Another diameters can solve the equation system, but it will be more expensive.

Of course, the Darcy - Weisbach and Colebrook - White - Pandtl - Von Karman equation will  be used..

You can find in this same WEB site: "Metodo de diseño Matricial para acueductos" - A. Gonzales 2011.
("Matricial Method for Hydraulic Desing of Pipelines"-A. Gonzales 2011). and "Longitudes verdaderas" ("Spatial Lengths of pipes") using Vectorial Analisys.

Alberto Gonzales Murillo, Potosi- Bolivia - Former AWWA Member as "Murillo A. Gonzales - Civil Engr- Number 61444- Grade 02 - 1980-1981"

viernes, 2 de enero de 2015


Sewer design

Using Darcy - Weisbach and Colebrook - White - Prandtl - Von Karman equations.

MathCad (R) product of PTC(R) was used for solve complex equations, also, Hewlett - Packard 49G and 50G can solve that.

Bolivia Sewerage Code NB 688 for relationships as:

- Mínimum tractive stress = 1 Pascal

- Rate of flow :   Design flow / Full flow = 0.15 for Sanitary Sewer  : q/Q = 0.15

- And Others, was used. You can find liks for NB688 in this WEB site.

Alberto Gonzales Murillo, former AWWA member (1978-1980), University Tomas Frias, Bolivia

domingo, 21 de septiembre de 2014

SEWER DESIGN Darcy-Weisbach equation and Colebrook-White-Prandtl-Von Karman equation

"The question of friction factors in open channels was studied by a commitee of the American Society of Civil Enginners [3] which found the Colebrook-White equation to be more reliable than the Manning equation with a constant value of n. For any given channel it was found that the roughness value k (used in the Colebrook-White equation) was more likely to be constant than Manning´s n.........."

"5. Conclusion
"..... The variation of Manning´s coefficient with both depth and pipe gradient, particularly for circular small -bore pipes (i.e. less than about one meter diameter) highlights the utility of empirical Colebrook-White equation"
[1] Henderson, F.M. Open Channel Flow. New York, NY: MacMillan; 1966,90-101
[3] Report, A.S.C.E. task force on friction factors in open channels. Proc. A.S.C.E. 89, HYD2:97-143;1963.
From:  JOURNAL OF RESEARCH of the  National Bureau of Standars. Vol. 88, No 6, November - December 1963
By :     J.A. Swaffield and S. Bridge.   Brunel University, Uxbridge, Middlesex, U.K.


"........ ASCE (1963) has disapproved the Manning equation and recommend the use of the Darcy -Weisbach equation for open-channel resistance. On other hand, in detailled study Liou (1998) strongly discouraged the use of the Hazen-Willams equation."
From: Journal of Environmental Engineering . Vol 127, No. 9, september 2001 (c) ASCE, ISSN 0733-9372/01/0009-0776-078.
Design of Sewer Line
By :  Prabhata K. Swamee

Therefore,  next, Alberto Gonzales Murillo present Hydraulic Analysis using his own equations:
1. For determination of minimun slope of invert on basis Darcy - Weisbach equation and Colebrook - White- Prandtl - Von Karman equation, that involve the "Friction Factor variation for variable flow depth on sewers" - ( see this WEB site or SCRIBD as: "Pendientes Mínimas de Alacantarillado tomando en cuenta la variación del factor de fricción con la profundidad).
2. The relationship between design flow and full flow capacity.

The autor works with "real actual flow" ( for initial period of the network) to found slope for each link to get tractive tension 1 Pascal or more, and the future flow (about 30 year later) for determine the pipe full capacity.
Alberto Gonzales Murillo , Potosi, Bolivia.  Formerly  AWWA Member (1979 - 1980) .


For the other links, was adopted 1, 2 and 3 cm for invert fall at each manhole, for 1, 2 or 3 input pipes (Azevedo Netto ).

PTC (c) Product and Service Advantage . Mathcad (c) was used for mathematical analysis.
See Mathcad´s  (c) : oficial WEB site: 
 For free -trial version:

For Minimun Slope using Colebrook - White - Prandtl - Von Karman equation and Darcy - Weisbach and friction factor variation with flow depth, see: