Noche Potosi

Noche Potosi
Iglesia San Bernardo

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: