JACIII Vol.20 No.1 pp. 76-83
doi: 10.20965/jaciii.2016.p0076


Pipe Sizing of District Cooling Distribution Network Using Implicit Colebrook-White Equation

Gerardo L. Augusto*,**, Alvin B. Culaba*, and Renan Ma T. Tanhueco*

*Gokongwei College of Engineering, De La Salle University
2401 Taft Avenue, Manila, Philippines
Quezon City, Philippines

April 10, 2015
July 12, 2015
Online released:
January 19, 2016
January 20, 2016
distribution network, pipe sizing, colebrook-white equation, newton-raphson method, friction factor

An implicit solution of Colebrook-White equation was used in calculating the friction factor for commercial steel pipes using Newton-Raphson method with Reynolds number ranging from 4.0 × 103 to 1.3 × 107. Initial value for iterative friction factor estimation was based on expanded form of Colebrook-White equation for larger values of Reynolds number with tolerance value of 1.0 × 10-8. Numerical results were compared with known explicit solutions and iterative procedure proposed by Lester in which, their mean difference, root-mean square deviation, mean relative error and correlation coefficient were evaluated. Correlation coefficients equal to unity and overall mean relative error of 4.821 × 10-8 were achieved for all fifteen (15) pipe cases with nominal diameters ranging from 100 mm to 1,500 mm when compared with iterative solution suggested by Lester. Student’s t-test for paired data was also used which yielded a calculated t-value of -5.406 × 10-4. Combining the piping network design criteria with the logical structure of friction factor calculation determines the pipe size of distribution network and defines the boundaries of chilled-water velocities at different pressure drop limits as a function of commercial steel pipe diameter according to ANSI B36.1.

  1. [1]  “ASHRAE Handbook – Fundamentals,” American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., pp. 22.1-22.13, 2013.
  2. [2]  F. W. Daugherty, “Equal friction solution for duct sizing,” ASHRAE J., Vol.51, pp. 50-54, 2009.
  3. [3]  T. G. Lester, “Calculating pressure drops in piping systems,” ASHRAE J., Vol.44, pp. 41-43, 2002.
  4. [4]  T. G. Lester, “Solving for friction factor,” ASHRAE J., Vol.45, pp. 41-44, 2003.
  5. [5]  T. G. Lester, “Using Excel for duct calculations user defined functions,” ASHRAE J., Vol.51, pp. 42-46, 2009.
  6. [6]  G. L. Augusto, A. B. Culaba, and R. R. Tan, “Identification of design criteria for district cooling distribution network,” Philippine Science Letters, Vol.6, pp. 182-197, 2013.
  7. [7]  P. K. Swamee and A. K. Jain, “Explicit equations for pipe flow poblems,” J. of Hydrailic Division ASCE, Vol.102, pp. 657-664, 1976.
  8. [8]  S. E. Haaland, “Simple and explicit formulas for the friction factor in turbulent pipe flow,” J. of Fluids Engineering, Vol.105, pp. 89-90, 1983.
  9. [9]  T. K. Serghides, “Estimate friction factor accurately,” J. of Chemical Engineering, Vol.91, pp. 63-64, 1984.
  10. [10]  C. T. Goudar and J. R. Sonnad, “Turbulent flow friction factor calculation using a mathematically exact alternative to the Colebrook-White equation,” J. of Hydraulic Engineering, Vol.132, pp. 863-867.
  11. [11]  T. J. Akai, “Applied Numerical Methods for Engineers,” John Wiley & Sons, pp. 124-135, 1994.
  12. [12]  E. Kreyszig, “Advanced Engineering Mathematics, 6th ed.,” John Wiley & Sons, pp. 952-955, 1988.
  13. [13]  L. F. Moody, “Friction factors for pipe flow,” Trans. ASME, Vol.66, pp. 671-684, 1944.
  14. [14]  G. F. Round, “An explicit approximation for the friction factor – Reynolds number relation for rough and smooth pipes,” Canadian J. of Chemical Engineering, Vol.58, pp. 122-123, 1980.
  15. [15]  D. J. Wood, “An explicit friction factor relationship,” Civil Engineering, Vol.36, pp. 60-61, 1966.
  16. [16]  W. E. Stewart and Ci. I. Dona, “Water flow rate limitations,” ASHRAE Trans., Vol.93, pp. 811-825, 1987.
  17. [17]  G. A. Antaki, “Piping and Pipeline Engineering: Design, Construction, Maintenance, Integrity and Repair,” Marcel-Dekker Inc., 2003.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, IE9,10,11, Opera.

Last updated on Mar. 28, 2017