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

Abstract

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 × 103to 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 × 10-8were 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.