Background, [1] The friction factor in fully developed turbulent pipe flow depends on the Reynolds number and the relative roughness /D, which is the ratio of the mean height of roughness of the pipe to the pipe diameter. The functional form of this dependence cannot be obtained from a theoretical analysis, and all available results are obtained from painstaking experiments using artificially roughened surfaces (usually by gluing sand grains of a known size on the inner surfaces of the pipes). Most such experiments were conducted by Prandtl's student, J. Nikuradse in 1933, followed by the works of others. The friction factor was calculated from the measurements of the flow rate and the pressure drop. The experimental results obtained are presented in tabular, graphical, and functional forms obtained by curve-fitting experimental data. In 1939, Cyril F. Colebrook (1910 -1997) combined the available data for transition and turbulent flow in smooth as well as rough pipes into the following implicit relation known as the Colebrook equation =-2.0 log(E c/D 2.51 3.7 Ref +R ) This equation is only applicable for turbulent flow, Re 2 4000. For laminar and transitional flow Re