Generalized numerical and nomographic solutions of simple pipe flow problems

The relation formulated by Swamee and Jain through the combination of the Darcy-Weisbach, on the one hand, and the Colebrook-White equation, on the other, in order to eliminate the Darcy-Weisbach resistance coefficient f, was placed in dimensionless form in two different ways. Each of the new equations contains three dimensionless variables and thus it can be depicted on a single diagram as a family of one-parameter curves. Each of the two equations yields a direct solution to simple pipe flow problems of category 2 and an iterative solution to problems of the other two categories while the corresponding diagrams yield each a direct solution to flow problems of categories 1 and 2 the first and of categories 2 and 3 the second. Regarding the iterative solution of the new equations, an appropriate technique was devised for the direct computation of the correction required in order to proceed from one to the next iteration. Convergence of the iterative process is rapid and the solution is as accurate as the original Colebrook-White equation warrants.