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58 percent for 4000 < Re < 108 and 0 < e/D < 5 X KT2 [34]. Jain [40] proposed (p) Swamee and Jain [41] proposed The Jain and Swamee-Jain relationships have an accuracy of ± 1 percent for 5000 < Re < 108,and 10'6 < e/D < lO"2. Collins [42] has confirmed them as excellent approximation of the Colebrook-White equation. 20)] are almost the same. 18)] in 1973 [34], the credit of proposing this type of explicit relationship first goes to Churchill. 19) for direct use in practice. 20) is also now included in a textbook of fluid mechanics [9].

Minor head loss, is considered in the next chapter. 2 DARCY-WEISBACH FORMULA The frictional head loss ht for incompressible flow in a pipe depends on the fluid properties such as the density Q and viscosity /JL, the flow characteristic such as the average velocity V, the pipe characteristics such as the length L and the internal diameter D, the pipewall roughness characteristics such as the size of the roughness projections e (dimensions, L), arrangement or spacing of the roughness projections e' (dimensions, L), and a dimensionless form factor m depending upon the shape of the individual roughness elements.

1 [9,13-15]. Johnson [16] provided a diagram for commercial pipes using several nondimensional groups. Rouse [17] presented a graph of \l\ff versus Karman number K = Re \ff = D3n \l2gSlv upon which the Colebrook transition curves [12] for various values of the relative roughness were superimposed. Moody suggested that Rouse should convert the diagram to the more customary / versus Re form. In the belief that the PrandtlKarman parameters were the more significant ones and therefore the form used by him was superior to that suggested by Moody, Rouse refused to convert the diagram [18].

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