By Pramod R. Bhave
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Additional info for Analysis of Flow in Water Distribution Networks
R value is for L and D in meters and Q in cube meters per second. 2 Simple Pipe Flow Problems 45 Manning coefficient N are generally assumed to remain constant for a given pipe, the value of R remains constant for a given pipe and is independent of the discharge through it. However, for the Darcy-Weisbach formula, as the coefficient of friction/is a function of the Reynolds number, the value of the pipe resistance constant R of a pipe depends on the discharge through it. 10 SIMPLE PIPE FLOW PROBLEMS Three types of simple pipe flow problems are encountered in practice.
3 SMOOTH TURBULENT FLOW Using the results of the experiments performed by Saph and Schoder in 1903, Blasius  suggested a relationship f- ^ ^ which is valid in the range 4,000 < Re < 10s. 9) is known as Karman-Prandtl equation for smooth turbulent flow. This equation is implicit and the value of/must be obtained by trial and error. Several investigators such as Schimemi, Barnes, Blair, Lamont  and Ger and Holley  have suggested relationships similar to that of Blasius for smooth turbulent flow.
3. 4. Values of Hazen-Williams Coefficient for Clean New Pipes of Different Materials. 5. Correction Factors for Hazen-Williams Coefficients. 3 m and S = 1/1000, it is used by design engineers over wide ranges of diameters and friction slopes. This may result in an error as high as ± 3 0 percent in the evaluation of the velocity of flow . Therefore, after comparing the HW formula with the rational and dimensionally homogeneous DarcyWeisbach formula, Jain, Mohan, and Khanna  modified the HW formula.