The following figure shows the comparison between the Hazen-Williams coefficient and the equivalent friction factor f values for a range of pipe diameters and flow velocities. [ For given C_{HW}, D, v , the slope S_{f} was calculated from the **Hazen-Williams equation** and this was used in the **Darcy-Weisbach equation** to give the equivalent value of the friction factor f.] In this case the points for a given C_{HW} all fall on a single straight line.

Two conclusions can be drawn from this plot :

- In the transition or smooth turbulent zone, the plot for C
_{HW}= 140 parallels approximately the relative roughness lines. This means that a given C_{HW}is equivalent to a particular relative roughness not a roughness height and that C_{HW}should increase with increasing diameter. - For rough pipes, a particular C
_{HW}doesn't represent any particular relative roughness buy cuts diagonally across the relative roughness lines.

The Hazen-Williams equation does not describe rough pipes adequately and its use when C_{HW} < 120 is hard to justify.

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