# Darcy Weisbach e (How to determine)

Hi,

I have a watergems model wherein the client wants me to use Darcy Weisbach as a friction method.

But the info I have is the friction factor which is at 0.15, but in the model, the data needed is the Darcy Weisbach e (ft), which is the roughness height.

How will I be able to determine the Darcy Weisbach e (ft) if what i only have is the friction factor? Also, as an additional info, I am using an HDPE pipe.

• Use any of the equations relating roughness height and friction factor (e.g. Colebrook-White, Swamee-Jain) and solve them backwards for Darcy Weisbach roughness height. You can find them on pages 33-34 of our Advanced Water Distribution Modeling and Management book or any other good hydraulics book.

•   if this a real-life system, you may wish to check with your Client exactly what engineering data they are actually supplying.

The "Friction Factor" f in Darcy-Weisbach of H = f.L / D x (v^2 / 2.g) is variable.  It isn't a constant number like "This pipe has a friction factor of 0.15".   It is a function of the Reynolds number and Relative Pipe Roughness, which themselves vary by Pipe Diameter,  Flow Rate (which modifies Velocity).   So unless it is a pipe network all of the same Diameter and Material, and runs at a constant velocity, it will not have a constant Friction Factor value of 0.15.

Can see this better by Moody's Diagram that graphed the solutions to Darcy-Weisbach that showed how Friction Factor varies for different pipes, liquids and flow velocities:

https://en.wikipedia.org/wiki/Moody_chart

Now WaterCAD uses an implicit approximation of Darcy-Weisbach to calculate Friction Factor "f" at each calculation timestep through an approximation researched by Swamee-Jain (or it used to at least! There are other alternative approximator formulae that have been researched through the years)

It could be that the client is actually advising the equivalent sand roughness value Ks.   This is typically expressed in units of mm, and Ks = 0.15 mm is within a typical range of  roughness for common pipe materials.

If this is an academic model, then sure the learning institute may give the modeller a friction factor as an academic problem.............but a real-life engineering project?  It would be unusual for a Client to specify or even know what the Friction Factor was since at most they may have field tests that measured head losses that a client would give to their consultant to calibrate a Ks roughness value for.

In our utility, we specify to modellers the Ks values in mm,  not the friction factor as a) it is variable and b) all commerical modelling software calculates "f" within its head loss algorithms automatically and varies it  accordingly as flows go through different diameter pipes at different velocities through the real network.