Darcy-Weisbach Headloss Calculations in Steady State and EPS

Product(s):  WaterGEMS, WaterCAD, HAMMER
Version(s): CONNECT Edition, V8i
Area:  Calculations


What is the process that WaterCAD and WaterGEMS use to compute headloss using the Darcy Weisbach friction method, considering the ColeBrook-White and Swamee-Jain equations, Reynolds number and Moody diagram?

Also applies to the initial conditions (steady state) in HAMMER.


Below is the process used by WaterCAD and WaterGEMS (and the initial conditions solver in HAMMER) to compute pipe headloss with the Darcy-Weisbach friction method:

1) The user enters:

  • Roughness Height (the 'e', 'ε' or 'K' coefficient, also known as the "Ks", "bed roughness", "equivalent sand roughness")
  • Kinematic viscosity
  • Pipe Diameters

2) The EPANET-based hydraulic engine calculates velocity

3) The program uses this to calculate the Reynolds number and relative roughness.

Re = Reynolds number
D = pipeline diameter (L)
V = velocity
ρ = fluid density (M/L3)
μ = absolute viscosity (M/L/T)
ν = kinematic viscosity (L2/T)

4) The program inserts those values into the Swamee-Jain equation (essentially the same thing as the Moody diagram) to calculate the friction factor (f).

Re = Reynolds Number
ε = Equivalent sand roughness / roughness height (e or Ks - note that the Colebrook-White equation may refer to it as 'K' but it is the same thing)
D = pipe diameter

5) The program uses the friction factor (f) along with the diameter, length, and velocity to calculate head loss.

If you want verification that the equations are correct, please see Swamee, P. K. and Jain, A. K. 1976 Explicit equations for pipe flow problems. J. of Hydraulic. Engg., 102(5), 657-664.

In a paper that Dr. Tom Walski co-authored , it was shown that the Swamee-Jain equation and Colebrook-White differed by an average of 1% using roughly 90 million randomly generated test points.

Given that both equations are essentially empirical curve fits to lab data, they should be accurate for any engineering application.

Engineers all over the world use WaterCAD/GEMS and EPANET, which uses the same solver for the past few decades.

See Also

Darcy-Weisbach friction calculation in StormCAD and SewerCAD 

What is the difference between Darcy-Weisbach roughness coefficients e and f, and Bed Roughness Ks or K?