Worked example: a Hazen-Williams water main

Water-distribution and fire engineers usually size mains with the Hazen-Williams method, where a single coefficient C stands in for the pipe roughness. This worked example is a branched water main solved that way, with a one-click switch to Darcy-Weisbach so you can see how the two methods compare on the same network.

The setup

A reservoir at 65 m of head feeds a branched main. The project head-loss method is set to Hazen-Williams, and every pipe carries a C of 130, the usual value for new cast or ductile iron:

• The trunk main runs 600 m of DN300 from the reservoir to the first junction.
• A DN150 branch drops to the first demand, 18 L/s at an elevation of 12 m.
• The main continues 400 m of DN250 to a second junction, which feeds two more DN150 branches: 15 L/s at 20 m elevation, and 12 L/s at 8 m.

The 20 m demand is the highest point on the network, so it is the one that governs whether the reservoir head is enough.

The physics and the method

Hazen-Williams gives the head loss of each pipe directly from the flow, diameter, length and C, using the empirical relation h_f = 10.674 L Q^1.852 / (C^1.852 D^4.871). Fluid Network Studio applies it to every pipe and solves the branched network as a whole with the global-gradient method, so continuity holds at each junction and the pressures fall consistently from the reservoir out to the demands. C rolls the roughness into one water-only coefficient, which is why the method is convenient for water and fire work and not valid for other fluids.

Open Configuration and switch the head-loss method to Darcy-Weisbach, then re-solve. The same network now uses a physically based friction factor instead of C, and comparing the two head-loss profiles is the clearest way to see how much your answer depends on the method you chose.

The solved result

The governing 20 m demand holds 412.8 kPa of residual pressure:

Look at the head and the residual-pressure columns together. The first and second demands sit at practically the same hydraulic grade, 62.16 m and 62.17 m, and yet their residual pressures differ by 78 kPa. Every bit of that gap is the 8 m of ground between them. Total friction from the reservoir to the governing demand is only 2.83 m out of 65 m of available head, which is what generous mains at C = 130 buy you: on this network the head-loss method barely matters and the topography decides everything. Drop C towards 100 for old tuberculated pipe and the friction term grows by roughly two thirds at the same flow, which is when the choice of method starts to change your answer.

Note that C is a water-only, empirical coefficient, so these figures carry the method's own assumptions. Switching Configuration to Darcy-Weisbach and re-solving is the honest way to see how much of the result is the network and how much is the correlation.

Every number above is solver output, and it is reproducible: open the example, press Solve, and check the residuals against your own Hazen-Williams calculation.

What you learn

Solving the example gives the residual pressure at each demand and the head loss along each pipe. The 20 m demand governs, so watch its pressure most closely, and drop C towards 100 to mimic old, tuberculated pipe and see how quickly that residual erodes. The single-pipe version of this calculation is on the Hazen-Williams calculator, and the branched distribution example shows the same shape of network solved on Darcy-Weisbach.

Open this example in FNS and switch the head-loss method to Darcy-Weisbach to compare.