Pipe Network Solver: Worked Example

1. Network and Calculator Inputs

Use a steady water network with Hazen–Williams head loss and demand-driven analysis (DDA). All diameters below are actual inside diameters, not nominal pipe sizes. The coefficient C = 120 is a benchmark input.

Load this exact example

1. Open the Pipe Network Solver and choose Import EPANET .inp. Select the downloaded file above. Import switches the calculator to EPANET file mode.
2. Alternatively, select EPANET file — pumps, tanks, valves & time patterns under “Build your network with,” then replace the entire input text with the file below.
3. Stay in EPANET file mode and click Solve network. Compare the results at hydraulic time 0.000 h with Section 3.

The guided tables use SI units and Darcy–Weisbach. This example uses US units and Hazen–Williams in file mode. “Reset to loop example” loads a different network.

[TITLE]
Worked example: 100 gpm through two equal-resistance paths

[JUNCTIONS]
;ID Elevation_ft Demand_gpm
A 10 0
B 20 100

[RESERVOIRS]
;ID Head_ft
R 100

[PIPES]
;ID From To Length_ft Diameter_in H-W_C K Status
P1 R A 500 4 120 0 Open
P2 A B 500 4 120 0 Open
P3 R B 1000 4 120 0 Open

[OPTIONS]
UNITS GPM
HEADLOSS H-W
DEMAND MODEL DDA
ACCURACY 0.00001
UNBALANCED STOP

[TIMES]
DURATION 0

[REPORT]
STATUS FULL
NODES ALL
LINKS ALL

[COORDINATES]
R 0 0
A 500 400
B 1000 0

[END]

2. Step-by-step Math

Balance flow and compare the two paths

Junction A has no demand, so P1 and P2 carry the same flow. Their combined length is 1000 ft, equal to P3. Since the diameters and C values also match, the two paths have equal resistance and equal head loss between R and B.

Q1 = Q2
Q2 + Q3 = 100 gpm
h1 + h2 = h3

Equal path resistance → Q2 = Q3
Q1 = Q2 = Q3 = 50 gpm

Reservoir supply is Q1 + Q3 = 100 gpm. Adding all three pipe flows would count the series-path flow twice.

Convert units and calculate head loss

For the following US-unit Hazen–Williams equation, L and d are in feet, q is in ft³/s, and hL is in feet. C is dimensionless.

q = 50 / 448.831 = 0.111400505 ft³/s
d = 4 / 12 ≈ 0.333 ft
hL = 4.727 L q^1.852 / (C^1.852 d^4.871)

h3 = 4.727 × 1000 × 0.111400505^1.852
     / (120^1.852 × 0.333333333^4.871)
   ≈ 2.41 ft

h1 = h2 = (500 / 1000) × h3
        ≈ 1.21 ft

Calculate node heads and pressure heads

HA = HR − h1 = 100 − 1.207271 ≈ 98.8 ft
HB = HR − h3 = 100 − 2.414541 ≈ 97.6 ft

Check via A: HB = HA − h2 ≈ 97.6 ft
Pressure head at A = HA − zA ≈ 88.8 ft water
Pressure head at B = HB − zB ≈ 77.6 ft water

The calculator's Pressure head column is in feet of water for this file, not psi. Elevation is already included through H − z; do not subtract it again as a pipe loss.

Calculate pipe velocity and residuals

V = q / (π d² / 4) = 1.276556 ft/s in every pipe

Continuity at A: 50 − 50 = 0 gpm
Continuity at B: 50 + 50 − 100 = 0 gpm
Loop energy: h1 + h2 − h3 = 0 ft

3. Compare Your Answers

Keep full precision until the final step. Allow 0.01 gpm for flow, 0.01 ft for head and 0.001 ft/s for velocity to accommodate displayed precision, rounded conversion constants and numerical solver tolerance.

A negative reservoir demand denotes supply into the network. Reservoir pressure head is not used in this check.

Positive flow follows each pipe's listed start → end direction. With these open pipes and zero minor losses, the reported head difference equals the friction head loss.

Second check: close the direct path

In the EPANET text, change only P3's status from Open to Closed, then solve again:

P3 R B 1000 4 120 0 Closed

Q1 = Q2 = 100 gpm; Q3 ≈ 0 gpm
Total open-path loss = 2.41 × (100/50)^1.85
                     = 8.72 ft
HA = 100 − 8.72/2 = 95.6 ft
HB = 100 − 8.72 = 91.3 ft
Pressure head at B = HB − 20 = 71.3 ft water

P3 should report Closed. Its end nodes still have a head difference of about 8.72 ft; a closed link does not require equal end-node heads. Restore Open to return to the first case.

4. Assumptions and References

This benchmark assumes steady, fully filled water pipes, turbulent flow, fixed junction demands, a fixed reservoir head and no minor losses. It includes no pumps, tanks, controls or time-varying demands. Hazen–Williams is an empirical water-flow model; the assumed C is not a recommendation for a particular pipe material or age.

Method: EPANET 2.2 network model and pipe head-loss equations. File syntax and units: EPANET input keywords. See also calculation methodology.