Pipe Network Calculator (Hardy Cross Method)

What is the Hardy Cross method?

In a looped (ring) pipe network water can reach a point by more than one route. Two rules fix how much flows in each pipe: at every node the inflow equals the outflow, and around every closed loop the signed head losses sum to zero. The Hardy Cross method starts from a flow pattern that satisfies continuity and applies a correction flow to each loop: ΔQ = − Σh / Σ(n × |h| / |Q|). The corrections are repeated until they become negligible.

How to use it

Enter the nodes with their names and external flows: flow into the network is positive, demand taken out is negative, and the total must be zero. Then add each pipe with the two nodes it joins, its length, inside diameter and C factor (or roughness). The calculator builds the loops and the starting flows itself. The result lists the flow, direction, velocity and head loss of every pipe and the head at every node.

Example

Ten units of flow enter at node A, 4 are drawn at C and 6 at D. The pipes follow h = K × Q² with K = 1 for AB, 3 for AC, 3 for BC, 2 for BD and 5 for CD. The solution is AB 6, AC 4, BC 2, BD 4 and CD 2 units. It is easy to check: loop ABC gives 36 + 12 − 48 = 0 and loop BCD gives 12 + 20 − 32 = 0.

Limits

The calculator covers steady flow with known node flows. Pumps, tanks, valves and pressure reducers are not modelled. Hazen-Williams holds only for water in turbulent flow. Large networks and operating scenarios call for network analysis software.