The key solution methodology is how to solve for the pressure dependent demand. Conventionally, nodal demand is a known value. Applying the mass conservation law to each node and energy conservation law to each loop, the network hydraulics solution can be obtained by iteratively solving a set of linear and non-linear equations. A unified formulation for solving network hydraulics is given as a global gradient algorithm (GGA).

Where Q is the unknown pipe discharge and H is the unknown nodal head. q is the set of nodal demand that is not dependent on the nodal head H.

For pressure dependent demand, the demand is no longer a known value but a function of nodal pressure. The solution matrix becomes:

A new diagonal matrix A22 is added to the solution matrix. The non-zero diagonal element is given as