An Algorithm For The Exact Solution Of A Mesh Equation In The Hardy Cross Iterative Method For Ventilation Network Analysis

The Hardy Cross iterative method is the most popular technique for solving a ventilation network problem with natural air splitting. This method tradition-ally solves each mesh equation by an approximation during each iteration. It is thus interesting from both theoretical and computational viewpoints to be able to solve for an exact solution to the mesh equation. Presented in this paper is an algorithm for computing the exact solution to the mesh equation with a variable fan pressure. The algorithm uses signum functions for air quantities to generate an alternative mesh equation in the form of a quadratic equation, which has two solutions defined by the well-known quadratic formula. The condition that the derivatives of the alternative and the original equations must be the same provides a basis for the correct choice between the two solutions.