A FORTRAN CODE has been developed which predicts pressures and flow rates in a piping network for the regimes of laminar, transition, and turbulent flow. A novel and effective scheme for modeling the transition region between laminar and turbulent flow is demonstrated. A proposed linear indicator for the deviation from laminar behavior is introduced into the analysis in order to facilitate the computational task. Although the turbulent flow problem is inherently nonlinear, the method of analysis described herein, typically employed with linear electrical networks, is found to converge rapidly to an approximate solution without user-specified a priori guesses.