Solution for the Closed-Loop Problem in Pressurized Multipipe Systems

Abstract

The fundamental background of the solution for the steady-state flow in pressurized water closed-loop pipe systems, without any reservoirs in-between, is presented in this paper. The use of the steady-state mass balance and energy equations to calculate discharges and heads in this type of hydraulic system leads to an undetermined problem. The way to solve this indeterminacy is to consider an additional continuity equation associated with the difference between initial and final conditions, taking into account fluid compressibility and pipe-wall deformability. A complete formulation is derived considering pressure and temperature changes in the hydraulic system. Simplified formulae are presented for isothermal flows in simple systems and multiple closed-loops with pipes in series and in parallel. This problem can also be solved by a pseudotransient analysis technique applied to steady-state conditions. Proposed solutions for this problem are applied to steady-state flows and tested for different system configurations.