Flow Model of Pure Water in a Pipeline

Abstract

Potable water in Tunisia has well defined characteristics. Thus, the Water researches and Technologies Centre-Borj Cedria mainly processing Natural Waters Laboratory, has worked on the physic-chemical quality of the water. As the Higher Institute of Agronomy-chott mariem have studied the phenomena associated with flows. For this work shows that natural water flows that can be generated in a pipeline. During operation of agricultural pumps (centrifugal pumps), the speed of the electric motor increases from zero to the permanent regime speed. This change in regime influences the flow of the hydraulic installation and forced it to follow the starting dynamic law of the motor. Under the effect of the friction force, due to the fluid viscosity, the transient regime is dumped until reaching the normal operating conditions. In this work, we study this phenomenon and see the influence of the pump startup on the hydraulic behaviour of one dimensional flow throw a cylindrical pipe of linear elastic behaviour. The pipe is connected to constant level reservoir at the downstream end. The problem is governed by a two coupled linear hyperbolic partial differential equations which are the equations of continuity and motion. The mathematical model is solved by the method of characteristics where at the upstream end, that is, at the pump station, the boundary condition is given by the differential equation for speed change of the pump motor. A theoretical relationship is introduced to express the motor torque in terms of the time. At the downstream end the discharging reservoir is assumed to be at a constant level. The computed head and discharge time curves, caused by the starting of the pump, are plotted at some cross sections of the pipe. The results show that the evolution of the hydraulic variables is well influenced by the applied motor torque.