INVESTIGATION OF UNSTEADY EFFECTS OF FRICTION LOSS AND TRANSIENT FLOW USING 1D ENERGY RELATIONS

Leaks in pipes and water distribution systems might occur for various reasons, such as poor quality of pipe material, errors in operation and maintenance, corrosion, and internal or external high pressure. As a result, loss of water, environmental problems, extra energy consumption and unnecessary pump capacity could be observed. To avoid all these consequences, it is essential to provide advanced monitoring methods to observe resulting problems and their extent, and then to nd and implement solutions for water transportation and distribution systems to reduce loss and increase energy eciency. Several leak detection methods have been introduced up to now, such as inverse transient analysis, to overcome these problems. Application of the energy concept to uid transients in closed conduits leads to an alternative description of unsteady ow behavior. In this interpretation, a transient in a pipe system can be viewed as a sequence of energy transformations, which moves the system from some initial hydraulic conditions to some other nal states. During this conversion, mechanical energy is dissipated and work is done on the uid. When the rate of ow in a closed conduit is changed, large-scale conversions of mechanical energy often occur, particularly if the pipeline is carrying water or any other slightly compressible liquid. It is obvious that the side- ow volume ux has a marked eect on the unsteady frictional dissipation component of the uid. Mathematical expressions describing these transient energy transformations are rst derived from main principles and then the governing continuity and momentum equations are mathematically manipulated to provide the nal set. Those various terms, which must be accounted for in the analysis, include the energy dissipated by uid friction, the work done at the upstream and downstream ends of the pipe and the kinetic energy carried into and out of the conduit. In this paper, the leakage term is added into continuity and momentum equations and, therefore, the energy relation for the dissipated energy due to leakage could be derived. Then, in order to determine the appropriate condition for modeling the detection methods, based on transient ow simulation, the eects of the time of valve closing in laminar and turbulent ow, with low Reynolds numbers, have been investigated. The results show that by using lower Reynolds numbers and longer durations of valve closing, appropriate results could be obtained for leak detection. In this manner, not only is the reliability of the results increased, but those sharp uctuation indemnities caused by the fast transient ow are also avoided.