Mathematical Modeling of Lake Tap Flows

Abstract

A lake tap is the submerged piercing of a tunnel at the intake to connect the reservoir to the tunnel system. It is referred to as a dry lake tap if the tunnel is dry before the blasting of the last rock plug at the tunnel entrance. Transient state conditions in the tunnel following a dry lake tap are modeled using the lumped and distributed-system approaches. Fourth-order Runge-Kutta method and the method of characteristics are used in the lumped-system model and distributed-system models, respectively. The results computed by the lumped and distributed-system approaches agree with one another. Pressures computed by using distributed-system and lumped-system models are compared with the experimental results available in literature for rapid filling of a pipeline with closed end. The rate of dissipation of pressure oscillations in the measured air pressure during prototype lake tap at Crater Lake Snettisham project in Alaska, and in the experiments reported in the literature is higher than that computed by the mathematical models using steady state friction and constant wave velocity.