Upwind Finite Volume Solution of Water Hammer in Pipes without Column Separation in Unsteady Friction Model

The waves resulting from instantaneous and complete valve-closure in pressurized pipe systems, propagate upstream and/or downstream in the hydraulic system. The pressure (head) and velocity of the flow (waves) are important parameters in the design of pipeline systems. A simple and efficient approximation to the Vardy–Brown unsteady friction equation is implemented within a FVM solution for unsteady pipe flows. The model is compared with measured data and numerical data produced by a two-dimensional turbulence water-hammer model. The results show that the model is in good agreement with both laboratory and numerical results. The computed minimum and maximum values and the time period of the pressure waves are in close agreement with the 2-D numerical solution and experimental measurements.