Analysis of Rapid Unsteady Flow in Pipelines Using Unsteady Friction Model

Analysis of unsteady flows is very important as it leads to prevent severe damage to water supply system. In the current analysis, it is assumed that the relationship between wall shear stress and mean velocity in the pipe cross-sectional area in unsteady state flow is similar to that in steady state flow. In other words, the formula expressing the wall shear stress in steady state like Darsy- Visbakh or Hazen- Williams is true for unsteady flows in each time step. Meanwhile, in the analysis of rapid unsteady flows like water hammer, wall shear stress equations in steady state are invalid because they underestimate the losses due to friction loss. Therefore, in the present study, the phenomenon of rapid unsteady flow was examined in a reservoir, pipe and valve system that consisted of 63 mm diameter polyethylene pipe with 32, 47 and 80 m lengths. Each pipe was tested with 3 discharges and immediate closing of the valve at the presence of reservoir tank with static water level of 5 meters. This hydraulic condition also was simulated by a computer model that was coded with the programming language MATLAB and was calibrated with the experimental results. This program was able to simulate the rapid unsteady flows with quasi-steady and unsteady friction models. The results indicated that the model was well able to simulate experimental results, and unsteady friction model (RMSE=0.0529) and quasi-steady friction model (RMSE=0.0858) had better estimation of unsteady state condition, respectively. Also, the laboratory pressure waves that were simulated with unsteady and quasi-steady frictional model had a faster damping in their appearance, respectively.