Progress in Analytical Modeling of Water Hammer

Analytical formulas for laminar water hammer in horizontal pipes were extended and simplified into a compact mathematical form based on dimensionless parameters: dimensionless time, water hammer number, etc. Detailed treatment of turbulent water hammer analytical solutions is beyond the scope of this paper. In the Muto and Takahashi solution, novel Laplace and time domain formulas for flow velocity and wall shear stress were developed. A series of comparative studies of unified analytical solutions with numerical solutions and the results of measurements were carried out. The study shows that models that account for the frequency-dependent nature of hydraulic resistance agree very well with experimental results over a wide range of water hammer numbers Wh, particularly when Wh = 0.1.