Portal de Periódicos da CAPES

Analytical Solutions of Water Hammer in Metal Pipes. Part I—Brief Theoretical Study

2022; Springer International Publishing; Linguagem: Inglês

10.1007/978-3-030-97822-8_7

2522-5618

Kamil Urbanowicz, Anton Bergant, Michał Stosiak, Marek Lubecki,

Fluid Dynamics Simulations and Interactions

The work presents known analytical solutions concerning the unsteady phenomenon, the so-called water hammer that takes place in pressurized lines. The final form of the presented and discussed solutions has been unified. As can be seen from the final form of the presented formulas, they strongly depend on a dimensionless number, the so-called water hammer number Wh, which is a function of the viscosity of the fluid, the length of the pipe, the inner radius of the pipe and the pressure wave speed. The paper shows that there is no complete analytical solution of water hammer known to date, which would be correct in any dimensionless range of the water hammer number and include the frequency-dependent friction losses. The analysis of all the collected analytical solutions also revealed that the formulas determining the flow velocity and wall shear stress in the model represented the greatest consistency in the initial time period of this transient flow (in the Muto-Takahashi model) are not known. To fill this gap, the missing analytical solutions have been developed. This work is devoted to their derivation.