20.500.12556/RUL-137576 About inverse Laplace transform of a dynamic viscosity function A dynamic viscosity function plays an important role in water hammer modeling. It is responsible for dispersion and decay of pressure and velocity histories. In this paper, a novel method for inverse Laplace transform of this complicated function being the square root of the ratio of Bessel functions of zero and second order is presented. The obtained time domain solutions are dependent on infinite exponential series and Calogero–Ahmed summation formulas. Both of these functions are based on zeros of Bessel functions. An analytical inverse will help in the near future to derive a complete analytical solution of this unsolved mathematical problem concerning the water hammer phenomenon. One can next present a simplified approximate form of this solution. It will allow us to correctly simulate water hammer events in large ranges of water hammer number, e.g., in oil–hydraulic systems. A complete analytical solution is essential to prevent pipeline failures while still designing the pipe network, as well as to monitor sensitive sections of hydraulic systems on a continuous basis (e.g., against possible overpressures, cavitation, and leaks that may occur). The presented solution has a high mathematical value because the inverse Laplace transforms of square roots from the ratios of other Bessel functions can be found in a similar way. inverse Laplace transform analytical solution water hammer dynamic viscosity function fluid dynamics pipe flow Calogero–Ahmed sums inverzna Laplaceva transformacija analitična rešitev vodni udar dinamična viskozna funkcija dinamika tekočin tok v cevi Calogero–Ahmedove vrste true false true Angleški jezik Slovenski jezik Članek v reviji 2022-06-22 13:05:03 2022-06-22 13:05:09 2022-09-15 04:15:24 0000-00-00 00:00:00 2022 0 0 26 str. iss. 12, art. 4364 Vol. 15 Jun. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2022-06-01 532.522:517.44 1996-1944 10.3390/ma15124364 112475651 Urbanowicz_..._-_About_inverse_laplace_transform_of_a_dynamic_viscosity_function.pdf Urbanowicz_..._-_About_inverse_laplace_transform_of_a_dynamic_viscosity_function.pdf 1 2447CF09D4DD1F1D55AC1D977097611E 25299113b92391ac56c4ea8610cb5876aaee72d47018ebff7a78b2c25d5a07ec 4cdb5d7b-f21b-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=157580 https://www.mdpi.com/1996-1944/15/12/4364 1 fda958f7-f21a-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=157579 Fakulteta za strojništvo 0 0 0