**5. Conclusions**

The paper presents a modified unsteady discrete bubble cavity model DBCM. The new model is developed in a very simple form, which makes it easy for implementation in commercial programs for unsteady pipe flow analysis. The new model takes into account three very important phenomena: unsteady wall shear stress, vaporous cavitation, and pipe-wall retarded strain. The latter mentioned phenomenon occurs in plastic pipes.

The conducted comparative studies have shown that with the help of the presented model, it is possible to simulate pressure and velocity waveforms in which vapor areas appear as a result of the cavitation phenomenon in plastic pipes. It was noticed that the influence of unsteady friction was much smaller than the influence of retarded strain. An innovative method of calculating the convolutional integral describing the retarded strain was applied by using the analogy to the convolutional integral defining the wall shear stress (Schohl's method). Taking into account the commonly known boundary conditions related to the method of characteristics enables the use of the novel model in complex networks: water supply, oil hydraulics, heating, etc.

The modified solution is an alternative to the two commonly used transient cavitating pipe flow models, namely the DGCM (discrete gas cavity model) and the DVCM (discrete vapor cavity model). In our future work, we are planning to execute broad comparisons of the presented new model with the existing ones.

The use of the experimentally determined creep functions (obtained by Güney) showed that such functions can be an alternative to the calibration methods commonly developed today. This indicates that the creation of the so-called "maps" of creep function curves for various polymeric materials currently used in the world for pressure pipes will significantly help designers at the design stage and will enable the study of the most dangerous unsteady cases "a priori". Presentation of such "maps" obtained for different temperatures should be a priority of the current scientific research.

**Author Contributions:** Conceptualization, K.U., A.B. and M.S.; methodology, K.U. and A.K.; software, K.U., A.M. and A.B.; validation, K.U., A.M. and M.K.; formal analysis, K.U., P.B. and M.S.; investigation, K.U., A.B, M.S. and M.K.; resources, K.U.; data curation, K.U.; writing—original draft preparation, K.U. and A.B.; writing—review and editing, K.U., A.B., A.K., M.S.; visualization, K.U., P.B.; supervision, K.U. and A.B.; project administration, K.U. and M.S.; funding acquisition, K.U. All authors have read and agreed to the published version of the manuscript.

**Funding:** A.B. gratefully acknowledges the support of Slovenian Research Agency (ARRS) conducted through the research project L2-1825 and the programme P2-0162.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All codes generated during the study and experimental data are available from the corresponding author by request.

**Conflicts of Interest:** The authors declare no conflict of interest.
