## 5 Discussion  
The results of experimental tests presented in this paper, carried out on a stand equipped with a copper pipeline consisting of two pipes of different diameters connected in series, were subjected to detailed analyses. Thanks to two different methods of determining the pressure wave speed in the system from the experimental data, it has been shown, among others, that this quantity depends on the pressure level in the supply tank. The presence of an amount of gas (air) microbubbles in the water, which could not be completely eliminated before the tests, despite leaving the water at rest for several days, was considered the most probable cause of this. The presence of undissolved air may introduce additional uncertainty in the results obtained using the proposed methods. This uncertainty can be minimized by conducting a detailed analysis of the effect of air content on the pressure wave speed according to the  
Figure 9: Analysis of the gas fraction content in the liquid during laboratory tests. methodology presented in [46] (chapter 8-2, pp. 139-142). It is based on the dependence of pressure wave speed changes on the pressure level and gas fraction content in the air-water mixture. This dependence results from taking into account the changes in the bulk modulus and density caused by the presence of air in water. This is reflected in the formula for the pressure wave speed, which, after some simplifying assumptions, shows its dependence on the pipeline geometry (\(D\), \(e\)) and the Young's modulus of the pipeline material (\(E\)), as well as on the liquid (water) bulk modulus \(K\), absolute pressure \(p_{abs}\) and the gas fraction content determined from the ratio of the gas volume to the total volume of the gas-water mixture \(V_{g}/V\):  
\[a=\sqrt{\frac{\frac{K}{\rho}}{1+\frac{KD}{E\epsilon}+\frac{V_{g}}{V}\frac{K}{P _{abs}}}} \tag{10}\]  
The analysis carried out for different values of the \(V_{g}/V\) ratios is presented in Figure 9 and concerns changes in the pressure wave speed in pipeline #2. The changes in the pressure wave speed measured during the experiment using method #1 under the pressure conditions \(p_{abs}\) during the laboratory tests (from 36 m wc to 130 m wc) allowed for determining the gas fraction in the gas-water mixture at approx. \(V_{g}/V=0.005\%\). As it results from the presented analysis, the air content in the laboratory conditions causes a change in the propagation speed by \(\pm 1.3\%\). The range of these changes justifies the statement that the content of undissolved air in the water present in the laboratory conditions does not introduce significant uncertainty into the presented considerations. The dependence of the pressure wave speed on the gas fraction in the fluid is shown in Figure 10. It is worth emphasizing that for high gas contents the change in wave velocity increases rapidly, but in the range up to \(V_{g}/V=0.15\%\), this change is not greater than 10%. It should be emphasized that the change in pressure wave speed with the change in gas volume, especially at low \(V_{g}/V\), does not affect the uncertainty of the proposed methods because they are based on precise time measurements (method #1 determines the pressure wave speed based on the wave transit time between two pipeline cross-sections, while method #2 is based on the wave period in the free oscillation phase). The test results show the relatively high frequency of free pressure oscillations (for a pipeline of full length \(L=L_{1}+L_{2}\)) in the final (developed) phase of the water hammer. Its value in the cases tested on the stand was higher than the results from the theory of pressure wave propagation in individual pipes, without considering the process of their mutual interaction.