## 2 Laboratory Stand  
One of the most important elements of the work presented in this paper is laboratory tests carried out on a test stand built in the laboratory hall of the Institute of Fluid-Flow Machinery of Polish Academy of Sciences in Gdansk--Figure 1. The stand consists of two copper pipes connected in series with the following geometric parameters:  
* Pipe #1: inner diameter \(D_{1}\) = 20 mm, wall thickness \(e_{1}\) = 1 mm, length \(L_{1}\) = 49.3 m
* Pipe #2: inner diameter \(D_{2}\) = 16 mm, wall thickness \(e_{2}\) = 1 mm, length \(L_{2}\) = 58.9 m  
The change in diameter between the pipes is stepwise. The pipeline system is supplied from the upstream tank (horizontally arranged cylindrical pressure tank with a diameter of 2 m and total volume equal to 10 m\({}^{3}\), with an air cushion). The maximum pressure in the upstream tank that could be maintained during the tests was 1.2 MPa of absolute pressure. Water from the pipeline is directed to the downstream tank (tank opened to an atmosphere of total volume equal 8 m\({}^{3}\): cube shape with side 2 m). The water in the stand flows in a closed circuit--it is pumped from the downstream tank by a pump unit equipped with a variable rotational speed drive through auxiliary pipelines to the upstream tank. From the upstream tank, it flows through the measuring pipeline system and auxiliary pipelines, which, together with the installed control fittings, are used to stabilize the initial conditions during the tests (pressure and flow in the measuring pipeline system). At the end of the measuring pipeline (looking in the direction of water flow, i.e., at the end of pipe #2), a quick-closing ball valve is installed, which enables an almost stepwise shut-off of the water flow. A high degree of repeatability of the valve closing processes was achieved using a special spring drive. In the tested cases, the closing time, \(T_{c}\), was close to 2 ms. The laboratory stand is equipped with six pressure transducers installed in the initial, middle and end sections of each pipe, looking in the direction of the initial flow, and in the upstream tank. This paper focuses on the results measured at the valve (end of the pipe #2) because this is where the water hammer is most intense [19; 46]. Each of the pressure transducers produced by KELLER Druckmestechnik AG (Winterthur, Switzerland) was mounted on the pipeline with the use of a short (approx. 0.07 m) flexible impulse tube, which allows for significantly reducing the influence of pipeline structure vibrations on the measured pressure signal. The small length of the impulse tubes in relation to the total length of the pipeline and very high relative stiffness of their material (approx. 10 times higher than the coating of the measuring pipeline) minimized their influence on the measured pressure changes during the tested phenomenon. The pressure transducers of the frequency band equal (0-2) kHz and the accuracy class: \(\pm\)0.1% were used to measure the absolute pressure within the range of (0-4) MPa abs. The transducers characteristics were checked before the tests and immediately after their completion. It was estimated (according to [47]) that the uncertainty of the pressure measurements was ca. 0.47 m wc (meters of water column). A turbine flow meter (manufacturer: Turbines Inc. (Altus, OK, USA), type: HA) with measurement inaccuracy (maximum measurement error) of 0.25% of the measured flow rate in the range (0.5-10) m/s and 1% in the range (0.1-0.5) m/s was used to measure the flow. The flowmeter indications were checked before and after the tests using the volumetric method. The degree of opening of the quick-closing ball valve was monitored with a single-turn potentiometer. Before the tests, the potentiometer readings were calibrated with the appropriate valve positions: potentiometer signal readings for a fully closed valve position was defined as 0% of opening and respectively the signal for a fully opened valve was defined as 100% of its opening.