**2. Measurements**

The experimental apparatus, as shown in Figure 1, is composed of PVC pipes and a transparent PVC compressed air vessel (CAV) with 0.10 m diameter and 0.60 m height. The CAV includes an air pocket (AP) at the top and a water column (WC) at the lower part. A pump creates a circulation flow with different flow velocities. A fast closure electro-pneumatic ball valve (EBV) has been used to create one or several consecutive WH phenomena in the system. Three check valves (CV) are installed to block the returning way of the flow. A pressure transducer (PT) and an ultrasound velocity profiler (UVP) were used for recording the pressure and flow velocity during the tests. The UVP represents both a method and a device for measuring an instantaneous velocity profile in the water flow along the ultrasonic beam axis by detecting the doppler shift frequency of echoed ultrasound as a function of time. The doppler was installed on a horizontal pipe before the EBV location. There are two PT in the system; one located at the top of the CAV and the other upstream of the EBV. Tests are fulfilled in two different conditions of the BV located at the lower level of the CAV for discharging the water; (i) closed BV for measuring the stored pressure within the AP; (ii) open BV for measuring the relocated water volume. An open water tank is placed downstream of the outflow pipe from the CAV, which provides a tool to collect water and measure the relocated water volume after each test.

Different AP sizes (and related VFRs) and flow velocities are considered during the tests. To cover a wide range of AP sizes, seven AP lengths, i.e., 2, 3, 4, 5, 10, 20 and 40 cm were tested with corresponding VFRs of 3.17%, 4.75%, 6.33%, 7.92%, 15.84%, 31.67% and 63.35% respectively. Also, seven flow velocity values of 1.00, 1.50, 2.00, 2.50, 3.00, 3.50, 4.00 and 4.50 m/s and Re of 36,000, 56,000, 75,000, 93,000, 115,000, 132,000 and 155,000 are used for testing each VFR value with different combinations of VFR and Re.

Several WH tests, i.e., 1WH, 5WH and 9WH have been fulfilled, induced by EBV for different Re and VFR magnitudes. The numerous part of 1WH, 5WH and 9WH symbols shows the number of WH repetitions during each test. During these series of tests, the surge pressure obtained in WH action is conducted toward the CAV to store the pressure in the AP. Measurements for different tests were carried out in similar initial conditions of velocity and pressure in the pipe system and AP. The initial AP pressure was adjusted to a constant value equal to the atmospheric pressure throughout all the tests to achieve the maximum pressure during the transient action [16].

**Figure 1.** Scheme of experimental apparatus and components; (**a**) system; (**b**) compressed air vessel (CAV); (**c**) upstream side of the apparatus; (**d**) downstream side of the apparatus.
