# Experimental Investigation of Column Separation Using Rapid Closure of an Upstream Valve
## 2 Experimental Apparatus  
A flexible experimental system for investigating water column separation on the downstream side of a fully closed upstream valve was designed and constructed at the Hydraulic Laboratory of Hohai University. The apparatus shown in Figure 1 consists of an upstream reservoir, a 12.714 m long, 40 mm inside diameter pipe, three quarter-turn ball valves, and a downstream reservoir. The pipeline has two L-shaped stainless steel pipes (with 40 mm inside diameter and 3 mm wall thickness) that are connected to a horizontal PMMA pipe (with 10 mm wall thickness) and two reservoirs. The length of the horizontal section of the pipeline is 11.614 m. The upstream and downstream reservoirs have the same dimensions: 1.3 m long, 1.0 m wide, and 4.0 m high. The maximum pressure head in both tanks could reach 4.55 m.  
Nine piezoelectric pressure transducers were used to measure the pressure variation in the pipeline. The installation locations are provided in Table 1. All the pressure transducers used were BYP300. Pressure ranged from \(-\)0.1 to 3 MPa with an output range from 0 to +5 V. The lag error was less than 0.15% of the full range. An electromagnetic flow meter was installed at 1.445 m downstream in Tank 1 to measure the steady flowrate that ranged from 0 to 25 m\({}^{3}\)/h with a DC voltage output ranging from 1 to 5 V. The error was less than 0.2% of the full range. A fast-response data acquisition system was utilized to collect, digitize, and record voltages from the transient signals: flowrate and nine pressures. A software package for date acquisition and analysis, National Instruments software LabVIEW v2016, was used to control the data acquisition. The ten signals were fed into a National Instruments 16-bit A-D card, Model OCI 6221. The data acquisition software was set to initiate data collection automatically. The pressure and flowrate oscillation histories were displayed on the computer screen. Both data sampling frequencies for pressure and flowrate were 5000 Hz. A high-speed, high-resolution digital video camera (Memrecam Q1m) was used to record changes in the cavity during column separation. The shooting frequency of the high-speed camera was 1000 Hz.  
The wave speed \(a\) was measured during water hammer events with no cavitation by using Equation (1):  
\[a=\frac{4L}{2T}=\frac{2L}{T} \tag{1}\]  
where \(L\) is the length of the pipeline, and \(T\) is the pipeline period of pressure wave reflection. Using the average wave speed values under different single-phase water hammer conditions, the wave speed value for the pipeline was determined as 763 \(\pm\) 21 m/s.  
The friction factor in the steady flow state was evaluated using the Darcy-Weisbach formula [25]:  
\[h_{f}=f\frac{L}{D}\frac{V^{2}}{2g} \tag{2}\]  
where \(h_{f}\) is the total pressure head loss, \(D\) is the inner diameter of the pipes, \(V\) is the flow velocity, and \(g\) is the gravitational acceleration. For our experimental system, the friction factor ranged between 0.034 and 0.055.  
The valve closure time, \(t_{c}\), recorded using the high-speed camera, ranged from 0.02 to 0.05 s. The delay time of the ball valve ranged from 0.02 to 0.03 s.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**No.** & **PT1\#** & **PT2\#** & **PT3\#** & **PT4\#** & **PT5\#** & **PT6\#** & **PT7\#** & **PT8\#** & **PT9\#** \\ \hline Horizontal distance from Tank 1 (m) & 0.726 & 1.3 & 2.006 & 3.112 & 5.596 & 6.241 & 8.222 & 9.805 & 10.42 \\ \hline \end{tabular}
\end{table}
Table 1: Installation locations of pressure transducers.  
Figure 1: Schematic diagram of the hydraulic transient apparatus.