# Identification of Water Hammering for Centrifugal Pump Drive Systems
## 3 Real-Time Simulation Results  
The pressure head for different valve opening and closing times at different flow rates were evaluated. From the flow-rate values, the velocity is calculated using Equation (5). The diameter of the pump is 0.102 m based on PVC material collected from the datasheet given by the manufacturer, and the pressure head is calculated to meter from the bar for comparisons. The vapor pressure head at 68\({}^{0}\) F is 1.42 m, calculated for this pump using the vapor pressure chart. The pipe martial is ASTM D2467 SCH 40 PVC. The diameter of the pump and the length of the pipeline have significant effects on water hammering problem detection [22]. For simplicity of the calculation, the flow-rate value of the pumping system is converted to m\({}^{3}\)/s. The pumping system valve opening and closing data were collected from the experimental set-up (Table 1). At different set pressures and times, the flow rate and velocity values of the pumps have been calculated where the pressure head of the pump changes for sudden closing and opening of the valves. This experiment was done with a time difference of  
Figure 5: Total power consumption. 0.5-s gaps. Nevertheless, valve-closing time T\({}_{\text{C}}\) is less than 1 s, i.e., 0.07 s, whereas returning wave time T\({}_{\text{r}}\) is 0.123 s, based on pipe length and wave propagation velocity change. Generally, T\({}_{\text{C}}\) is less than T\({}_{\text{r}}\) for rapid water hammering. As the pipe length and diameter is small in the experimental set-up, the water hammering that occurs in the proposed research is rapid water hammering [23,24]. As the Vib Sensor app has some limitations to take data such, as it is unable to take data for more than 1 min, and variations of pressure are up to 2 bars only, so as to check the variations of the healthy and faulty condition at every 5-s gap, a fault has been created. Nevertheless, the pipe length is small, so the valve-closing time is less than 1 s, i.e., 0.07 s. The master-follower pump takes some time to reach an optimum point, which is also one reason that every 5-s time gap fault has been created for experimental analysis. The pumping system was made to run at a constant speed, and the different pressure values were assigned by the user to collect the flow rate, velocity, and pressure-head value of different valve-closing and -opening times. At different pressure bars, other parameters, i.e., velocity and flow rate, are measured for faulty and not-faulty conditions. Table 1 shows sudden variations in the flow rate when the valves of the pumps are closed and opened suddenly. For that reason, the pressure-head value also drops suddenly. Initially, one valve is closed, and the pressure-head variation is noted, then for the two-valves and further for three-valves condition, the same procedure is repeated. The corresponding variation in the flow rate also is recorded. The pressure and flow-rate values are collected at different times. In different cases, i.e. at different times, pressure-head and velocity values are calculated where the flow of water starts fluctuating, and water hammering status is observed (Figures 6 and 7). Usually, during the changes of velocity, sudden pressure-head drops for sudden closing and opening of valves, water hammering occurs. When one valve is suddenly closed, and opened pressure head values, do not drop below vapor pressure head value which is 1.42 m for any time and therefore no water hammering occurs. But when two valves are suddenly closed and opened pressure head drops rapidly from 3.998 m to 1.336 m, which is below vapour pressure head value that is 1.42 m, and therefore water hammering occurs. When three valves are suddenly closed and opened pressure head values drop from 1.580 m to 0.5099 m, from 2.243 m to 0.928 m, from 2.029 m to 0.928 m. In all these cases, pressure head values are below vapor pressure head value, i.e. 1.42 m, and water hammering occurs.