# Identification of the Wear Margin of a Pipeline-Machine Subsystem
## 2 Pipeline-Machine Subsystem: Boundaries, Characteristics, Curves and Losses
To detect leakages in a working subsystem, pipeline leak detectors are used, e.g., ultrasound detectors. These instruments generally do not allow measuring leakage value (mass loss). Special systems are created for leakage identification in pipelines [23]. The leakage value or the area of substitute section of the leak in a machine can be measured during tests of nonworking elements of a subsystem [24]. Wear leads to changes in the characteristic curves of the machine and the pipes. In systems with rotodynamic pumps, the subsystem efficiency may reach more than 90% [25]. The wear over several years may reduce the efficiency by 8-15%, occasionally up to 20% [19]. Figure 3 shows hypothetical curves of the discharge pipe and rotodynamic machine with nominal wear margins \(p_{d1}\big{(}\dot{V}\big{)}\), \(p_{1}\big{(}\dot{V}\big{)}\) and \(\eta_{1}\big{(}\dot{V}\big{)}\), and exhausted wear margins \(p_{d2}\big{(}\dot{V}\big{)}\), \(p_{2}\big{(}\dot{V}\big{)}\) and \(\eta_{2}\big{(}\dot{V}\big{)}\). Figure 3: Effects of wear. Index: 1—nominal wear margin; 2—exhausted wear margin. Intersections of the discharge pipe and machine curves give four operating points, OP\({}_{1}\), OP\({}_{2}\), OP\({}_{3}\) and OP\({}_{4}\), defining the field of subsystem's wear margin (shaded area). In the absence of leakages in the discharge pipe, we can assume that the volume flow rate for OP\({}_{1}\) is a nominal flow rate \(\dot{V}_{2}\) of the subsystem and that the interval of volume flow rate values determined by points OP\({}_{1}\) and OP\({}_{4}\) is equal to \(\Delta\dot{V}_{2}\) of the subsystem. In the same manner, \(\eta\) and \(\Delta\eta\) can be found. It follows from Figure 3 that the discharge pressure \(p_{d}\) value, depending on the wear, may be higher or lower than the nominal pressure for point OP\({}_{1}\). An excessive value of discharge pressure \(p_{d}\) may lead to secondary failures of the machine and pipeline. In the case of pumps, a drop in the wear margin of the suction pipe can cause the suction pressure to become lower than the cavitation pressure, which may result in cavitation wear of pump elements. Simultaneous and uniform wear of the discharge pipe and the machine is not a regular occurrence. Fast wear of the pipe or the machine only is more likely. Figure 3 also presents a hypothetical curve \(p_{3}\big{(}\dot{V}\big{)}\) for the machine with values of wear margin below an acceptable value. A situation is possible where the machine wear margin is exhausted and the subsystem has the volume flow rate \(\dot{V}_{2}\) within the desired range, in which case the efficiency value will be outside the desired range. The subsystem efficiency is a characteristic whose value depends on the subsystem wear margin. The drop in efficiency under the same operating conditions of the subsystem is due to increased losses in the subsystem. The drop in efficiency below the limit value should initiate looking for the cause of the decease in efficiency. Methods of energy efficiency identification can be developed using the hydrodynamic and thermodynamic models of the pipeline-machine subsystem.