# Identification of the Wear Margin of a Pipeline-Machine Subsystem
## 2 Pipeline-Machine Subsystem: Boundaries, Characteristics, Curves and Losses  
Pipeline-machine subsystems serve to transfer fluids (liquids, gases) from areas of lower mechanical energy to areas of higher mechanical energy and to transfer fluids from areas of higher thermal energy to areas of lower thermal energy. They also may be used to handle fluids in order to discharge contaminants, transfer heat or accomplish other goals. Fluid behavior is described by hydromechanics (with the prefix \"hydro-\" indicating or denoting water, liquid or fluid) and thermodynamics. The type of fluid is considered to be specified if the fluid density \(\rho\) and specific heat \(c_{w}\) are known. There are two types of pipeline-machine subsystems:An open subsystem for continuous or intermittent operation, with constant or variable pressure and constant or variable temperature at the beginning of a suction pipe;  
A subsystem with a closed vessel at the end of the discharge pipe or suction pipe. Figure 1 presents the boundaries of an open subsystem: the beginning (point 1) and end (point 2) of the transport process and the source and type of supplied energy \(E_{d}\). The pipeline in Figure 1 is shown as consisting of straight sections, and the change in height above reference plane was replaced by appropriate changes in pressure, i.e., height change indicated by \(\Delta H\) was replaced with pressure change indicated by \(\Delta H\)-\(g\)-\(\rho\). Indicated subsystem elements include a suction pipe, an engine-driven machine and a discharge pipe. A machine and a driving engine make up a machine set. Pumps and compressors are generally driven by electric motors. In such cases, the subsystem is supplied with electric energy \(E_{d}\ =\ E_{d}\). Suction and discharge systems consist of pipeline sections and fixtures (valves, connectors, fittings) and devices built into pipeline sections. Physical quantities describing transported fluid are pressure \(p\), mass flow rate \(\dot{m}\), volume flow rate \(\dot{V}\) and temperature \(T\). The values of these quantities change along a pipeline length (Figure 1). Changes are due to the operation of a machine and losses. The value of pressure drop in a pipeline \(\Delta p_{\text{pipeline}}\) (Figure 1) depends on the volume flow rate \(\dot{V}\). Following [15; 16], we can assume that \(\Delta p_{\text{pipeline}}\ =\ \alpha\cdot\dot{V}^{2}\). The pressure-flow rate relationship is referred to as the pipeline curve \(p\big{(}\dot{V}\big{)}\). Such curves can be drawn for the discharge pipe \(p_{d}\big{(}\dot{V}\big{)}\) and the suction pipe \(p_{s}\big{(}\dot{V}\big{)}\). According to available literature, the values of \(\Delta p_{\text{machine}}\ =\ p_{d}-p_{s}\), machine differential pressure and machine efficiency \(\eta_{\text{machine}}\) are also dependent on volume flow rate \(\dot{V}\). Machine volume flow rate \(p\big{(}\dot{V}\big{)}\) and machine efficiency \(\eta\big{(}\dot{V}\big{)}\) curves are plotted after these relationships are found experimentally. The plotted curve shapes depend mainly on the type of machine: rotodynamic or positive displacement. Figure 1: Boundaries of an open pipeline–machine subsystem and qualitative changes of \(p\), \(\dot{m}\) and \(T\) along the pipeline. For machines with a steep flow curve, the efficiency curve is made as \(\eta(p)\). The method of plotting is presented in a standard appropriate for a given machine and its type (e.g., [17]). Once the suction and discharge unit curves and machine curves are drawn, an operating point (OP) is obtained (Figure 2). The values of pressure and flow rate at the operating point are \(p_{d}\) (discharge pressure) and \(\dot{V}_{d}\) (volume flow rate), respectively (Figure 1). Decomposing desired characteristics of a production system, we can assume that the pipeline-machine subsystem is generally expected to have proper capability, efficiency, reliability and availability.