This series on troubleshooting piping systems draws on past columns in Pumps & Systems discussing the operation of individual components found in piping system. We'll use that knowledge to establish the connection between items with the goal of developing a model of the piping system. We will then see how to use the model to determine if the equipment is operating within the confines of the model, and then compare the model to the physical piping system. This approach can identify and isolate problems within the piping system to arrive at a course of corrective action. Piping systems vary in size and complexity, but the methods presented here can break down even the largest systems to troubleshoot and improve system operation.

## The Example System

Figure 1 shows the example system. We will use this example to build the model and then demonstrate a variety of troubleshooting techniques.

The system starts at supply tank TK-101. The base of the tank is located at 0 feet above our common datum elevation and is open to atmosphere. The tank has a working level of 10 feet above the tank bottom and is equipped with a level indicator. The process fluid is delivered to the supply tank by a collection system outside the boundary of our system example. The process fluid has a temperature of 60 F, a density of 62 pounds per cubic foot (lb/ft^{3}), a viscosity of 1.2 centipoise (cP) and a vapor pressure of 1 pound per square inch (lb/in^{2}) absolute.

From the supply tank, the fluid travels through a suction pipeline to centrifugal pump PU-101. The pump's suction and discharge nozzles are at 0 feet elevation. The pump is equipped with both suction and discharge pressure gauges PI-100 and PI-101. The shell and tube type heat exchanger maintain fluid at 100 F. The heat exchanger has only an outlet temperature gauge.

Flow control loop 101 has a flow meter FT-101 for the process value (PV), with the FCV-101 globe style control valve as the final element. The loop has a flow rate indicator and a positioner on the control valve showing the valve position.

The fluid is travels to the destination tank. Tank PV-102 is the outlet boundary of our piping system. The tank bottom elevation is 50 feet with a normal operating level of 15 feet with pressure maintained at 25 psi. The PV-102 tank provides the fluid to other users within facility.

## Understanding the Connections

Every piping system consists of three elements: the pump, process and control elements. The pump adds energy to the fluid; process elements make the product or provide the service while control elements improve product or service quality. Working together these elements meet the system's design objectives.

The key to understating the interaction between the equipment in the system, as well as its operation, is energy usage. Since we know that energy must be conserved in any system, we can develop an equation for energy usage:

h_{PU} = h_{pg} + h_{C}

Where:

h_{PU}=Pump gain (feet)

h_{pg}=Process losses (feet)

h_{C}=Control losses (feet)

We will use head in feet of fluid as our energy units. Every system must have a known reference for comparing energy measurements so all values are made in reference to a common datum; i.e., 0 feet of elevation in this case.

*The Pump Elements*

A centrifugal pump adds energy to the fluid by converting mechanical from the pump shaft to fluid energy. This is accomplished by converting velocity head to pressure head. The performance of centrifugal pumps is documented by the manufacturer in the form of a pump curve, which shows the pump head developed, and the efficiency in converting mechanical energy to fluid energy as a function of flow rate.^{1}

*The Process Elements*

The process elements consist of the supply tank, interconnecting piping, heat exchanger and destination tank. The supply and destination tanks represent our system's boundary.

Since we are starting our system at the supply tank, we must determine the fluid energy content at this point. This is determined by calculating the energy due to the elevation of the liquid surface in the tank (referred to as elevation head), and the energy due to the pressure on the surface of the liquid (referred to as pressure head). The combination of the elevation and pressure head is referred to as the static head. The amount of system energy starts as the static head of the liquid in the supply tank. This calculation is outlined in the Bernoulli equation described in fluid dynamic textbooks.

The pipelines transport fluid throughout the system. Due to the friction between the stationary pipe and the moving fluid, and the change in fluid momentum due to valves and fittings, energy is lost in the system. This is referenced in feet of fluid. The energy expended to move the fluid through the pipeline is called dynamic head, because it is a function of the flow rate through the pipe. Calculating head loss in pipelines for Newtonian fluids is performed using the Darcy formula.