Part 1 of this series (*Pumps & Systems*, September 2015, online here) discussed the engineering principles that dictate the operation of various elements of a piping system. Using those principles, we built a mathematical model of the example piping system based on information supplied by the equipment manufacturers and design data about the tanks and pipelines. This model can be used to simulate the operation of the physical piping system under any expected operating condition.

Once the model is available, the next step is to gather the plant's operating data, which is broken down into system boundary parameters and operating results, to compare it with results of the system model.

Figure 1 depicts the model piping system with plant operating data listed next to the installed instrumentation. The installed instrumentation consists of the supply tank level, the destination tank level and pressure, the pump suction PI-100 and discharge PI-101 pressures, the position of the control valve, and the flow meter FT-101, which is part of the flow control loop.

Using this data, the actual operation of the system can be compared with the model. These calculations were demonstrated in past *Pumps & Systems* articles and will be referenced in the following discussion.

## Starting Energy

The starting energy of the system can be calculated by converting the tank level to feet of fluid using the Bernoulli equation.

In this system, the datum elevation is set a 0 feet. Equation 1 can be used to determine the energy at the liquid level in the supply tank.

Substituting the values from the plant operating data, we can determine that the static head at the supply tank is 15 feet of fluid.

Next, we will calculate the head loss in the pipeline connecting the supply tank TK-101 to the pressure gauge PI-100. The process fluid for the entire system has a density of 62 pounds per cubic feet (lb/ft^{3}), a viscosity of 1.2 centipoise (cP). The suction pipeline is 25 feet in length, has an inside diameter of 10.02 inches and a roughness value of 0.0018 inches.

The pipeline has two gate valves, one 90-degree long radius elbow and a sharp-edge entrance. The K value for the pipeline equals 0.91 (see the table on page A-27 to A-30 in Reference 1 listed at the end of the article).

The head loss in the pipeline is calculated using the Darcy method^{1} (see Equation 2).

The head loss through the valves and fittings are calculated using Equation 3. Using the method outlined in the Crane Technical Paper 410, we can determine the K value. The head loss in the pipeline is the loss associated with the pipe, valves and fittings. This results in a head loss in the pipeline of 0.35 feet of fluid.

## Pressure at PI-100

With a starting total energy of 15 feet in the supply tank and a head loss of 0.35 feet of fluid in the pipeline, the total energy at the PI-100 is 14.65 feet of fluid. Using the Bernoulli equation, we will calculate the static pressure (the pressure displayed on pressure gauges) at location PI-100. The elevation of PI-100 is 0 feet above the datum. The velocity of the fluid in a 10-inch schedule 40 steel pipe with a flow rate of 1,000 gallons per minute (gpm) is 4 feet per second. Substituting the values into the Bernoulli equation and solving for P results in a static pressure of 6.2 psig (see Equation 4) .

Pressure gauge PI-100 reads a value of 6.2 pounds per square inch gauge (psig), which corresponds with the calculated value above. As a result, we can say the model has been validated with actual reading at PI-100.

## Looking at Pump PU-101

Next we will look at the operation of the centrifugal pump PU-101. Figure 2 displays a copy of the manufacturer's pump curve.

The pump curve indicates that the head developed by the pump at a flow rate of 1,000 gpm is 192 feet of fluid. The total energy at the pump suction as calculated is 14.65 feet of fluid. Adding the total head developed by PU-101 results in a total head of 206.65 feet.

Using the Bernoulli equation, we will calculate the pressure at PI-101, which is 2 feet above the datum elevation. Pressure gauge PI-101 is connected to an 8-inch schedule 40 steel pipe, and, with a flow rate of 1,000 gpm through the pipe, the fluid velocity is 6.4 feet per second. Equation 5 shows the calculation for pressure using the Bernoulli equation.

The calculated pressure of PI-101 is 87.84 psig, and the observed value at pressure gauge PI-101 is 87.8 psig. The observed pressure at PI-101 matches, validating the model at PI-101.

## Calculating the Control Valve Inlet Energy

Next, we will calculate the total energy at the inlet of the heat exchanger. The pipeline from PI-101 to the inlet of HX-101 is 250 feet of - inch schedule 40 pipe, with two gate valves, one swing check valve with an angle seat and four long radius elbows. Using the Darcy equations as outline previously, the head loss in the pipeline is 5.46 feet of fluid. Subtracting the head loss from the total energy at PI-101 results in 201.19 feet of total energy at the inlet of HX-101 (206.65 – 5.46). Because the model does not have a pressure gauge at the inlet of HX-101, we will not be able to validate the calculated results.

Next, we will determine the head loss across the heat exchanger HX-101. The heat exchanger manufacturer provided a graph that shows the head loss across the heat exchanger as a function of the flow rate (Figure 3).

Looking at the graph for 1,000 gpm, the heat exchanger has a head loss of 23.3 feet of fluid, which results in a total energy of 177.89 feet at the discharge of HX-101 (201.19 – 23.3). Because no pressure gauge is located at the outlet of HX-101, this pressure value cannot be validated.

The pipeline connecting the heat exchanger to the inlet of the flow meter is 50 feet of 8-inch steel schedule 40 pipe with a single gate valve. This results in a head loss of .85 feet of fluid. The total energy at the inlet of the flow meter is 177.04 feet (177.89 – 0.85). Because there is no pressure gauge at this location, this value cannot be validated.

The next item in the system is the flow meter FT-101. This meter is designed according to the American Society of Mechanical Engineers (ASME) standard MFC-3M Measurement of Fluid Flow in Pipes Using Orifices, Nozzles and Venturi. The formula to calculate the permanent (non-recoverable) pressure drop across the flow meter is included in the reference standard. That information is also be provided by the manufacturer of the flow element.

The manufacturer's supplied differential pressure graph for flow element FT-101 shows that at 1,000 gpm the differential pressure is 1.35 pounds per square inch (psi), equating to a head loss of 3.14 feet of fluid. The total energy at the outlet of the flow element is 173.9 feet (177.04 - 3.14). Because there is no pressure gauge at this location, this value is also not validated.

The head loss in the 50-foot section of 8-inch steel schedule 40 pipeline with no valves and fitting is 0.78 feet. The total energy at the inlet of the control valve FCV-101 is 173.12 feet (173.9 - .78). Because there is no pressure gauge at this location, this value is also not validated.

## Determining the Control Valve Outlet Energy

The control valves outlet energy can be determined in two ways. One method is to calculate the head loss across the control valve using the flow rate and C_{v} value (based on the valve manufacturer's operating data). Then, continue down the pipeline connecting the outlet of the control valve to the destination tank. The resulting energy of the fluid going into the destination tank PV-102 can be validated based on the static head (level and pressure) in the destination tank.

The second way to find the head loss across the control valve is to determine the total energy at the destination tank and work upstream until reaching the outlet of the control valve. The difference in the total energy between the control valve inlet and outlet is the head loss across the control valve. We can then convert the head loss across the control valve to a differential pressure. With the control valve differential pressure and the flow rate through the valve, we can determine the C_{v} required. We can then compare the valve position calculated using the sizing equation and manufacturer's data to the actual valve position. If they match, then the control valve can be validated. For the purposes of this article, we will use the second method: determining the total energy at the destination tank and working upstream.

## Calculating the Total Energy at the Control Valve Outlet

The base of PV-102 is 50 feet above the datum, with a tank level of 15 feet above the tank bottom, and the pressure above the liquid level is 25 psi. Using the Bernoulli equation, we can determine the total energy at the destination tank (see Equation 6).

The head loss for 1,000 gpm in the pipeline connecting the outlet of the control valve to the inlet of the destination tank is 5.47 feet. The pipeline length is 280 feet of 8-inch schedule 40 steel pipe with a gate valve, three long radius 90-degree elbows and pipe exit into a tank.

Because we are looking upstream, we will need to add the head loss (5.47 feet) to the total energy of the destination tank (123 feet), resulting in a control valve outlet pressure of 128.47 feet.

This results in a head loss of 44.65 feet (173.12 – 128.47). Converting the head loss to differential pressure results in a value of 19.2 psi across control valve FCV-101.

The system has no pressure gauges between PI-101 and destination tank PV-102. So the total energy at the intermediate results cannot be validated with the observed values. We will use the control valve to validate some of the intermediate results.

Next month we will talk about results and model validation. We will also examine ways to evaluate the model. Read it here.

Read the first part of this series here.