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.