Last month’s column described the process of creating an energy cost balance sheet for a piping system (see Figure 1). The manufacturer’s curve was used to calculate the cost of operation for the centrifugal pump. This column explains how to perform the detailed cost calculation for other items in the system.

## Evaluating Parts

Figure 1 shows the operating data from the installed plant instrumentation. This operating data and the manufacturer’s equipment data sheets will be used to calculate the differential pressure and flow rate through each item. With that information, the cost of electrical power and the annual rate of operation, the annual operating cost and energy use can be calculated for each item in the system’s energy cost balance sheet.

To calculate the operating cost for an item in the system, its head loss and corresponding flow rate must be determined. Insufficient installed instrumentation means these values need to be calculated with data from the equipment manufacturers.

## Determining Pump Flow Rate

Last month’s column calculated a pump head of 235 feet (ft) and a flow rate of 4,000 gallons per minute (gpm). From the pump curve, it was determined that the pump had an efficiency of 83 percent at its flow rate. The pump’s operating costs were calculated after looking at the pump’s motor efficiency, annual hours of operation and cost of electrical power.

So how was the flow rate through the pump of 4,000 gpm established? The flow to the destination tank is 2,500 gpm, but because there is no flow element in the bypass circuit, the pump’s total flow rate cannot be calculated. Without this value, the pump efficiency and power consumed also cannot be calculated.

The pump curve is the key to this process because it provides manufacturer-supplied test data on how the pump operates for its flow range. Knowing the pump’s total head, the pump curve can be entered on the head axis and move across until the known pump head value intersects the pump curve. Dropping straight down on the pump curve gives the flow rate, and the intersection point provides the pump efficiency.

In Figure 1, the process pump’s discharge pressure is 102.8 pounds per square inch (psig). Centrifugal pump curves use head instead of pressure, so the discharge pressure must be converted to feet of fluid using Equation 1.

Where:

H = Head in feet of fluid

P = Pressure in lb/inch^{2}

ρ = Fluid density in lb/ft^{3}

144 is a conversion factor for ft^{2} to in^{2}

A pressure gauge is not installed on the pump suction, so a temporary gauge was mounted on a suction vent. The temporary suction pressure gauge reads 1.7 psig, resulting in 3.95 ft of fluid. Subtracting the discharge and suction heads (239 ft minus 3.95 ft), the pump’s total head is 235 ft. Reading from the pump curve (see Figure 2), the resulting flow rate through the pump is 4,000 gpm, and the pump is 83 percent efficient.

Next, the cost to operate the system’s process elements will be evaluated using their flow rates and head loss.

## Static Head Cost

The static head accounts for the difference in fluid energy between the destination and supply tanks. Per the Bernoulli equation, fluid energy is composed of three types of head: elevation, pressure and velocity. Because the fluid is at rest in the supply and destination tanks, the velocity head has no value (see Equation 2).

Where:

Z_{B} = Elevation of tank bottom in ft

L_{FS} = Level of fluid surface above tank bottom in ft

P_{FS} = Pressure on fluid surface in psi

ρ = Fluid density in lb/ft^{3}
_{1} = Supply tank
_{2} = Destination tank

The static head is the energy difference between the supply and destination tanks. It remains the same regardless of the flow rate between the tanks. The static head can be used to calculate the annual operating cost due to the head component within the process circuit.

The 2,500 gpm flow rate through the process circuit is used in the annual operating cost formula (see Equation 3). The 83 percent pump efficiency comes from the pump curve with a 4,000 gpm flow rate. The pump efficiency applies to the 4,000 gpm flow rate because the pump supplies both the process and bypass circuits. Inserting the static head pump efficiency, flow rate, hours of operating and cost of power results in an annual energy cost of $22,800 for the static head.

Where:

Q = Flow rate

H = Head

ρ = Fluid density

η_{ρ} = Pump efficiency

η_{m} = Motor efficiency

## Process Element Cost

Process equipment—characterized by a head loss that is a function of flow rate—is the next item in the energy cost balance sheet. In the system shown in Figure 1, the process element has no installed pressure gauges. The manufacturer’s equipment data sheet will be used to calculate head loss.