Understanding Velocity Head

"Testing Centrifugal Pumps in the Field,” Pumps & Systems, February 2011, featured an Excel spreadsheet designed to simplify the field test procedure. The equation for total dynamic head (TDH) showed the components that led to its calculation. One of those components is velocity head, and I have received several requests to revisit its effect on a pump’s TDH when tested in the field. This month is perfect timing since we spent the last two months discussing the achievements of the man who defined it—Daniel Bernoulli.

Velocity Head & Discharge Pressure

Velocity head can be an important component when measuring the discharge pressure of a pump in the field. After all, the bourdon tube pressure gauge measures pressure just like a piezometer and measures only the static pressure. In some instances, velocity head can contribute significantly to the TDH. If it is not taken into account, an accurate comparison of the field test data to the manufacturer’s test curve is not possible. The location at which a gauge reading is taken can have a significant effect on the actual pressure reading. It is not unusual for a centrifugal pump to be connected to a pipeline that is sized for low friction losses via a short length of pipe that is the same size as the pump discharge. If the discharge pressure is measured in that section, it can be different than a measurement taken on the larger diameter pipe. For example, many pumps with 3-inch discharges can produce flows of more than 700 gallons per minute (gpm), and 4-inch models can exceed 1,100 gpm. In fact, almost all pump sizes are capable of flows that exhibit extremely high discharge velocities. When this occurs, velocity head becomes an important component when measuring TDH.

Examples

Let’s take a look at a couple examples. A 3x4x9 end-suction pump operating at 3,500 rpm is connected to the flanged concentric increaser shown in Figure 1. The gauge located on the short section of the 3-inch diameter pipe reads 107 psi (247 feet). A flow meter, installed downstream in the 5-inch diameter section, measures a flow of 650 gpm. When we compare these measurements to the manufacturer’s H/Q curve, this pump should be producing 650 gpm at 112.5 psi (260 feet). The indication would be that this pump does not meet the manufacturer’s test conditions. Now, suppose we do not have a flow meter, and we use the pressure measurement to find the flow point on the H/Q curve. A head of 247 feet would show a flow of 740 gpm. Neither method provides the actual pump performance. The manufacturer’s test curves include velocity head as calculated or measured during testing. Our tests did not. When 650 gpm flows through a 3-inch diameter, Schedule 40 steel pipe, its velocity is 28.2 feet per second. Computing the velocity head (v²/2g) gives an additional 5.4 psi (12.4 feet) that was not accounted for using the pressure gauge measurement. If the pressure had been measured in the 5-inch diameter pipe, it would be far more accurate. The gauge in the 5-inch pipe shows a pressure of 111.8 psi (258 feet). There, the velocity is only 10.4 feet per second and the velocity head is just 0.7 psi (1.69 feet). The pressure measurement in this example is off by 4.7 percent, and the error will always be smaller for higher head pumps. When lower head pumps are involved, the error percentage can increase substantially. A good example of lower head applications is wastewater pump down. Many lift stations that pump into a gravity main require relatively low heads that can range from 15 to 30 feet. Wet wells that use submersible pumps will often use discharge piping that is the same diameter as the pump discharge and base elbow since the piping runs are relatively short. This can lead to high velocities and inaccurate pressure measurements. Since many stations are not equipped with flow meters, a combination of pump downtime and discharge pressure is used to determine pump performance. This is an example of the effect of high velocity in low-head applications. A lift station has 4-inch submersible pumps that are designed to provide a flow of 650 gpm at a TDH of 8.6 psi (20 feet) at the beginning of the pump down cycle. The pumps are connected to individual 4-inch, Schedule 40 steel discharge pipes. The gauge used to measure the discharge pressure is mounted on the discharge pipe at an elevation that is 10 feet above the surface of the water in the wet well. When the pump starts, the gauge reads 2.5 psi (5.8 feet). Correcting for the gauge elevation (10 feet), we reach a corrected measurement of 6.8 psi (15.8 feet). Based on the performance curve, flow would be 800 gpm at this pressure. At 650 gpm, the flow velocity is 16.4 feet per second, and the calculated velocity head is 1.8 psi (4.2 feet). In this example, ignoring velocity head results in a TDH error of 21 percent. Velocity head can be an important factor when testing pumps in the field. At a flow velocity of 8 feet per second, the velocity head is just 1 foot, but it increases exponentially with any increase in flow velocity.