Editor's Note: This is the second part of a series based on Optimizing Pumping Systems: A Guide to Improved Energy Efficiency, Reliability, and Profitability, written by pump systems experts. This new guidebook continues the mission of Pump Systems Matter (PSM) and the Hydraulic Institute (HI) to advance knowledge on pumping systems.
Click here for Part One, Part Three, Part Four, Part Five and Part Six.
The Basic Calculations
To optimize a fluid piping system, it is important to have a clear understanding of how the various system items interact. Regardless of the methods used to gain a thorough picture of piping system operations, a variety of calculations must be performed. Among the formulas are the Bernoulli equation to calculate the pressure in the system, and the Darcy-Weisbach equation, which is commonly used to calculate head loss in a pipe run.
The Bernoulli Equation is a way of expressing the total energy of fluid as it flows through a pipe run. The total energy of the fluid at any point in the pipe run when referenced to a horizontal datum is equal to the sum of the elevation head, the pressure head and the velocity head as expressed below:
A pipe run consists of the pipe and the associated valves and fittings. When fluid flows through a pipe, friction occurs between the fluid and the pipe walls. The Darcy-Weisbach equation describes this pipe run friction or head loss:
The Piping System
A piping system is configured of individual pipe runs connected in series and parallel combinations with pumps, control valves, flowmeters and components. It is essential to recognize how these unique elements interact and work together as a system.
There are both graphical and analytical methods that provide an understanding of how the various items interact as a total system. The head loss is calculated using the graphical method for a variety of flow rates for each pipe run. The results can be read off the graph after the information is plotted. Using the analytical method, the results are calculated directly, which eliminates the need for further graphics.
Pipe Runs
A piping system is composed primarily of individual pipe runs connecting all system elements together. Because a pipe run is the basic building block of a piping system, examine the losses associated with individual pipe runs when connected in series and parallel configurations.
The pipe head loss in a single pipe run can easily be calculated using the Darcy-Weisbach equation. Performing the head loss calculation for a range of expected flow rates helps to develop a curve showing the pipe run head loss for any flow rate within a defined range. The Bernoulli equation allows for calculation of pressure anywhere in the pipe run.
Multiple pipe runs connected end-to-end form a "series" of individual pipe runs. The flow rate through each pipe run in a series configuration is identical. As a result, the head loss for a series of pipe runs is simply the sum of the head losses for each of the individual pipe runs.
When multiple pipe runs are placed in parallel, determining the head loss through them becomes more difficult because the flow is distributed through the various pipe runs. The head loss across the parallel paths can be calculated after determining the flow rate in each pipe run and the head loss across each pipe run in a parallel configuration.
A component-including filters, strainers, towers, columns and heat exchangers-is an item placed in a piping system that has a head loss for a given flow rate. The function describing the head loss across the component versus the flow rate is similar to that of the head loss through valves and fittings.
Pump Curves
A pump curve describes the operation of a pump for a range of flows at a defined speed. Many design elements affect the shape of the pump curve, and most of these cannot be changed by the user. As a result, centrifugal pumps are usually selected from the manufacturer's available designs to match the system requirements. An engineered or assembled-to-order pump can be specified, and the manufacturer can often provide a pump performance characteristic well suited to the specific application depending on the type of pump.
Characteristics that can be changed by users to change the pump (performance) curve are the impeller diameter and the rotational speed. The pump curve change will cause the pump curve to intersect the system curve at a different rate of flow. When selected properly, the pump will operate near its best efficiency point (BEP). This relationship of speed change or diameter change is often referred to as the pump affinity rules (described in Part One).
Control valves are inserted into a piping system to regulate the rate of flow or pressure in the piping system. Remember, control valves control the flow by providing a variable hydraulic resistance between the upstream and downstream components in the system. In other words, the control valve does not change the basic shape of the system curve; it provides additional resistance to the system to enable the valve to control the flow.
System Curves
Pump and system curves can illustrate the basic interaction in the total system. Pump and system curves consist of a system curve showing the head required to pass a given flow rate through the piping system, and a pump curve superimposed on the system curve. The point where the system curve and the pump curve intersect is the balanced flow rate through the pump. Figure 1 shows a system curve and pump curve. In the absence of control valves, the system will operate at the intersection of the pump and system curves.
Figure 1. System curve shown with pump curve
System curves help demonstrate pumping system behavior in a graphical manner. If a system curve can be determined, it can help identify the effects of pump and/or system modifications. As systems get more complex, system curves lose usefulness; in fact, a unique system curve cannot be determined in some cases.
Friction Dominated Systems
Closed systems are always purely frictional-all the fluid in the system circulates from the pump suction, through the pump, to the discharge pipe run, then back to the pump suction. Because all the fluid in the system returns to the same point, the only resistance in the system comes from the friction loss in the pipe runs and the components. Open systems that coincidentally have the same pressure and elevation at all supplies and discharges are purely frictional, as well. For systems with pure friction, the system head is zero at zero flow (see Figure 2).
Figure 2. System curve resulting from only frictional losses
Static Head Dominated Systems
A system dominated by static head is one in which the primary function of the pump is to overcome static head (i.e., gravity, a difference in liquid elevation or pressure difference). Figure 3 shows a system curve dominated by static head. In an open system, the fluid is pumped from a source to a destination. Often the fluid source and destination are at different elevations and/or different pressures, which introduces a static head element in the system total head.
Figure 3. Static head dominated system curve
Pump Efficiency and the Best Efficiency Point
Figure 4 shows the system curve, the pump head curve and the pump efficiency curve plotted as a function of flow. Every centrifugal pump has a maximum efficiency point (also called the BEP). Figure 4 also shows the actual operating point. In this example, the pump is operating to the right of its BEP. For most pumps, the peak value of pump efficiency does not change significantly with speed.
Figure 4. Pump and system curves with the pump efficiency curve shown
Multiple Pump Operation
Multiple pumps can operate in series or parallel. Pumps placed in parallel provide additional flexibility in the range of flow rates. Pumps placed in series provide greater head without having to increase the impeller diameter.
Pumps should not be operated in series or parallel unless specifically procured for this purpose, since serious equipment damage may occur.
For parallel operation, the pumps must have approximately matching head characteristics, or the system operating head may exceed the shut-off head of one or more pumps and result in zero output flow. This result would have the same effect as operating against a closed discharge valve.
In series operation, the pumps must have approximately the same flow characteristics. Since each pump will take suction from the preceding pumps, the stuffing boxes and casing must be designed for the higher pressure, and the thrust bearing requirements may also increase.
Clearly understanding how the constituent parts of the system interact and function together-whether the system is a new design or an existing one undergoing a revamp-must be foremost in the design team's minds. In addition, having a thorough understanding of the fundamentals of each part of the system and how they operate together is the important first step. These fundamentals will be explored in greater detail in Part Three of this series of articles based on Optimizing Pumping Systems: A Guide to Improved Energy Efficiency, Reliability, and Profitability, now available for purchase at www.pumpsystemsmatter.org or www.pumps.org or call 973-267-9700 ext. 10.
Pumps & Systems, July 2008
