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Unlike positive displacement pumps, a centrifugal pump operating at constant speed can deliver any capacity from zero to a maximum value dependent upon the pump size, design, and suction conditions. The total head developed by the pump, the power required to drive it, and the resulting efficiency vary with the capacity.
When a pump manufacturer develops a new pump the pump is tested for performance under controlled conditions. The results are plotted in the form of graphs that show flow rate versus Head, Power Consumption, Efficiency, _NPSH_ _R_.
The interrelationships of capacity, head, power, and efficiency are called the pump characteristics. These interrelationships are best shown graphically, and the resulting graph is called the pump's “characteristic” or “performance” or “head-capacity (H-Q)” or “pump curves”. At constant speed, as the head required to be furnished by the pump increases, the flow rate decreases. Fig. 3.14 also shows values to develop the curve from “shutoff” head to maximum flow, and the pump efficiency curve. Fig. 3.14 B shows the difference between a theoretical and an actual pump curve due to losses due to shock, turbulence, recirculation, and friction. As shown in Fig. 3.14 B, the actual performance is less than design and will always be curved, rather than straight line performance. The losses will vary on each pump, but all will be affected by shock, turbulence, recirculation, and friction. Every pump manufacturer will provide certified test curves on each pump. Most manufacturers make their pumps and impellers to comply with the Hydraulic Institute standard for pump performance.
Some applications require each pump to be provided with a performance test to provide information of actual pump performance across a complete range of given conditions. Each test will provide a large range or performance points across the full range of performance/data points across the full range of values to develop the curve from shutoff head to maximum flow.
For a given impeller shape, the efficiency is a maximum, called the best efficiency point (BEP), at a design throughput rate. As the rate varies upward and downward from this point, the efficiency decreases. Under similar operating conditions, an installed pump is expected to demonstrate the same performance characteristics as shown on its performance curves. If it does not, indicates that something is wrong with the system and/or pump. Comparison of actual pump performance with rated performance curves can aid in the determination of a pump malfunction.
By varying the pump speed the throughput at a given head or the head for a given throughput can be changed. In Fig. 3.15 B, as the speed decreases from _N_ 1 to _N_ 2 to _N_ 3, the flow rate decreases if the head required is constant, or the head decreases if the flow rate is constant.
The centrifugal pump's rotating impeller primarily determines the pump's performance. Head, _NPSH_ _R_, efficiency, horsepower, and power requirements vary with capacity. Fig. 3.16 A and C shows the effects of impeller size on the pump's characteristic curve.
Most performance curves will show a number of important points of performance. Some of these points are as follows: Maximum and minimum impeller diameters available, Efficiency of the impellers at different points, Brake horsepower requirements at different points, Model number, Suction and discharge size, RPM of driver required, GPM range or each diameter impeller, Total head rating of each curve, NPSH rating at various flows.
Each manufacturer will provide a performance curve for every pump they manufacturer.
Ideally, it would be best to operate the pump at the BEP, but this is not normally feasible. Alternatively, the pump should operate only in the area of the curve closest to the BEP, and only in the moderately sloping portion of the head curve. Operating in the flat or steeply sloping portions of the curve results in wasted energy and flow control instability. Pumps that run at or near this BEP will run smoother and have better run lives. Any time the actual flow drops below 50% of the BEP flow, it is wise to consult the manufacturer. Shaft deflections may increase dramatically (especially with single-stage overhung design pumps), which may lead to higher maintenance costs and failures.
The total developed head (TDH) is a measure of the energy a pump delivers to a fluid. It is equal to the total discharge head minus the total suction head in feet (m) of liquid. The word “total” is used because each of these heads is composed of the pressure head, velocity head, static head, and head loss. The TDH can be approximated by measuring the suction and discharge pressures at the pump flanges, subtracting the suction pressure from the discharge pressure (both in units of in units of psig), and then converting to units of head in feet (m). The approximation neglects the velocity head component, which usually results in an error of less than 1%.
The TDH depends on the impeller diameter, pump speed, fluid viscosity, impeller and case design, and pump mechanical condition. It also varies with capacity, largely due to frictional losses in the impeller and casing. Total head is greatest at zero capacity (shutoff head) and falls off with increasing flow rates.
The power (BHP) curve, starts out at some small value at zero flow, increases moderately up to a point where it reaches a maximum and may even taper off slightly.
The pump efficiency curve starts out at zero, increases rapidly as flow increases, levels off at BEP, and decreases in value.
The _NPSH_ _R_ is a finite value at zero flow and increases as a square function of the increase in flow rate.
Every centrifugal pump will operate on its characteristic curve if there is enough _NPSH_ _A_ for a given specific gravity and viscosity. For any given capacity, there will be one total head rise, one efficiency, one horsepower, and one _NPSH_ _R_.
In general, it is desirable to choose a pump that operates at its maximum efficiency point or slightly to the left; however, this is not always possible. Pumps are sold to operate over wide ranges, even at the extreme ends of the curve. Normally, if the _NPSH_ _A_ is sufficient to prevent cavitation, the pump should operate satisfactory.
The slope and shape of the head-capacity characteristic curve is affected by individual pump design. Centrifugal pump head-capacity characteristic curves are classified as follows:
Fig. 3.17 illustrates a head-capacity curve where the head rises continuously as the capacity is decreased. As a rule of thumb, steady “rising” curves are those showing a 10%–25% increase in head between the capacities of peak efficiency and shutoff. Pumps with this type of curve have continuously rising head as capacity is decreased. Pumps with this characteristic curve are often used in parallel operations; because of their stability they continue to operate at lower and lower throughput volumes.
Centrifugal pumps with steady-rise curves are most commonly used. Since the head varies distinctly with a change in capacity, precise flow control can be maintained with this type of curve. The rising curve is a stable curve; for every head, only one corresponding capacity occurs.
Fig. 3.18 illustrates a head-capacity curve where the head developed at shutoff is less than that developed at some other capacity. These curves are characterized by multiple flow points for a given head. As can be seen from the example curve, there are two stable head points for some capacities. Pumps designed to deliver maximum head per inch of impeller diameter generally have this characteristic. They are almost never used in general oil field pumping applications.
Pumps with drooping characteristic curves should be avoided because they may exhibit unstable operating characteristics. In some cases, however, such as systems with mostly dynamic loss and no requirements for parallel operation, drooping characteristics could be acceptable.
A “steep-rise” head-capacity curve is one in which there is a large increase in head between that developed at shutoff. In this type of pump curve, there is a large increase in head between that developed at design capacity and that developed at shutoff. This pump is stable and will operate in parallel over the entire range. It is best suited for operations requiring minimum capacity changes with pressure, but it is stable over a wide range of capacity vs. head. Sometimes it is applied to a limited portion of the curve. For example, as shown in Fig. 3.19, a pump may have a steep characteristic between 100 % and 50% of the design capacity. As a rule of thumb, “steep-rise” curves typically show a 140% increase in head between the capacities peak efficiency and shutoff.
A “flat” head-capacity curve is one in which the _head varies only slightly with capacity over its entire range_ of operation. The characteristic might also be either drooping or rising. All drooping curves have a portion where the head developed is approximately constant for a range in capacity, called the flat portion of the curve. As shown in Fig. 3.20, some curves are qualified as flat either for their full range or for a limited portion of their range. As a rule of thumb, “flat” curves are those with no more than a 5% increase. Pumps with this type of curve are best suited for duties having wide fluctuation of capacity with nearly constant pressure.
Fig. 3.21 summarizes the four typical shapes of head-capacity curves.
Figs. 3.17 and 3.19 illustrate a head-capacity curve where only one capacity can be obtained at any one head.
Figs. 3.18 and 3.22 illustrate a head-capacity curve where the same head is developed at two or more capacities.
Head-power characteristic curves are also classified to their shape.
Fig. 3.23 illustrates a power-capacity characteristic curve that flattens out and then decreases as the capacity increases beyond the maximum efficiency point.
Pumps with nonoverloading power-capacity characteristic curves are preferred because the driver will not become overloaded under any operating condition. That said, they are not obtainable in all specific speed types of pumps.
Fig. 3.24 illustrates a power-capacity characteristic curve that continues to increase with an increase in capacity. The shape of the power-capacity curve varies with the specific speed type. As a result, the power-capacity curve may have a very low value at shutoff (Figs. 3.23 and 3.24), high value at shutoff (Fig. 3.25), or any value in between.
Fig. 3.24 illustrates an overloading characteristic curve with a decrease in head and increase in capacity, whereas Fig. 3.25 illustrates an overloading curve with an increase in head and decrease in capacity. The power of the driver should always be selected for the range of operating conditions that could possibly occur.
Pump manufacturers use a number of methods to present centrifugal pump characteristic curves. Three commonly used methods to depict pump performance are shown as follows.
Fig. 3.26 shows a typical 6-in. double-suction centrifugal pump characteristic “performance” curve with speed and impeller diameter fixed. This format results from a pump test at constant speed. Manufacturers commonly use these characteristic curves to predict and guarantee pump performance.
Fig. 3.27 shows a typical 6-in. double-suction centrifugal pump characteristic “performance” curve used to express more fully the entire range of a pump, with various impeller diameters at continuous speed. These curves are commonly used in the selection of a pump for a specific service. The curves are generally made up from the average results of tests for various diameter impellers plotted as shown in Fig. 3.26.
Fig. 3.28 shows a typical 6-in. double-suction centrifugal pump characteristic “performance” curve driven at variable speeds with a fixed impeller diameter.
Most characteristic “performance” curves furnished by manufacturers are based on water as the pumped liquid. If the pump is handling some other liquid, adjustments must be made for viscosity and specific gravity before flow rate and discharge pressure (psi) can be predicted.
A pump operates at the intersection of its head-capacity curve and the system head curve, in which the pump operates. Against a given head, the pump will deliver a given flow rate. A pump must also operate within the envelope of the _NPSH_ _A_ curve. The system in which a pump operates is composed of pipe, valves, fittings, and any number of components such as heat exchangers, filters, boilers, and so on.
In most piping systems both the head and the flow rate vary because the system has its own required pump head for a given flow rate. This can be seen in Fig. 3.29. As shown in the figure, the head required by the system, which is to be provided by the pump, is merely the friction drop in the pipeline between points “A” and “B,” assuming the levels in both tanks are identical. This is a function of flow rate; it can therefore be plotted as a “system head curve” on the pump head-capacity performance curve. For this reason, as the pump speed is increased or decreased, a new equilibrium of head and flow rate is established by the intersection of the piping system head curve and pump performance curve.
Fig. 3.30 shows how the throughput can be changed by imposing an artificial backpressure on the pump. Adjusting the control valves orifice may shift the piping system head curve which establishes a new head-flow rate equilibrium point. As the pressure drop across the control valve increases from Δ _P_ 1 to Δ _P_ 2 to Δ _P_ 3, the flow rate through the system decreases from _Q_ 1 to _Q_ 2 to _Q_ 3.
The system head represents a complete piping system, for example, the friction losses of all the piping, elbows, valves, and so on, and the total static head vs. flow rate. It is a graphical representation of how much TDH, in feet, is required to pump various capacities through the piping system.
The system head curve consists of a constant (static) and an increasing (variable) portion (Fig. 3.31).
_Static portion_: Instantaneous elevation differential between the source and termination, including pressures that exist on the surface of the liquid. As the liquid levels in the system can change over time, this change must be accounted for in the overall review of the system. This value is constant and is not dependent on flow. The static portion is plotted as a straight line at the appropriate head. The constant (static) portion represents the static head difference between the suction and the discharge at zero flow and is equal to: (3.4)H Static=P 2−P 1 2.31 SG+H 2−H 1
_Variable portion_: Head of motion or friction. The Hydraulic Institute has compiled a book of tables showing pipe and fitting frictions for various pipe components and flows. Fitting friction is generally expressed in equivalent lengths of straight run pipe. Pressure drops for process components such as heat exchangers must be obtained from the equipment manufacturer. These pressure drops can be converted in feet of head loss across them. Once a system is laid out and all components are identified, including changes in pipe size, the variable head can be calculated for a number of flow rates. One must remember that different pipe and fitting sizes will have different friction losses for identical flow rates. For ease of calculation, all lengths and fittings of the same size should be lumped together. This will minimize the number of calculations. The variable portion represents the head required to overcome friction as a result of flow, and it varies as the square of the flow and is equal to: (3.5)H Variable=P f 1+P f 2+P C 2.31 SG
The system head curve (Fig. 3.31) is obtained by combining the system friction curve (Fig. 3.32) with a plot of the TDH.
The determination of friction losses is usually rough approximations at best as the roughness of the pipe is not known. The friction loss will increase as pipe deteriorates with age. Therefore it is common practice to base friction loss calculations on old pipe, thus allowing for friction losses in excess of those that will be obtained when the pipe is new. As a result, the pump is generally designed for excess head and delivers overcapacity when installed in a new system.
The flow of any liquid is accompanied by two types of friction: Internal friction (viscosity) caused by the rubbing of the fluid particles against one another; and external friction caused by the rubbing of the fluid particles against the pipe walls or against the static layer of liquid adhering to the walls. Energy must be expended to overcome this friction.
If the flow is turbulent, the friction developed is partially dependent upon the roughness of the walls. Since the interior surfaces of pipes of the same material are practically the same irrespective of pipe diameter, small pipes are relatively rougher than larger ones. Thus, for equal velocities, the larger the pipe, the smaller will be the friction loss. The roughness of the pipe wall also depends upon the material from which the pipe is made and, after the pipe has been in service, upon any change that occurs at the inner surface.
_Volume 3, Chapter 6_ of this series presents detailed calculation methods for determining the friction loss in piping systems. Table 3.6 lists the friction, in feet of water, for the flow of water through new Schedule 40 steel pipe. This table is based on the Darcy-Weisbach formula:
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