8.5: Pumps
- Page ID
- 44581
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Irrigation systems are designed to operate at specified pressures and flow rates. In order to develop the required pressure and to lift water from a reservoir or a well, it is often necessary to pump the water.
Pumps that lift and pressurize water in irrigation most commonly use the principal of centrifugal force to convert mechanical energy into hydraulic energy. This category includes horizontal centrifugal pumps and vertical turbine or submersible pumps. Horizontal centrifugal pumps are often used for pumping from an open water source (e.g., Figure 8.7) or for boosting the pressure in an irrigation pipeline. A vertical turbine pump has a vertical axle with the power source (motor or engine) above ground (e.g., Figure 8.8). A submersible pump is similar, except that both the pump and an electric motor are submersed, with the motor below the pump. The submersible and vertical turbine pumps are the most commonly used pumps for irrigation wells.
Figure 8.7. Application of horizontal centrifugal pump.
Figure 8.8. Vertical turbine pump installed in a well (left), cutaway of bowls with impellers in series (middle), and vertical turbine pump discharging to open ditch (right).
The flow rate that is delivered by a pump is dependent upon the design of the impeller (the device that puts the energy into water), the diameter of the impeller, the speed of the impeller, and the total dynamic head that the impeller develops. Total dynamic head is the total head produced by the pump at a given flow rate. The total dynamic head (TDH) is the sum of the pressure head and elevation head (lift), i.e.
\(TDH = 2.31 P + L\) (8.13)
where: P = discharge pressure of the pump (psi) and
L = vertical distance water is moved from source to the pump discharge elevation (ft).
Solving for TDH in this manner is an approximation. We have ignored the velocity head and friction and minor losses required to move the water to the land surface. It is adequate for many, but not all, pumping conditions. When a horizontal centrifugal pump is used as a booster pump the total dynamic head equation is.
\(TDH = 2.31 (P_{out}-P_{in}) \) (8.14)
where: Pout = discharge pressure (psi)
Pin = inlet pressure to pump (psi)
A characteristic of a horizontal centrifugal pump is that as the total dynamic head increases the flow rate from the pump will decrease. Envision closing a valve downstream of the pump. As the valve is closed, the flow rate decreases. If a pressure gauge were mounted upstream of the valve, it would indicate a rise in the pressure as the valve is closed. The pressure rise is an increase in the total dynamic head. The variable flow nature of centrifugal pumps is illustrated in the headcapacity relationship shown in Figure 8.9. Pump efficiency is a measure of the proportion of the energy transmitted to the pump that is transferred to the water. A pump should be selected so that it operates near its maximum efficiency at the desired flow rate (capacity) and the corresponding total dynamic head. In the example in Figure 8.9, it is evident that the pump reaches its peak efficiency at about 1,100 gpm and 190 feet of head. As you move to the left on the head-capacity curve, the pump efficiency goes down. As you move to the right of the peak efficiency point, the efficiency also goes down. Note that the peak pump efficiency is approximately 80% for the example shown. You can expect peak efficiencies to range from 55 to 82% for pump sizes most commonly used in irrigation.
The head discharge relationship shown in Figure 8.9 applies to a pump operating at a constant speed. If the pump speed is changed, the head discharge relation also changes. This is illustrated in Figure 8.10. As the speed of the pump decreases, its discharge pressure decreases at a given flow rate. Therefore, there is a different head discharge relationship for the slower speed. The slower speed head discharge curve is approximately parallel to the curve for the higher speed. Note that as the speed of the pump is lowered, the point for peak efficiency has shifted to the left, that is, to a lower flow rate.
Another factor affecting the head capacity relationship is the diameter of the impeller. Figure 8.11 illustrates what happens as an impeller is trimmed to reduce its diameter. Again, as the impeller diameter is decreased, the point of peak efficiency of the pump shifts to a lower flow rate, much like what happened when the speed was reduced.
Figure 8.9. Head-capacity curve for a centrifugal pump.
Figure 8.10. Head-capacity curve for centrifugal pump with various pump speeds.
Figure 8.11. Head-capacity curve for centrifugal pump with various pump diameters. (Figure credit: Flowserve.)
How are irrigation pumps selected? The key is to select a pump that is efficient at the system flow rate and total dynamic head. For example, a system having a flow rate of 800 gpm and lifting water out of a well a distance of 100 feet with a discharge pressure of 50 psi, the pump must be able to deliver the 800 gpm at a total dynamic head of 216 feet. Now, suppose the manufacturer has a pump that operates at 800 gpm, very efficiently, but the total dynamic head produced by that pump with a single impeller is only 54 feet. How can we develop the total dynamic head that is required for the irrigation system? One approach is to place the pump bowl and impeller assemblies in a series. With the vertical turbine pump (Figure 8.8) and submersible pump, several bowl and impeller assemblies are placed into a series. The same flow rate goes through each impeller, hence the concept of “in series”. As water passes from one impeller to the next, the total dynamic head in the water is increased. This is called a multistage pump. How many stages of this pump would be necessary for 216 feet of total dynamic head if each stage of the pump produces 54 feet of total dynamic head? Four stages are required. This is determined by multiplying 54 feet of head per stage times 4 which equals 216 feet of total dynamic head. The concept of pumps-in-series is illustrated in Figure 8.12. The two pump curves have different head discharge relationships but can be combined to form a composite or combined curve for the series operation. Keep in mind that the flow that passes through pump A also passes through pump B and as the water passes from one pump to the other, the total dynamic head in the water increases.
Another pumping option is to operate pumps in parallel. Parallel operation is very useful when the flow demands of the system vary greatly. The head capacity relationship for this parallel operation is illustrated in Figure 8.13. With pumps in parallel, the pressure downstream of the pumps is the same for both pumps. This is illustrated in Figure 8.14. Remember, in the series operation the two pumps had the same flow rate through each pump. In the parallel operation, there can be a different flow rate through each pump, but the total dynamic head for each pump will be the same. Thus, the total flow rate of pumps A and B, operating in parallel will be the sum of the flow rate of pump A at the total dynamic head plus the flow rate of pump B at the same total dynamic head.
The pump curves shown in Figures 8.10 and 8.11 are good examples of curves published by manufacturers. These curves obey what are called the affinity laws for pumps. The affinity laws are useful and necessary if a head-capacity curve and horsepower curve must be developed for a condition that is not provided by graphs from the manufacturer. For example, what if you want to operate at a speed that is different than what is shown if Figure 8.10? Or, what if pump speed is fixed and the pump does not perfectly match expected pumping conditions, how much should the impeller be trimmed (reduced in diameter) to better match the expected conditions? In Figure 8.11, four trims are shown, but the most appropriate trim may not be shown on the graph. The affinity laws shown below are useful for determining appropriate pump speeds and impeller diameters:
Figure 8.12. Head-capacity curves for centrifugal pumps in series.
Figure 8.13. Head-capacity curve for centrifugal pumps in parallel.
Figure 8.14. Centrifugal pumps connected in parallel.
\(\dfrac{Q_2}{Q_1}=\dfrac{RPM_2}{RPM_1} \dfrac{TDH_2}{TDH_1}=\left(\dfrac{RPM_2}{RPM_1}\right)^2 \dfrac{BHP_2}{BPH_1}=\left(\dfrac{RPM_2}{RPM_1}\right)^3 \) (8.15a)
\( \dfrac{Q_2}{Q_1}=\dfrac{DIA_2}{DIA_1} \dfrac{TDH_2}{TDH_1}=\left(\dfrac{DIA_2}{DIA_1}\right)^2 \dfrac{BHP_2}{BPH_1}=\left(\dfrac{DIA_2}{DIA_1}\right)^3 \) (8.15b)
where: RPM = pump speed in revolutions per minute,
DIA = impeller diameter,
BHP = brake horsepower (discussed in section 8.6 below), and
Subscripts 1 and 2 = current condition and new condition, respectively. For example, Q1 is the current flow rate and Q2 is the future or predicted flow rate. The affinity laws can be used to generate head-capacity and horsepower curves based on known or current conditions. Pumps still operate efficiently if you change diameter or speed, and the affinity laws will be obeyed. Note how the laws behave. While flow rate is directly proportional to speed and diameter, TDH and power vary by the square and cube, respectively, of the speed and diameter.
An irrigation pumping system should be planned so that the pump operates at near peak efficiency. If the operating conditions change, the efficiency of the irrigation pump is likely to change at the same time. It is best to avoid undersizing or oversizing a pump; when pumps are oversized, they are sometimes throttled with a valve which leads to excess energy consumption. This concept and energy management are discussed further in Section 8.7.