12.2.4: Pressure Distribution
- Page ID
- 44645
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)You will recall from Chapter 11 that the pressure variation along the lateral should not vary more than 20% of the average pressure. When a larger pressure range occurs, irrigation is not applied uniformly; therefore, excess water must be applied to adequately irrigate the drier portions of the field. The best way to evaluate the pressure variation along the lateral is to measure the pressure at critical points. The sketch in Figure 12.8 shows locations along a lateral that should be monitored. Usually, the highest pressure will occur near the inlet to the lateral. It could occur directly at the inlet or at a lowlying sprinkler close to the inlet. The lowest pressure locations will generally be near the distal end of the lateral. This could be at the end or at a high elevation near the end. These are good locations to measure the pressure.
Figure 12.8. Locations along a lateral where pressure measurements should be made.
The pressure can be measured in several ways. First a good quality pressure gauge that is accurate to within 1 or 2 psi should be used. The gauge can be attached to a pitot tube as shown in Figure 12.9 to measure the pressure. Care must be taken to place the pitot tube directly in the center of the jet from the sprinkler. The tube can be moved around in the jet to determine the maximum pressure reading. The maximum pressure read on the pitot is generally the true pressure. The pitot tube can be made from 1 /8-inch flexible copper tubing attached to the gauge with an appropriate tube fitting. The pressure can also be measured by removing the sprinkler from the riser and directly attaching the pressure gauge. This, however, will require more time to conduct the test.
Figure 12.9. Pressure gauge connected to a pitot tube to measure nozzle pressure.
Instead of measuring pressure you can also measure the discharge from the sprinkler at selected locations along the lateral. This can be done by placing a soft, flexible hose over the nozzle and measuring the time required to fill a container to a specified volume. Several measurements should be made on each nozzle to determine the mean flow rate. While pressure can vary 20% of the mean along the lateral, discharge is only allowed to vary 10%. After performing the pressure tests, you should compute the average pressure. The average pressure (Pa)for the lateral will be approximately:
Pa = Pmin + 0.25 (Pmax – Pmin)
As previously stated, the maximum acceptable range of pressure for the four points shown in Figure 12.8 is 20% of the average pressure. If the flow rate was measured the variation should be less than 10% of the average discharge. The average discharge equals the minimum discharge plus about 40% of the variation in flow that you measured.
Suppose that the pressure or discharge variation is too large, what could the problem be and how can you correct the situation? First compare the pressure or discharge at the lateral inlet to the design value. If the pressure or discharge is too small the problem may be with the pump or mainline system and the entire lateral is simply under pressurized.
Excessive variation in pressure may be due to a lateral that is too long, or the pipe diameter may be too small. The lateral could also run up a hill that was not considered in design. Correcting problems can be difficult. It is probably infeasible to replace the lateral unless the variation is bad, or the lateral is worn and will be replaced soon anyway. Recall from Chapter 11 that about half of the pressure loss occurs in the first third of the lateral. Thus, the initial section of the lateral could be replaced with larger diameter pipe to reduce the pressure loss. This is practical for side-roll and hand-move systems where the larger pipe will always be located near the mainline. This solution will not work for tow-line systems since the larger pipe would be at the distal end of the lateral half of the time.
The nozzles could be replaced with a smaller size to reduce the average flow rate of the lateral and to increase pressure at the downstream end. This will reduce the average discharge along the lateral. Some will think that this will reduce the ability to meet crop water requirements. However, the critical area along the lateral is the area receiving the smallest amount of water. Assuming that this area was used for scheduling, the poor uniformity contributed to deep percolation or runoff in the early portions of the lateral. If the flow rate at the critical distal end is not reduced, the depth of water applied at the critical area will be the same or more than when the nozzles were too large. Smaller nozzles could be used on sprinklers near the mainline if the smaller nozzles provide an adequate diameter of coverage.
Another alternative is to install either flow control nozzles or pressure regulators in the sections of the lateral that are likely to have excess pressure. These devices reduce the discharge in the high-pressure areas and produce better uniformity. It may not be necessary to install regulators along the entire lateral. Keep in mind that there is a pressure loss of about 5 psi across regulators, so you may not want to install them in the areas already low in pressure. You may also need to change the nozzle(s) in the sprinklers equipped with pressure regulators. Pressure regulators are more expensive than flow control nozzles, but they also operate over a wider range of pressures. Pressure regulators may be needed all along a tow-line lateral since the sprinklers are changing locations on the landscape every set.
An example may help illustrate the evaluation of lateral distribution and some alternatives for solving pressure distribution problems (Example 12.4).
You evaluated the pressure distribution along a lateral and need to determine if the lateral conforms to pressure variation guidelines. Recommend changes if the lateral is inadequate.
Given: The pressure at the second sprinkler nozzle is 45 psi and the nozzle pressure at the next to last sprinkler on the lateral is 32 psi.
The lateral is a 4-inch aluminum pipe with sprinklers spaced every 40 ft along the lateral.
The first sprinkler is 40 feet from the mainline.
Risers 5 ft tall are used to elevate sprinklers above the crop.
The sprinklers have one 15/64 nozzle per sprinkler except the first and last sprinklers which are 5/32 nozzles.
The land is generally flat.
Solution
The average pressure will be approximately:
\(P_a=P_{min}+0.25(P_{max} - P_{min})=32+0.25(42-32)=35\text{ psi} \)
The pressure variation along the lateral is 13 psi (45 – 32).
Since the pressure variation of 13 psi is larger than 20% of the average pressure, the lateral does not conform to the pressure variation guideline.
The cheapest way to bring the pressure variation into an acceptable range would be to use pressure regulators. Pressure regulators cause a pressure loss of approximately 5 psi so the nozzle size may need to be adjusted to provide the needed flow.
Analyzing solutions for existing laterals is complex, so a spreadsheet program was developed to assist evaluation. The program is called Lateral Analysis. Performance for an existing lateral is shown in Figure 12.10. The shaded cells are where operators input data about the lateral. The unshaded areas cannot be changed. The variation of nozzle pressure for the existing lateral is 14.7 psi which represents about 40% of the average pressure—double the guideline.
Figure 12.10. Existing conditions in the Lateral Analysis program for the example lateral.
Suppose pressure regulators are used to minimize variation. Examining the data for the sprinklers along the lateral in Figure 12.10, the pressure at the distal end of the lateral is about 33 psi. A 35-psi pressure regulator would give about the same nozzle pressure. Additionally, regulators cause about 5 psi loss when regulation is not active. Thus, a nozzle pressure of 38 psi without regulation will give an outlet pressure of about 33 psi. The first ten sprinklers have a nozzle pressure above 38 psi when regulators were not used. So, regulators are installed on the first ten sprinklers. The lateral analysis program was used to evaluate the results when using the ten regulators. Table 12.4 shows a comparison of the performance analysis when no regulators were used on the lateral and when 10 regulators were used at the inlet of the lateral. The results show that using regulators reduced the nozzle pressure variation to 14% and the discharge variation to about 7%. Both quantities are within the acceptable guidelines for uniformity. Ten regulators represent an investment of approximately $100 which would work for a long time, so pressure regulation is a relatively inexpensive and efficient way to achieve the uniformity goals. Of course, it is essential that the regulators are always used at the inlet to the lateral which would require some organization for hand-move systems. The spreadsheet can be used to analyze laterals and refining designs for special needs. Laterals with two pipe diameters can also be evaluated.
| Values | Lateral Pressure (psi) | Nozzle Pressure (psi) | Sprinkler Discharge (gpm) |
|---|---|---|---|
| Performance—No Regulators | |||
| Maximum | 49.7 | 47.6 | 10.96 |
| Minimum | 35.0 | 32.8 | 9.11 |
| Average | 38.8 | 36.7 | 9.62 |
| Variation | 14.7 | 14.7 | 1.85 |
| Percent variation | 38% | 40% | 19% |
| Performance—With Regulators for First 10 Sprinklers | |||
| Maximum | 49.4 | 37.7 | 9.76 |
| Minimum | 35.0 | 32.8 | 9.11 |
| Average | 38.8 | 34.3 | 9.32 |
| Variation | 14.4 | 4.9 | 0.65 |
| Percent variation | 37% | 14% | 7% |