12.2.6: Uniformity Evaluation
- Page ID
- 44647
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The ultimate evaluation of uniformity is to measure the distribution using an array of collector cans to compute the coefficient of uniformity as described in Chapter 5. It is impractical to measure the distribution along the entire lateral; thus, a representative area should be selected near the downstream end of the lateral where uniformity will be lowest. The configuration of catch cans is illustrated in Figure 12.11 for a lateral with sprinklers 40 ft apart along the lateral and a set width of 60 ft. The spacing of cans should be selected so that each container represents the same area. A common denominator should be determined that is convenient—either 5, 10 or 20 ft for Figure 12.11. In this case a ten-foot spacing was selected for collector spacing. Initially, the column of cans is placed one-half of the nominal can spacing from the lateral and the first row is one-half the can spacing from the sprinkler— i.e., first can is placed 5 ft from the lateral and 5 ft from the sprinkler. The remaining rows and columns of cans are space the full distance (10 ft) apart. This orientation ensures that each container represents the same area (10 ft x 10 ft) which simplifies computation of uniformity. Cans are placed on both sides of the lateral to evaluate the effect of wind. Tests should be conducted when wind, temperature, and humidity conditions are representative of the area.
It is impractical to measure the depth of water applied by all laterals for moved-lateral systems, so it is necessary to numerically overlap the catch data from one lateral. The lateral for the second set in Figure 12.11 should be operated for the test. Water is measured on both sides of the lateral. An adequate distance along the lateral should be tested to avoid bias from one or two sprinklers. Sprinklers should be evaluated to ensure they represent the system. However, the number of containers increases quickly. For example, the layout in Figure 12.11 requires 112 catch cans. Cans should be placed at least one row beyond adjoining laterals if wind is expected during the test. The system should be operated long enough to provide adequate water to accurately measured the depth in the cans. The water caught in cans is measured with a graduated cylinder. The diameter of the top of several catch containers should also be measured. The volume caught is converted to a depth by dividing the volume by the area of the top of the container.
The depth of water from the second lateral must be overlapped to determine the depth applied to the area by adjoining laterals. The depth of water applied during successive sets is computed based on the distance of the lateral from the point of interest. The following example shows how to overlap depths to evaluate the uniformity.
Figure 12.11. Layout for testing the uniformity of application using catch can collectors.
The uniformity of a moved-lateral system was measured by placing catch cans around the central lateral (second set) as shown in Figure 12.11. The central lateral was operated for 2 hours to provide measurable quantities of water. Results of the test are summarized in Table 12.5.
Find: The depth of water applied between laterals and the coefficient of uniformity.
Solution
- The volume of water caught in the cans and the depth of water are given in Table 12.5.
- Consider the can located 5 feet north and 5 feet east of the central sprinkler (delineated by red box). A volume of 235 cm3 of water was caught during the test.
- This is equivalent to: 235 cm3 / 81.1 cm2 = 2.90 cm.
- Dividing by 2.54 cm/in gives a depth applied of 1.14 inches (cell with red border).
- However, this is only the water applied when the lateral is located at the second set.
- The depth applied by the first and third sets of the lateral must be determined. The distance from the first set is 65 ft north of lateral one (5 ft east of the sprinkler). The depth in the container was 24 cm3 which is equivalent to 0.12 in (blue cells).
- The depth when the lateral is at set 3 is equivalent to the depth caught in the container 55 feet south of the lateral from set 2. The depth caught was 19 cm3 which is equivalent to 0.09 in (blue cell).
- The overlapped depth for the three sets is 1.14 + 0.12 + 0.09 = 1.35 in (red cell).
- This procedure was used to compute the depth for all container locations in Table 12.5. The average depth of water caught in the containers was 1.26 in. The deviation from the mean depth is 1.35 – 1.26 = 0.09 in for the red cell.
- The average deviation for all containers is 0.13 in.
- Then, the coefficient of uniformity is then given by:
\(CU=100\left(1-\dfrac{\sum |d_i-d_a|}{nd_a} \right)=100\left(1-\dfrac{0.13}{1.26} \right)=90\%\)
The coefficient of uniformity in Table 12.5 is 90, which is good, even though the application ranges from a minimum of 0.98 to a maximum of 1.57 inches over a relatively small distance. The areas between the sprinklers along the lateral (i.e., those 15 and 25 ft east and west of the central sprinkler) seem to be the driest. The DU for this area is about 84%, so you would need to apply about 20% more water than the average depth (i.e., 1.26 ÷ 0.84 = 1.5 in) to adequately irrigate the dry spots. The CU for the entire lateral will be less than for the area of the test.
A great deal can be learned about the operation of sprinkler systems with catch-can tests; however, evaluations are quite time consuming and wind conditions make tests difficult. When a catch can test is conducted, the pressure and flow rate measurements described in earlier sections should also be conducted. This is a short overview of evaluating sprinkler systems. Merriam and Keller (1978) developed a good reference on system evaluation that provides examples and charts for computation.
| Distance North of Central Sprinkler (ft) | Distance East of Central Sprinkler: -35 ft | Distance East of Central Sprinkler: -25 ft | Distance East of Central Sprinkler : -15 ft | Distance East of Central Sprinkler: -5 ft | Distance East of Central Sprinkler: 5 ft | Distance East of Central Sprinkler: 15 ft | Distance East of Central Sprinkler: 25 ft | Distance East of Central Sprinkler: 35 ft |
|---|---|---|---|---|---|---|---|---|
| 65 | 23 cm3 [a] | 20 cm3 [a] | 19 cm3 [a] | 23 cm3 [a] | 24 cm3 [a] | 19 cm3 [a] | 18 cm3 [a] | 22 cm3 [a] |
| 55 | 76 cm3 [a] | 63 cm3 [a] | 60 cm3 [a] | 73 cm3 [a] | 76 cm3 [a] | 61 cm3 [a] | 58 cm3 [a] | 70 cm3 [a] |
| 45 | 118 cm3 [a] | 98 cm3 [a] | 94 cm3 [a] | 114 cm3 [a] | 119 cm3 [a] | 94 cm3 [a] | 90 cm3 [a] | 109 cm3 [a] |
| 35 | 160 cm3 [a] | 134 cm3 [a] | 127 cm3 [a] | 154 cm3 [a] | 161 cm3 [a] | 128 cm3 [a] | 123 cm3 [a] | 147 cm3 [a] |
| 25 | 191 cm3 [a] | 160 cm3 [a] | 153 cm3 [a] | 185 cm3 [a] | 193 cm3 [a] | 153 cm3 [a] | 147 cm3 [a] | 176 cm3 [a] |
| 15 | 212 cm3 [a] | 177 cm3 [a] | 169 cm3 [a] | 205 cm3 [a] | 214 cm3 [a] | 170 cm3 [a] | 163 cm3 [a] | 196 cm3 [a] |
| 5 | 233 cm3 [a] | 195 cm3 [a] | 186 cm3 [a] | 225 cm3 [a] | 235 cm3 [a] | 187 cm3 [a] | 179 cm3 [a] | 215 cm3 [a] |
| -5 | 210 cm3 [a] | 176 cm3 [a] | 167 cm3 [a] | 203 cm3 [a] | 212 cm3 [a] | 168 cm3 [a] | 161 cm3 [a] | 194 cm3 [a] |
| -15 | 191 cm3 [a] | 160 cm3 [a] | 152 cm3 [a] | 184 cm3 [a] | 192 cm3 [a] | 154 cm3 [a] | 147 cm3 [a] | 176 cm3 [a] |
| -25 | 163 cm3 [a] | 136 cm3 [a] | 129 cm3 [a] | 156 cm3 [a] | 163 cm3 [a] | 132 cm3 [a] | 125 cm3 [a] | 149 cm3 [a] |
| -35 | 112 cm3 [a] | 93 cm3 [a] | 87 cm3 [a] | 105 cm3 [a] | 111 cm3 [a] | 93 cm3 [a] | 87 cm3 [a] | 100 cm3 [a] |
| -45 | 50 cm3 [a] | 40 cm3 [a] | 35 cm3 [a] | 43 cm3 [a] | 47 cm3 [a] | 45 cm3 [a] | 39 cm3 [a] | 41 cm3 [a] |
| -55 | 22 cm3 [a] | 17 cm3 [a] | 12 cm3 [a] | 15 cm3 [a] | 19 cm3 [a] | 23 cm3 [a] | 18 cm3 [a] | 14 cm3 [a] |
| -65 | 0 cm3 [a] | 0 cm3 [a] | 0 cm3 [a] | 0 cm3 [a] | 0 cm3 [a] | 0 cm3 [a] | 0 cm3 [a] | 0 cm3 [a] |
| 65 | 0.11 in [b] | 0.10 in [b] | 0.09 in [b] | 0.11 in [b] | 0.12 in [b] | 0.09 in [b] | 0.09 in [b] | 0.11 in [b] |
| 55 | 0.37 in [b] | 0.31 in [b] | 0.29 in [b] | 0.35 in [b] | 0.37 in [b] | 0.30 in [b] | 0.28 in [b] | 0.34 in [b] |
| 45 | 0.57 in [b] | 0.48 in [b] | 0.46 in [b] | 0.55 in [b] | 0.58 in [b] | 0.46 in [b] | 0.44 in [b] | 0.53 in [b] |
| 35 | 0.78 in [b] | 0.65 in [b] | 0.62 in [b] | 0.75 in [b] | 0.78 in [b] | 0.62 in [b] | 0.60 in [b] | 0.71 in [b] |
| 25 | 0.93 in [b] | 0.78 in [b] | 0.74 in [b] | 0.90 in [b] | 0.94 in [b] | 0.74 in [b] | 0.71 in [b] | 0.85 in [b] |
| 15 | 1.03 in [b] | 0.86 in [b] | 0.82 in [b] | 1.00 in [b] | 1.04 in [b] | 0.83 in [b] | 0.79 in [b] | 0.95 in [b] |
| 5 | 1.13 in [b] | 0.95 in [b] | 0.90 in [b] | 1.09 in [b] | 1.14 in [b] | 0.91 in [b] | 0.87 in [b] | 1.04 in [b] |
| -5 | 1.02 in [b] | 0.85 in [b] | 0.81 in [b] | 0.99 in [b] | 1.03 in [b] | 0.82 in [b] | 0.78 in [b] | 0.94 in [b] |
| -15 | 0.93 in [b] | 0.78 in [b] | 0.74 in [b] | 0.89 in [b] | 0.93 in [b] | 0.75 in [b] | 0.71 in [b] | 0.85 in [b] |
| -25 | 0.79 in [b] | 0.66 in [b] | 0.63 in [b] | 0.76 in [b] | 0.79 in [b] | 0.64 in [b] | 0.61 in [b] | 0.72 in [b] |
| -35 | 0.54 in [b] | 0.45 in [b] | 0.42 in [b] | 0.51 in [b] | 0.54 in [b] | 0.45 in [b] | 0.42 in [b] | 0.49 in [b] |
| -45 | 0.24 in [b] | 0.19 in [b] | 0.17 in [b] | 0.21 in [b] | 0.23 in [b] | 0.22 in [b] | 0.19 in [b] | 0.20 in [b] |
| -55 | 0.11 in [b] | 0.08 in [b] | 0.06 in [b] | 0.07 in [b] | 0.09 in [b] | 0.11 in [b] | 0.09 in [b] | 0.07 in [b] |
| -65 | 0.00 in [b] | 0.00 in [b] | 0.00 in [b] | 0.00 in [b] | 0.00 in [b] | 0.00 in [b] | 0.00 in [b] | 0.00 in [b] |
| 55 | 1.39 in [c] | 1.16 in [c] | 1.10 in [c] | 1.34 in [c] | 1.40 in [c] | 1.11 in [c] | 1.06 in [c] | 1.28 in [c] |
| 45 | 1.50 in [c] | 1.25 in [c] | 1.19 in [c] | 1.45 in [c] | 1.51 in [c] | 1.20 in [c] | 1.15 in [c] | 1.38 in [c] |
| 35 | 1.57 in [c] | 1.31 in [c] | 1.24 in [c] | 1.51 in [c] | 1.57 in [c] | 1.26 in [c] | 1.20 in [c] | 1.44 in [c] |
| 25 | 1.47 in [c] | 1.23 in [c] | 1.17 in [c] | 1.57 in [c] | 1.48 in [c] | 1.19 in [c] | 1.14 in [c] | 1.34 in [c] |
| 15 | 1.27 in [c] | 1.05 in [c] | 0.99 in [c] | 1.48 in [c] | 1.27 in [c] | 1.04 in [c] | 0.98 in [c] | 1.15 in [c] |
| 5 | 1.35 in [c] | 1.13 in [c] | 1.05 in [c] | 1.28 in [c] | 1.35 in [c] | 1.11 in [c] | 1.04 in [c] | 1.22 in [c] |
| 55 | 0.13 in [d] | 0.10 in [d] | 0.16 in [d] | 0.08 in [d] | 0.14 in [d] | 0.15 in [d] | 0.20 in [d] | 0.02 in [d] |
| 45 | 0.24 in [d] | 0.01 in [d] | 0.07 in [d] | 0.19 in [d] | 0.25 in [d] | 0.06 in [d] | 0.11 in [d] | 0.12 in [d] |
| 35 | 0.31 in [d] | 0.05 in [d] | 0.02 in [d] | 0.24 in [d] | 0.31 in [d] | 0.00 in [d] | 0.06 in [d] | 0.18 in [d] |
| 25 | 0.21 in [d] | 0.03 in [d] | 0.10 in [d] | 0.15 in [d] | 0.22 in [d] | 0.07 in [d] | 0.12 in [d] | 0.08 in [d] |
| 15 | 0.01 in [d] | 0.21 in [d] | 0.27 in [d] | 0.06 in [d] | 0.01 in [d] | 0.22 in [d] | 0.28 in [d] | 0.11 in [d] |
| 5 | 0.09 in [d] | 0.13 in [d] | 0.21 in [d] | 0.02 in [d] | 0.09 in [d] | 0.15 in [d] | 0.22 in [d] | 0.04 in [d] |
| Additional Information |
[a]= Volume of Water Caught (cm3) [b]= Depth of Water Applied (in) [c]= Overlapped Depth for the Three Sets (in) [d]= Absolute Deviation from Mean Depth (in) Coefficient of Uniformity = 90 |
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