1-3 - Lecture 4 Set Sprinkler Uniformity & Efficiency...

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Unformatted text preview: Lecture 4 Set Sprinkler Uniformity & Efficiency I. Sprinkler Irrigation Efficiency 1. Application uniformity 2. Losses (deep percolation, evaporation, runoff, wind drift, etc.) • • • • • It is not enough to have uniform application if the average depth is not enough to refill the root zone to field capacity Similarly, it is not enough to have a correct average application depth if the uniformity is poor Consider the following examples: We can design a sprinkler system that is capable of providing good application uniformity, but depth of application is a function of the set time (in periodic-move systems) or “on time” (in fixed systems) Thus, uniformity is mainly a function of design and subsequent system maintenance, but application depth is a function of management Sprinkle & Trickle Irrigation Lectures Page 39 Merkley & Allen II. Quantitative Measures of Uniformity Distribution uniformity, DU (Eq. 6.1): ⎛ avg depth of low quarter ⎞ DU = 100 ⎜ ⎟ avg depth ⎝ ⎠ • • (46) The average of the low quarter is obtained by measuring application from a catch-can test, mathematically overlapping the data (if necessary), ranking the values by magnitude, and taking the average of the values from the low ¼ of all values For example, if there are 60 values, the low quarter would consist of the 15 values with the lowest “catches” Christiansen Coefficient of Uniformity, CU (Eq. 6.2): ( n ⎛ ∑ j=1abs z j − m CU = 100 ⎜ 1.0 − n ⎜ ⎜ ∑ j=1z j ⎝ ⎞ )⎟ ⎟ ⎟ ⎠ (47) where z are the individual catch-can values (volumes or depths); n is the number of observations; and m is the average of all catch volumes. • • • • • Note that CU can be negative if the distribution is very poor There are other, equivalent ways to write the equation These two measures of uniformity (CU & DU) date back to the time of slide rules (more than 50 years ago; no electronic calculators), and are designed with computational ease in mind More complex statistical analyses can be performed, but these values have remained useful in design and evaluation of sprinkler systems For CU > 70% the data usually conform to a normal distribution, symmetrical about the mean value. Then, ⎛ avg depth of low half ⎞ CU ≈ 100 ⎜ ⎟ avg depth ⎝ ⎠ (48) another way to define CU is through the standard deviation of the values, ⎛ σ 2⎞ CU = 100 ⎜ 1.0 − ⎟ ⎜ ⎟ m π⎠ ⎝ Merkley & Allen Page 40 (49) Sprinkle & Trickle Irrigation Lectures where σ is the standard deviation of all values, and a normal distribution is assumed (as previously) • • Note that CU = 100% for σ = 0 The above equation assumes a normal distribution of the depth values, whereby: ∑ z − m = nσ • • 2/ π (50) By the way, the ratio σ/m is known in statistics as the coefficient of variation Following is the approximate relationship between CU and DU: CU ≈ 100 − 0.63 (100 − DU) or, • • • • (51) DU ≈ 100 − 1.59 (100 − CU) (52) These equations are used in evaluations of sprinkler systems for both design and operation Typically, 85 to 90% is the practical upper limit on DU for set systems DU > 65% and CU > 78% is considered to be the minimum acceptable performance level for an economic system design; so, you would not normally design a system for a CU < 78%, unless the objective is simply to “get rid of water or effluent” (which is sometimes the case) For shallow-rooted, high value crops, you may want to use DU > 76% and CU > 85% III. Alternate Sets (Periodic-Move Systems) • • • The effective uniformity (over multiple irrigations) increases if “alternate sets” are used for periodic-move systems (½Sl) This is usually practiced by placing laterals halfway between the positions from the previous irrigation, alternating each time The relationship is: CUa ≈ 10 CU (53) DUa ≈ 10 DU • • • The above are also valid for “double” alternate sets (Sl/3) Use of alternate sets is a good management practice for periodic-move systems The use of alternate sets approaches an Sl of zero, which simulates a continuous-move system Sprinkle & Trickle Irrigation Lectures Page 41 Merkley & Allen IV. Uniformity Problems • • Of the various causes of non-uniform sprinkler application, some tend to cancel out with time (multiple irrigations) and others tend to concentrate (get worse) In other words, the “composite” CU for two or more irrigations may be (but not necessarily) greater than the CU for a single irrigation 1. Factors that tend to Cancel Out • • • • Variations in sprinkler rotation speed Variations in sprinkler discharge due to wear Variations in riser angle (especially with hand-move systems) Variations in lateral set time 2. Factors that may both Cancel Out and Concentrate • Non-uniform aerial distribution of water between sprinklers 3. Factors that tend to Concentrate • • • Variations in sprinkler discharge due to elevation and head loss Surface ponding and runoff Edge effects at field boundaries V. System Uniformity • The uniformity is usually less when the entire sprinkler system is considered, because there tends to be greater pressure variation in the system than at any given lateral position. ( ) ( ) ⎡1 ⎤ system CU ≈ CU ⎢ 1 + Pn / Pa ⎥ ⎣2 ⎦ ⎡1 ⎤ system DU ≈ DU ⎢ 1 + 3 Pn / Pa ⎥ ⎣4 ⎦ (54) (55) where Pn is the minimum sprinkler pressure in the whole field; and Pa is the average sprinkler pressure in the entire system, over the field area. • • • These equations can be used in design and evaluation Note that when Pn = Pa (no pressure variation) the system CU equals the CU If pressure regulators are used at each sprinkler, the system CU is approximately equal to 0.95CU (same for DU) Merkley & Allen Page 42 Sprinkle & Trickle Irrigation Lectures • • If flexible orifice nozzles are used, calculate system CU as 0.90CU (same for DU) The Pa for a system can often be estimated as a weighted average of Pn & Px: Pa = 2Pn + Px 3 (56) where Px is the maximum nozzle pressure in the system VI. Computer Software and Standards • • • • There is a computer program called “Catch-3D” that performs uniformity calculations on sprinkler catch-can data and can show the results graphically Jack Keller and John Merriam (1978) published a handbook on the evaluation of irrigation systems, and this includes simple procedures for evaluating the performance of sprinkler systems The ASAE S436 (Sep 92) is a detailed standard for determining the application uniformity under center pivots (not a set sprinkler system, but a continuous move system) ASAE S398.1 provides a description of various types of information that can be collected during an evaluation of a set sprinkler system Sprinkle & Trickle Irrigation Lectures Page 43 Merkley & Allen VII. General Sprinkle Application Efficiency The following material leads up to the development of a general sprinkle application efficiency term (Eq. 6.9) as follows: Design Efficiency: Epa = DEpaReOe (57) where DEpa is the distribution efficiency (%); Re is the fraction of applied water that reaches the soil surface; and Oe is the fraction of water that does not leak from the system pipes. • • • • The design efficiency, Epa, is used to determine gross application depth (for design purposes), given the net application depth In most designs, it is not possible to do a catch-can test and data analysis – you have to install the system in the field first; thus, use the “design efficiency” The subscript “pa” represents the “percent area” of the field that is adequately irrigated (to dn, or greater) – for example, E80 and DE80 are the application and distribution efficiencies when 80% of the field is adequately irrigated Question: can “pa” be less than 50%? Merkley & Allen Page 44 Sprinkle & Trickle Irrigation Lectures Relative Applied Depth C U 20% of area underirrigated 80% of area overirrigated w Lo h Hig CU Desired Net Application Depth 1.0 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Area Receiving at Least the Desired Application VIII. Distribution Efficiency • • • CU 94 92 90 88 86 84 82 80 78 76 74 72 70 • This is used to define the uniformity and adequacy of irrigation DE is based on statistical distributions and application uniformity For a given uniformity (CU) and a given percent of land adequately irrigated (equal to or greater than required application depth), Table 6.2 gives values of DE that determine how much water must be applied in excess of the required depth so that the given percent of land really does receive at least the required depth 95 87.6 83.5 79.4 75.3 71.1 67.0 62.9 58.8 54.6 50.5 46.4 42.3 38.1 90 90.4 87.1 83.9 80.7 77.5 74.3 71.1 67.9 64.7 61.4 58.2 55.0 51.8 85 92.2 89.6 87.0 84.4 81.8 79.2 76.6 74.0 71.4 68.8 66.2 63.6 61.0 Percent area adequately irrigated (pa) 80 75 70 65 93.7 94.9 96.1 97.1 91.6 93.2 94.7 96.1 89.4 91.5 93.4 95.2 87.3 89.8 92.1 94.2 85.2 88.2 90.8 93.2 83.1 86.5 89.5 92.3 81.0 84.8 88.2 91.3 78.9 83.1 86.8 90.3 76.8 81.4 85.5 89.4 74.7 79.7 84.2 88.4 72.6 78.0 82.9 87.4 70.4 76.3 81.6 86.5 68.3 74.6 80.3 85.5 60 98.1 97.5 96.8 96.2 95.6 94.9 94.3 93.6 93.0 92.4 91.7 91.1 90.5 55 99.1 98.7 98.4 98.1 97.8 97.5 97.2 96.8 96.5 96.2 95.9 95.6 95.3 50 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 See Fig. 6.7 Sprinkle & Trickle Irrigation Lectures Page 45 Merkley & Allen IX. Wind Drift and Evaporation Losses • • • These losses are typically from 5% to 10%, but can be higher when the air is dry, there is a lot of wind, and the water droplets are small Effective portion of the applied water, Re. This is defined as the percentage of applied water that actually arrives at the soil surface of the irrigated field. This is based on: • • • • • climatic conditions wind speed spray coarseness Figure 6.8 gives the value of Re for these different factors The Coarseness Index, CI, is defined as (Eq. 6.7): ⎛ P1.3 ⎞ CI = 0.032 ⎜ ⎜B⎟ ⎟ ⎝ ⎠ (58) where P is the nozzle pressure (kPa) and B is the nozzle diameter (mm) CI > 17 fine spray • CI < 7 coarse spray When the spray is between fine and coarse, Re is computed as a weighted average of (Re)fine and (Re)coarse (Eq. 6.8): Re = • 17 ≥ CI ≥ 7 between fine and coarse (CI − 7) (17 − CI) (Re )fine + (Re )coarse 10 10 (59) Allen and Fisher (1988) developed a regression equation to fit the curves in Fig. 6.8: 2 Re = 0.976 + 0.005 ETo − 0.00017 ETo + 0.0012 W −0.00043 (CI) (ETo ) − 0.00018 (CI) ( W ) (60) −0.000016 (CI) (ETo ) ( W ) • where ETo is the reference ET in mm/day (grass-based); CI is the coarseness index (7 ≤ CI ≤ 17); and W is the wind speed in km/hr For the above equation, if CI < 7 then set it equal to 7; if CI > 17 then set it equal to 17 Merkley & Allen Page 46 Sprinkle & Trickle Irrigation Lectures X. Leaks and Drainage Losses 1. Losses due to drainage of the system after shut-down • • • upon shut-down, most sprinkler systems will partially drain water runs down to the low elevations and or leaves through automatic drain valves that open when pressure drops fixed (solid-set) systems can have anti-drain valves at sprinklers that close when pressure drops (instead of opening, like on wheel lines) 2. Losses due to leaky fittings, valves, and pipes • • • • • pipes and valves become damaged with handling, especially with hand-move and side-roll systems, but also with orchard sprinklers and end-tow sprinklers gaskets and seals become inflexible and fail These losses are quantified in the Oe term For systems in good condition these losses may be only 1% or 2%, giving an Oe value of 99% or 98%, respectively For system in poor condition these losses can be 10% or higher, giving an Oe value of 90% or less XI. General Sprinkle Application Efficiency • As given above, Eq. 6.9 from the textbook, it is: Epa = DEpaReOe (61) where DEpa is in percent; and Re and Oe are in fraction (0 to 1.0). Thus, Epa is in percent. XII. Using CU or DU instead of DEpa 1. Application Efficiency of the Low Quarter, Eq • Given by Eq. 6.9 when DU replaces DEpa • Useful for design purposes for medium to high-value crops • Only about 10% of the area will be under-irrigated • Recall that DU is the average of low quarter divided by average 2. Application Efficiency of the Low Half, Eh • • Given by Eq. 6.9 when CU replaces DEpa Useful for design purposes for low-value and forage crops Sprinkle & Trickle Irrigation Lectures Page 47 Merkley & Allen • • Only about 20% of the area will be under-irrigated Recall that CU is the average of low half divided by average XIII. Procedure to Determine CU, Required Pressure, Se and Sl for a Set System 1. Specify the minimum acceptable Epa and target pa 2. Estimate Re and Oe (these are often approximately 0.95 and 0.99, respectively) 3. Compute DEpa from Epa, Re and Oe 4. Using DEpa and pa, determine the CU (Table 6.2) that is required to achieve Epa 5. Compute the set operating time, tso, then adjust f’ and dn so that tso is an appropriate number of hours 6. Compute qa based on I, Se and Sl (Eq. 5.5) 7. Search for nozzle size, application rate, Se and Sl to obtain the CU 8. Repeat steps 5, 6 and 7 as necessary until a workable solution is found XIV. How to Measure Re • • The textbook suggests a procedure for estimating Re You can also measure Re from sprinkler catch-can data: 1. Compute the average catch depth over the wetted area (if a single sprinkler), or in the area between four adjacent sprinklers (if in a rectangular grid) 2. Multiply the sprinkler flow rate by the total irrigation time to get the volume applied, then divide by the wetted area to obtain the gross average application depth 3. Divide the two values to determine the effective portion of the applied water XV. Line- and Point-Source Sprinklers • • • • Line-source sprinklers are sometimes used by researches to determine the effects of varying water application on crop growth and yield A line-source sprinkler system consists of sprinklers spaced evenly along a straight lateral pipe in which the application rate varies linearly with distance away from the lateral pipe, orthogonally Thus, a line-source sprinkler system applies the most water at the lateral pipe, decreasing linearly to zero to either side of the lateral pipe A point-source sprinkler is a single sprinkler that gives linearly-varying application rate with radial distance from the sprinkler Merkley & Allen Page 48 Sprinkle & Trickle Irrigation Lectures • With a point-source sprinkler, the contours of equal application rate are concentric circles, centered at the sprinkler location (assuming the riser is vertical and there is no wind) Sprinkle & Trickle Irrigation Lectures Page 49 Merkley & Allen Merkley & Allen Page 50 Sprinkle & Trickle Irrigation Lectures ...
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This note was uploaded on 03/01/2012 for the course BIE 6110 taught by Professor Sprinkle during the Fall '03 term at Utah State University.

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