Cooperative Extension Service
College of Tropical Agriculture and Human Resources
University of Hawaii at Manoa
U. S. D. A. Cooperating
NUMBER 43 - December 1979
THE MANUFACTURER'S COEFFICIENT OF VARIATION OF EMITTER FLOW
Harris M. Gitlin, Specialist in Agricultural Engineering
In the lateral line design, emitter flow variation is used as a design criterion. The emitter flow variation that is determined from the emitter flow profile of the lateral line considers only the variation caused hydraulically and assumes that there is no emitter flow variation from the manufacturer. In fact, for any drip irrigation emitter or orifice in the lateral line, there will be manufacturer's variation that depends on the manufacturer's quality control in production. It is important to consider the manufacturer's variation in the selection of emitters or lateral and in the lateral line design.
The manufacturer's variation is determined statistically. Samples of emitters or a section of lateral line selected randomly are tested under a fixed pressure. If there is no manufacturer's variation, the emitter flow should be identical for each pressure. If a manufacturer has a good quality control program, the manufacturer's variation could be kept at a minimum level. The manufacturer's variation is actually caused by the nonuniform production from the manufacturer. For emitter flow or orifice flow, it may be considered that so-me emitters (or orifices) are different from the specified shape and size; therefore, different emitter flow rates are obtained from the same water pressure in a drip lateral line.
The manufacturer's variation is determined from the following statistical equation:
Vm= Sq /qave (1)
where Vm is the manufacturer's coefficient of variation of emitter flow, Sq is the standard deviation of emitter flow, and qave is the mean emitter flow.
The manufacturer's coefficient of variation of emitter flow will be reduced if a number of emitters can be grouped and considered as a unit. This condition exists for tree crops where a number of emitters are installed per tree, or for vegetables where a section of length can be considered as a unit based on the soil-moisture movement situation. The manufacturer's coefficient of variation of emitter flow can now be expressed as:
Vm(e)=Sq /e½ qave (2)
where Vm(e) is the manufacturer's coefficient of variation of emitter flow and e is the number of emitters that can be grouped together as a unit.
Determination of the Manufacturer's Variation
The manufacturer's coefficient of variation of emitter flow can be determined from laboratory tests. A UH 100-foot testing facility equipped with catchment cylinders at each foot can be used for such tests. The testing facility is also equipped with a pressure regulator, pressure gage, flow meters, and an automatic control that can turn on a-ad shut off the test instantaneously. If a 100-foot lateral line with a 12-inch orifice spacing is tested, 100 emitter flows can be collected. All 100 emitter flow readings can be used to determine the manufacturer's coefficient of variation if the pressure drop is small between the inlet and the outlet of the 100-foot lateral line. When a 100-foot lateral line is tested under the situation in which the downstream end is plugged, the friction drop is only a few inches (water pressure head), which is considered small if a 10 to 15 psi pressure (23 to 34 feet of water pressure head) is used. However, a more precise calculation can be made by using only the last 50 readings from the downstream end. This technique adds assurance that the water pressure at all emitters will be practically constant throughout the laterallangth (the last 50 feet) and the time during which the emitter flow is collected.
A total of 102 tests were conducted for single wall and bi-wall lateral lines; 54 tests for single wall lateral line and 48 tests for bi-wall. It was found that the manufacturer's coefficient of variation of emitter flow for the single wall lateral line ranged from 0.04 to 0.08, with an overall average of 0.06, and the bi-wall lateral line ranged from 0.06 to 0.16, with an average figure of 0.11.
Emitter Flow Variation Caused by Manufacturer's Variation
An expression used for emitter flow variation in the lateral line design is simply a comparison of the maximum and minimum emitter flows
qvar=qmax - qmin/qmax (3)
qvar= 1-(qmin/qmax) (4)
where qmax is the maximum emitter flow, qmin is the minimum emitter flow, and qvar is the emitter flow variation. It is assumed that the manufacturer's emitter flow variation follows a normal distribution, and the mean value plus and mean value minus two standard deviations are considered as maximum and minimum emitter flow values. This maximum and minimum range will cover more than 95 percent of the emitter flows collected in the tests. Therefore, equation 4 can be shown as
qvar= 1-(qave - 2Sq/qave + 2Sq) (5)
or, it can be expressed by the manufacturer's coefficient of variation as follows:
qvar= 1-(1 - 2Vm/1 + 2Vm)(6)
Equation 6 can be simplified as
qvar= 4Vm / 1+ 2Vm (7)
The effects of the manufacturers coefficient of variation of emitter flow on emitter flow variation can be determined from equation 7 or Figure 1, which is plotted from equation 7. It can be seen from Figure 1 that a 0.06-manufacturer's coefficient of variation of emitter flow will cause a 20 percent emitter flow variation, and an 11 percent manufacturer's variation will cause a 36 percent emitter flow variation.
If a number of emitters can be grouped together as a unit, the manufacturers variation can be reduced. When four emitters can be considered as a unit, the manufacturer's coefficient of variation can be reduced to one-half of its value. Equation 7 or Figure 1 can be used by substituting Vm(e) for Vm to determine the emitter flow variation.
Emitter flow variation caused by friction and slope on a lateral line was first established theoretically and later verified on the UH test stand. However, the manufacture's variation can only be determined by testing, and is subject to change with each change in the manufacturing system, materials, and equipment.
Emitter flow variation contributes to the total emission uniformity (EU)of an irrigation system. An article on emission uniformity (EU) can be read here.
Bralts, Vincent F. The Effects of Emitter Flow Variation on the Design of Single and Dual Chamber Drip Irrigation Systems. Master of Science Thesis.Agricultural Engineering Department, University of Hawaii. December 1978.