15.4.1: Injection Rates and Calibration of Injection Devices
- Page ID
- 44716
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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 injection device must be calibrated so that the correct amount of chemical is applied per unit of land area. Kranz and Eisenhauer (1996) tested chemical injection pumps and found that even with positive displacement packed-piston and diaphragm pumps there is some sensitivity of pump discharge to irrigation pipeline pressure. Thus all types of injection devices should be calibrated in the field with the irrigation system operating at normal pressure.
For stationary irrigation systems e.g. surface irrigation systems, set-type sprinkler systems and microirrgation systems, the rate of chemical injection is calculated by:
\(q_i=\dfrac{G_p A_s}{t_i} \) (15.1)
where: qi = injection rate of solution (gal/h),
Gp = amount of chemical solution to apply (gal/ac),
As = area of the irrigation set or zone (ac), and
ti = total time of injection during the irrigation set (h).
With set-type systems the time period for injection does not have to be equal to the set-time or zone run time; it can be equal to or less than the set-time. For certain chemicals such as insecticides or fungicides it may be advantageous to inject near the end of the set-time so more chemical remains on the plant leaves following the event. In other cases it may be advantageous to apply the chemicals at the beginning in the event and then flush the irrigation system at the end of the event. Some controllers can be programmed so that the injection pump is shut off near the end of the event for flushing purposes. In Example 15.1 we illustrate the use of Equation 15.1 for a subsurface drip irrigation system.
It is desired to inject a fertilizer solution into an irrigation system at a rate of 17.5 gal/h. The injection pump has a maximum capacity of 20 gal/h. The pump has a percentage dial that can be adjusted for the desired pumping rate. At what percentage would you set the dial? After setting the pump it is calibrated at the appropriate pressure. It requires 2.5 minutes (2 min:30 sec) to pump 3,000 mL from the injection tube. What is the injection rate? Find: Pump dial setting and injection rate?
Find: Pump dial setting and injection rate
Solution
\( \dfrac{17.5\text{ gal/h}}{20\text{ gal/h}}\times 100\%=88\%\)
\(\dfrac{3,000\text{ mL}}{2.5\text{ min}}=1,200\text{ mL/min} \)
\(1\text{ gal/h}=63.1\text{ mL/min} \)
\(\dfrac{1,200\text{ mL/min}}{63.1\dfrac{\text{mL/min}}{\text{gal/h}}}=19.0\text{ gal/h} \)
Thus the pump dial setting is initially set at 88%. Since 17.5 gal/h is desired and the injection rate is 19.0 gal/h the pump setting should be adjusted downward and followed by another test. Repeat these steps until the appropriate injection rate is reached.
For continuously moving irrigation systems the injection rate is dependent upon the rate of land being irrigated per unit time as follows:
qi = Gp Ri (15.2)
where Ri = rate of land area irrigated per unit of time (ac/h).
For travelers and lateral move systems Ri is the area of the irrigated field divided by the total time of irrigation. For travelers the area and time can be for an individual set. Ri varies with the lateral pipeline position with center pivots that are equipped with end guns or swing-boom corner watering systems which leads to error in chemical application when using constant injection rates and the angular speed remains constant. Eisenhauer and Bockstadter (1990) found that for a typical 1 /4-section center pivot equipped with an end gun for irrigating a portion of each of the four corners, the average absolute injection rate error was 7.5% when Ri was calculated based on the total irrigated area and the total time to make a revolution and the injection rate and pivot speed were constant. The chemical would be under applied in the corners when the end gun is operating and over applied whenever the end gun is off. As discussed in Section 15.2.1, using a flow proportional injection system is one way of reducing this chemical application rate error. Reducing the speed of the center pivot when the end gun is operating using an auxiliary timer or sector control variable rate center pivot is another way to reduce this error. Equation 15.2 is applied in Example 15.4. Calibration of an injection pump is usually done with a calibration tube, a clear plastic tube with volume gradations marked on the outside. The tube is plumbed at the outlet of the chemical supply tank and using valves it can be isolated from the tank so that the liquid flowing into the injection device is only from the calibration tube. The calibration process is illustrated in Example 15.1.

