13.3: Application Rate
- Page ID
- 44666
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Center Pivots
The rate of water application under a center pivot has unique characteristics that are important in design and management. A tower at the end of a conventional center pivot might move at 2 feet per minute. The first tower on the pivot might move at 1/10 that speed. Since each location should receive the same depth of water each irrigation, water must be applied 10 times as rapidly at the outer tower compared to the inner tower. The very high rate of water application can exceed the soils infiltration rate. If adequate storage is not provided on the soil surface to retain the water while infiltration occurs the water may run downhill. This runoff process can be acute with center pivot irrigation on steep slopes and soils that have low infiltration rates. Yet pivots can work in these conditions if they are properly designed. Therefore, it is important to determine the factors that control the rate of application. The typical application rate is shown in Figure 13.7. The example shows that water will only be applied for about 25 minutes at the distal end of the lateral for this pivot. The rate of water application reaches a peak when the pivot lateral is directly overhead of the point of concern. Then the rate decreases as the pivot continues to move forward. The application pattern is generally described as an elliptical rate. Two characteristics are important to evaluate the elliptical rate:
- the highest or peak rate of application when the pivot lateral is directly overhead and
- the total length of time that water is applied to the location, called the time of wetting.
The peak application rate is given by:
\(A_p=\dfrac{0.0177C_g R}{D_c}\) (13.4)
and the time of wetting is given by:
\(T_w=72\dfrac{D_c d_g}{RC_g}\) (13.5)
where: Ap = the peak application rate (in/hr),
Tw = the time of wetting (hr),
R = the radial distance from the pivot point (ft),
Dc = the diameter of coverage of the sprinkler at position R (ft),
Cg = the gross system capacity (gpm/ac), and
dg = gross application depth (in).
These relationships show that the peak application rate is totally determined by the design of the center pivot. The length of the pivot lateral, the type of sprinkler used, and the system capacity determine the peak application rate. The peak rate does not change with the speed of rotation of the pivot. The time of wetting at a point is a factor of these variables and the depth of water applied per irrigation. Thus, the time of application can be controlled by management, i.e., by changing dg.
The rate of infiltration of a hypothetical soil is also shown in Figure 13.7. The diagram shows that the application rate of the pivot exceeds the infiltration rate for most of the time of wetting. During this time water could runoff if it is not stored on the soil surface.
What can be done to reduce runoff? The three design variables, Cg , Dc, and R that affect the peak application rate and the time of wetting could all be changed when the pivot is designed and installed. The system capacity used in selecting an irrigation system is based on the crop needs for the soil and climate at the location. Thus, the system capacity should not be reduced much below the requirement just to prevent runoff. The length of the pivot lateral is determined by the geometry of the field. In some cases, there is a choice between installing one very long system or several shorter systems. The investment cost per acre will be less for the longer system but the potential for runoff is higher.
The primary alternative to reduce runoff problems is to select sprinkler devices that provide the necessary diameter of coverage. This is generally done at the time the system is purchased but can be changed later. Once the pivot is installed the only system management alternative to reducing runoff is to reduce the depth of application. The maximum depth of application and the appropriate types of sprinkler devices are discussed in the next section on sprinkler and nozzle selection.
Linear or Lateral Move
One inherent advantage of linear or lateral move systems over center pivots is that peak application rates are much lower for these systems. This is because with linear move systems, the discharge is distributed uniformly throughout the lateral’s length while with center pivots, discharge increases with distance from the pivot point. The peak application intensity of a linear move can be calculated with the following equation:
\(A_p=\dfrac{122.5 Q}{D_c L}\) (13.6)
where: Q = the system’s flow rate (gpm),
L = the lateral length, and
Dc = the diameter of coverage of the sprinkler heads on the system.