10.4: Efficiency
- Page ID
- 44615
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Calculation of Irrigation Efficiency
The concepts of in-field efficiency and water distribution uniformity as presented in Chapter 5 can be applied to surface irrigation by using the mass balance equations and water distribution graph. This is illustrated in Example 10.1. The efficiency calculated in Example 10.1 was for a system where runoff is not reused. Later in this chapter we will discuss the use of runoff recovery systems as one method for improving irrigation efficiency. The effects of runoff recovery on efficiency can be determined when two things are known: the amount of runoff and the effectiveness of the runoff recovery system itself, that is, how much of the runoff water is actually captured and applied. The efficiency depends upon whether the recovery system is a closed system in which the runoff water is captured and returned to the field of origin, or whether it is an open system where the runoff is captured from one field and applied to another field with runoff being allowed to leave the second field. These systems are illustrated in Figure 10.12. The equations that apply for calculating efficiency are shown below.
Closed System:
\(E_{LQ}=\left[\dfrac{d_e}{d_g-d_gR_rR_t}\right]100\% \) (10.6)
Open System:
\(E_{LQ}=\left[\dfrac{d_e(1+R_rR_t)}{d_g}\right]100\% \) (10.7)
where: de= effective depth stored,
de = dLQ if dLQ ≤ SWD,
de = SWD if dLQ > SWD;
dg = gross application;
Rr = runoff ratio; and
Rt = return ratio (efficiency of recovery system) = volume applied from the recovery system divided by volume of runoff.
The runoff ratio is:
\(R_r=\dfrac{d_r}{d_g}\) (10.8)
For the furrow-irrigated field with a loam soil described in Figures 10.7 and 10.9 to 10.11 and in Table 10.1, determine the gross application depth, runoff depth, percentage of runoff, and ELQ. Qt = 760 gallons per minute (gpm), L = 1200 feet, tco = 12 hours, 70 furrows are watered per set, row spacing is 30 inches, and every furrow is watered. Assume the SWD = 3.4 inches. The field slope is 0.3%.
Given: Qt = 760 gpm
tco = 12 hr
W = 30 in
dz = 3.6 in (Figure 10.11)
ds = 0 (since recession is complete)
N = 70
Find: dg
dr
Percent runoff
DU
ELQ
Solution:
\(d_g=1155\left(\dfrac{Q_t\times t_{co}}{N\times W\times L}\right) \) (Eq. 10.4)
\(d_g=1155\dfrac{(700\text{ gpm})(12\text{ hr})}{(70)(30 \text{ in})(1200\text{ ft})}=4.2\text{ in}\)
\(d_r=d_g-d_z-d_s \) (Eq. 10.2 rearranged)
\(d_r=4.2-3.5-0=0.7\text{ in}\)
\(\text{Percent runoff}=\left(\dfrac{0.7}{4.2}\right)(100\%)=17\% \)
\(\text{The average depth in the low quarter, 2.8 in, is from Figure 10.11} \)
\(DU=\dfrac{d_{LQ}}{d_z}=\left(\dfrac{2.8}{3.6}\right)=0.78 \) (Eq. 5.2)
\(\text{If } d<SWD, d_e=d_{LQ}\)
\(\text{Thus, }E_{LQ}=\left(\dfrac{2.8}{4.2}\right)(100\%)=67\%\) (Eq. 5.11)
What is the efficiency of the system given in Example 10.1 if a closed runoff recovery system were used? Assume Rt = 0.85
Given: dg = 4.2 in
dz = 3.5 in
Rt = 0.85
Find: Rr
ELQ
Solution
\(R_r=\dfrac{d_r}{d_g}\) (10.8)
\(R_r=\dfrac{(4.2\text{ in}-3.5\text{ in})}{4.2\text{ in}}=0.17\)
\(E_{LQ}=\left[\dfrac{d_e}{d_g-d_gR_rR_t}\right]100\% \) (Eq. 10.6)
\(E_{LQ}=\left[\dfrac{2.8}{4.2-4.2(0.17)(0.85)}\right]100\%=78\% \)
Thus, efficiency increased from 67% to 78% by the addition of runoff recovery.
Repeat Example 10.2 for an open-ended runoff recovery system.
Solution
\(E_{LQ}=\left[\dfrac{d_e(1+R_rR_t)}{d_g}\right]100\% \) (10.7)
\(E_{LQ}=\left[\dfrac{2.8(1+0.17\times 0.85)}{4.2}\right]100\%=76\% \)
The efficiency of this system is slightly lower than the closed system because some runoff is escaping the field irrigated with the runoff water.
Figure 10.12. Closed and open runoff recovery systems.
Improvement of Surface Irrigation Systems
The application efficiencies of field-scale systems are often reported to be quite low, in the range of 40-50%. Much work has been done to develop methods for improving the efficiencies including the following:
- Converting earthen field ditches to lined-ditches or gated pipe delivery systems to reduce seepage and/or evaporation.
- Recovery or reuse of tailwater to reduce runoff losses.
- Improved land forming methods especially with the use of laser and GPS controlled land grading equipment (Dedrick et al., 2007) for improved application uniformity.
- Cutback irrigation and blocked-end systems to reduce runoff losses (USDA, 2012).
- Surge flow irrigation (Walker and Skogerboe, 1987) to control infiltration and runoff, and to improve uniformity of infiltration.
- Automation of water delivery systems (Humphreys, 1986; Koech et al., 2010; Koech et al., 2014) and semi-automation to better match set times to optimal set times.
- Development of computer-based models for improvement in design and selection of more efficient management options such as set-time and stream size (Bautista et al., 2009).
In this book we concentrate mainly on the set-time and stream size management options as well as tailwater recovery and the management of surge flow systems.