10.3: Water Balance
- Page ID
- 44614
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In surface irrigation, just as in basic hydraulics, there must be conservation of mass. The primary components of the mass balance for surface irrigation may be represented as volumes. The volume balance is written as:
Vg = Vz + Vs + Vr
where: Vg = gross application volume,
Vz = infiltration volume,
Vs = storage volume on the soil surface, and
Vr = runoff volume.
We assume that evaporation of water during application is negligible. While water is being applied, some water exists as storage on the surface until the inflow is stopped and recession is complete. Thus, Vs is transient; it only occurs while water is on the surface. The water balance may also be described using the depth of water:
dg = dz + ds + dr
where: dg = average gross application depth,
dz = average infiltration depth,
ds = surface storage depth, and
dr = runoff depth.
As usual, depths represent the volumes divided by the irrigated area.
The gross application depth in furrow irrigation is calculated as:
\(d_g=1155\left(\dfrac{q_s \times t_{co}}{W\times L}\right) \) (10.3)
where: dg = average gross application depth (in),
qs = furrow stream size (gpm/furrow),
tco = cutoff time, i.e. set time (hr),
W = spacing of watered furrows (in), and
L = length of furrow (ft).
or for an entire set:
\(d_g=1155\left(\dfrac{Q_t \times t_{co}}{N \times W \times L}\right) \) (10.4)
where: N = number of furrows watered per set, and
Qt = total inflow rate to the field.
The total inflow rate is equal to the sum of the inflow from the water supply and, when a closed runoff recovery system is used, water reused on the same field. Thus, Qt = Qw + Qp where Qw = flow rate of the original supply and Qp = flow rate of the recovery system. The W equals the spacing of the furrows if every furrow is irrigated. If every other furrow is irrigated, then W equals twice the furrow spacing. Often the furrow stream size (qs) is constant for the duration of the irrigation. When the labor supply is available, efficiency can be improved by reducing furrow stream size after water advance across the field is complete. This is called cutback irrigation. The gross application depth for basins and border irrigation is:
\(d_g=96.3\left(\dfrac{Q_t \times t_{co}}{W_b \times L_b}\right) \) (10.5)
where: Wb = the width of the border or basin (ft), and
Lb = length of border or basin (ft).
The average infiltration depth (dz) can be determined from the infiltration profile such as Figure 10.11. It occurs at about 60% of the field’s length from the inlet for open-ended systems. In our example, it occurs at 720 feet and equals 3.5 inches. After the irrigation and recession has stopped, the water stored on the surface (ds) has either infiltrated or has run off; therefore, the depth stored is zero. In Equation 10.2, the only remaining variable is the runoff depth (dr). The depth of runoff is the total volume of runoff water divided by the area of the irrigation set, basin, or border, or the area irrigated by an individual furrow. By rearranging terms, Equation 10.2 can be used to determine the amount of runoff from a surface irrigated field.