An open-end border design example

The problem. In subsection 5.4.4, an example of furrow design was given in which the soil was quite heavy (low infiltration rates). To generate a basis for what might be an interesting

comparison of borders and furrow systems, suppose the original question for that field is extended to whether or not borders might be as good. Let us assume that the infiltration characteristics are the same except adjusted for an increased wetted perimeter.

The approximate wetted perimeter for the furrows is found by returning to the flow area, perimeter, and depth relationships. At a flow of 0.09 m3/min, the flow area found in the furrow example was (Eq. 48):

From Eq. 40 from which the furrow shape was extracted: y = (154 cm2

/ 3.331)1/1.732 = 9.15 cm From Eq. 41:

WP = 5.922 * 9.5.805 _{= 35.18 cm.}

Since the furrows were spaced at .5 m intervals, one could approximate the infiltration of a border by adjusting the k and f_o values by a factor of 1.4 based on the ratio of border to furrow wetted perimeter (50/35.18). If the furrows were operated in the 100 m direction where the slope is .8 percent, the multiplication factor would be about 2.0. For this exercise, the 1.4 factor will be utilized. Thus,

First Irrigation Conditions:

Later Irrigation Conditions:

Z = 0.0053 t .327 + 0.000052 t

The units of Z are again m3/m of length/unit width. One would not expect the border infiltration equation to more than double furrow infiltration with furrows spaced less than 1 m apart. Again Mannings n can be 0.04 for initial irrigations and .1 for later irrigations due to crop cover. Z_req is 8 cm.

Basic calculations. Assuming also that the soil is relatively stable, Eq. 67 is used to calculate the maximum inflow per unit width for the first irrigation along the 200 m length where erosion is most likely:

And similarly for irrigations along the 100 m (SO = 0.008) direction:

The minimum flow suggested by Eq. 93 using later field roughness where spreading may be a problem is for the 200 m lengths:

Q_min = 0.000357 * 200 * .001.5 / .10 = 0.0226 m3/min/m or in the 100 m direction:

Q_min = .000357 * 100 * .008.5 / .10 = 0.032 m3/min/m

The required intake opportunity times found according to the procedure suggested by Eq. 59 are:

First Irrigations r_req = 388.5 min Later Irrigations r_req = 678.9 min

The next basic calculation, as with furrows, must be to formulate the relationship between advance time and inflow discharge. Starting with a flow near the maximum and working downward using the processes already outlined, advance curves for both infiltration conditions and flow directions can be found. The results for this example are shown in Figure 59.

Figure 59. Discharge-advance relationship for the border example problem

The last of the basic calculations concerns the depletion and recession times for various values of flow. One illustration should demonstrate this procedure adequately. For an inflow of 0.06 m3/min/m, the advance time along the 200 m length under later conditions is about 145 min. From Eq. 48:

tr = r_req + t_L = 679 + 145 = 824 min

The time of depletion must be iteratively determined from Eqs. 96 - 98: a. t_d = t_r = 824 min

b.

c.

d.

e. Since T₁ is not close to T₂, steps b - d must be repeated with T₁ set equal to 677 min:

b.

c.

d.

e. Again another estimate of t_d seems to be required by the difference found between the iterations. If steps b - d are repeated, the new value of T₂ is 680 min and the procedure has converged.

The time of cutoff, t_co, is found from Eq. 99:

t_co = t_d - A_o L / (2 Q_o) = 680 - .0355 * 200 / .12 = 631 min.

Finally the application efficiencies of the alternative flows and flow directions are found using Eq. 56. An example for the 0.072 m3/min/m flow along the 200 m direction during the later irrigations is:

This series of computations is repeated for the full range of discharges, field lengths and infiltration conditions. The following table gives a detailed summary of selected options for the first and subsequent irrigation conditions running in both the 200 m and 100 m directions. First Irrigations L = 200 m

Sets

Border

Width FlowUnit AdvanceTime CutoffTime RecessionTime Field On-Time Application Efficiency Percent

2 50 0.036 6.36 11.34 12.83 22.67 65.3 3 33 0.0545 3.11 8.10 9.59 24.29 60.4 4 25 0.072 2.14 7.12 8.61 28.49 52.0 5 20 0.09 1.64 6.63 8.12 33.16 44.7 Later Irrigations L = 200 m Sets Border

Width FlowUnit AdvanceTime CutoffTime RecessionTime Field On-Time Application Efficiency Percent m _m3_/min hrs hrs hrs hrs 1 100 0.018 15.55 23.66 26.86 23.66 62.6 2 50 0.036 5.03 13.12 16.34 26.24 56.5 3 33 0.0545 3.15 11.25 14.47 33.76 43.4 First Irrigations L = 100 m Sets Border

Width FlowUnit AdvanceTime CutoffTime RecessionTime Field On-Time Application Efficiency Percent m _m3_/min hrs hrs hrs hrs 2 100 0.018 5.27 11.21 11.74 22.42 66.1 3 67 0.0269 2.35 8.30 8.83 24.89 59.8 4 50 0.036 1.44 7.39 7.92 29.55 50.1 5 40 0.045 1.03 6.98 7.51 34.91 42.4 Later Irrigations L = 100 m Sets Border

Width FlowUnit AdvanceTime CutoffTime RecessionTime Field On-Time Application Efficiency Percent

m _m3_/min hrs hrs hrs hrs

1 200 0.009 12.89 23.07 24.20 23.07 64.2

2 100 0.018 3.45 13.61 14.76 27.23 54.4

Field layout and configuration. The field water supply, Q_T, established in the furrow example was 1.8 m3/min which would have a duration of 48 hours. Usually, border irrigation would require a higher discharge than furrow systems, but as a first attempt at the problem, consider the field supply fixed.

The options for field layout are to align the borders in either the 200 m or the 100 m directions. The alternative configurations outlined by the data in the preceding tables indicate that there is probably not a strong advantage in irrigating in either direction and the decision can be based on other practical factors. For instance, dividing the field into two, 50 m wide borders running along the 200 m length may be preferable if farming operations are mechanized. During later irrigations, both borders would be irrigated simultaneously with the water supply. The potential application efficiency of this border design would be 63-65 percent which is better than furrow systems without cutback or reuse but not as good as the cutback or reuse options.